tag:blogger.com,1999:blog-39536807792480747612024-03-13T01:07:31.544+02:00Ο Κόσμος της ΦυσικήςΑσκήσεις,Θέματα Φυσικής...για όλες τις τάξεις του λυκείουPanagiotis Stamatiouhttp://www.blogger.com/profile/05743522665371107812noreply@blogger.comBlogger657125tag:blogger.com,1999:blog-3953680779248074761.post-75929360070410011212020-10-24T12:33:00.003+03:002020-10-24T12:33:52.629+03:00Γ΄Λυκειου Επαγωγή<!--[if gte mso 9]><xml>
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<p class="MsoNormal" style="margin-bottom: 4.0pt; margin-left: 0cm; margin-right: 22.4pt; margin-top: 0cm; margin: 0cm 22.4pt 4pt 0cm; text-align: justify;"><span style="font-family: arial;"><span style="font-size: 12pt; line-height: 105%;">Ευθύγραμμος αγωγός ΚΛ μήκους </span><span lang="EN-US" style="font-size: 12pt; line-height: 105%;">l</span><span style="font-size: 12pt; line-height: 105%;">=1</span><span lang="EN-US" style="font-size: 12pt; line-height: 105%;">m</span><span lang="EN-US" style="font-size: 12pt; line-height: 105%;"> </span><span style="font-size: 12pt; line-height: 105%;">και μάζας </span><span lang="EN-US" style="font-size: 12pt; line-height: 105%;">m</span><span style="font-size: 12pt; line-height: 105%;">=0,2</span><span lang="EN-US" style="font-size: 12pt; line-height: 105%;">Kg</span><span style="font-size: 12pt; line-height: 105%;">, είναι αρχικά ακίνητος με τα άκρα του σε επαφή με
δυο λείους μεταλλικούς οδηγούς Α</span><span lang="EN-US" style="font-size: 12pt; line-height: 105%;">x</span><sub><span lang="EN-US" style="font-size: 12pt; line-height: 105%;"> </span></sub><span style="font-size: 12pt; line-height: 105%;">και Γ</span><span lang="EN-US" style="font-size: 12pt; line-height: 105%;">y</span><span style="font-size: 12pt; line-height: 105%;"> μεγάλου μήκους και αμελητέας ωμικής αντίστασης, όπως
φαίνεται στο σχήμα. <span style="mso-spacerun: yes;"> </span>Τα άκρα Α και Γ των
δυο μεταλλικών οδηγών συνδέονται με έναν αντιστάτη που έχει αντίσταση </span><span lang="EN-US" style="font-size: 12pt; line-height: 105%;">R</span><sub><span style="font-size: 12pt; line-height: 105%;">1</span></sub><span style="font-size: 12pt; line-height: 105%;">=1Ω. Ο αγωγός ΚΛ έχει αντίσταση </span><span lang="EN-US" style="font-size: 12pt; line-height: 105%;">R</span><span style="font-size: 12pt; line-height: 105%;">=4Ω, και τη χρονική στιγμή </span><span lang="EN-US" style="font-size: 12pt; line-height: 105%;">t</span><span style="font-size: 12pt; line-height: 105%;">=0, ασκούμε
πάνω του σταθερή δύναμη μέτρου </span><span lang="EN-US" style="font-size: 12pt; line-height: 105%;">F</span><span style="font-size: 12pt; line-height: 105%;">=2Ν με
διεύθυνση που είναι παράλληλη στους δυο οδηγούς, οπότε ο αγωγός ΚΛ αρχίζει να
κινείται προς τα δεξιά χωρίς τριβές. Ολόκληρη η διάταξη βρίσκεται μέσα σε
κατακόρυφο ομογενές μαγνητικό πεδίο έντασης μέτρου Β=1Τ και φοράς από τον
αναγνώστη στο επίπεδο που ορίζουν οι μεταλλικοί οδηγοί.</span></span></p><span style="font-family: arial;">
</span><p class="MsoNormal" style="margin-bottom: 4.0pt; margin-left: 0cm; margin-right: 22.4pt; margin-top: 0cm; margin: 0cm 22.4pt 4pt 0cm; text-align: justify;"><span style="font-family: arial;"><span style="font-size: 12pt; line-height: 105%;">Α) <span style="mso-bidi-font-weight: bold;">Να εξηγήσετε ποιο είναι το είδος της κίνησης
που εκτελεί ο αγωγός ΚΛ, <span style="mso-spacerun: yes;"> </span>και να αιτιολογήσετε
γιατί αποκτά σταθερή (οριακή) ταχύτητα, την οποία να την υπολογίσετε.</span></span></span></p><span style="font-family: arial;">
</span><p class="MsoNormal" style="margin-bottom: 4.0pt; margin-left: 0cm; margin-right: 22.4pt; margin-top: 0cm; margin: 0cm 22.4pt 4pt 0cm; text-align: justify;"><span style="font-family: arial;"><span style="font-size: 12pt; line-height: 105%;">Β) <span style="mso-bidi-font-weight: bold;">Να υπολογίσετε το μέτρο της ταχύτητας του
αγωγού ΚΛ τη χρονική στιγμή που το μέτρο της επιτάχυνσής του ισούται με α<sub>1</sub>=
4</span></span><span lang="EN-US" style="font-size: 12pt; line-height: 105%;">m</span><span style="font-size: 12pt; line-height: 105%;">/</span><span lang="EN-US" style="font-size: 12pt; line-height: 105%;">s</span><sup><span style="font-size: 12pt; line-height: 105%;">2</span></sup><span style="font-size: 12pt; line-height: 105%;">.</span></span></p><span style="font-family: arial;">
</span><p class="MsoNormal" style="margin-bottom: 4.0pt; margin-left: 0cm; margin-right: 22.4pt; margin-top: 0cm; margin: 0cm 22.4pt 4pt 0cm; text-align: justify;"><span style="font-family: arial;"><span style="font-size: 12pt; line-height: 105%;">Γ)<span style="mso-bidi-font-weight: bold;"> Να υπολογίσετε τον ρυθμό μεταβολής της
κινητικής ενέργειας του αγωγού ΚΛ την παραπάνω χρονική στιγμή.</span></span></span></p><span style="font-family: arial;">
</span><p class="MsoNormal" style="margin-bottom: 4.0pt; margin-left: 0cm; margin-right: 22.4pt; margin-top: 0cm; margin: 0cm 22.4pt 4pt 0cm; text-align: justify;"><span style="font-family: arial;"><span style="font-size: 12pt; line-height: 105%;">Δ)<span style="mso-bidi-font-weight: bold;"> Να υπολογίσετε το ποσό της θερμότητας που
εκλύεται από το κύκλωμα (λόγω του φαινομένου </span></span><span lang="EN-US" style="font-size: 12pt; line-height: 105%;">Joule</span><span style="font-size: 12pt; line-height: 105%;">), από τη χρονική στιγμή </span><span lang="EN-US" style="font-size: 12pt; line-height: 105%;">t</span><span style="font-size: 12pt; line-height: 105%;">=0 μέχρι τη χρονική που ο αγωγός ΚΛ αποκτά οριακή
ταχύτητα. Να δεχτείτε ότι στο παραπάνω χρονικό διάστημα ο αγωγός μετακινήθηκε
κατά </span><span lang="EN-US" style="font-size: 12pt; line-height: 105%;">d</span><span style="font-size: 12pt; line-height: 105%;">=5</span><span lang="EN-US" style="font-size: 12pt; line-height: 105%;">m</span><span style="font-size: 12pt; line-height: 105%;">.</span></span></p><p class="MsoNormal" style="margin-bottom: 4.0pt; margin-left: 0cm; margin-right: 22.4pt; margin-top: 0cm; margin: 0cm 22.4pt 4pt 0cm; text-align: justify;"><span style="font-family: arial;"><span style="font-size: 12pt; line-height: 105%;"> </span></span></p><p class="MsoNormal" style="margin-bottom: 4.0pt; margin-left: 0cm; margin-right: 22.4pt; margin-top: 0cm; margin: 0cm 22.4pt 4pt 0cm; text-align: justify;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 105%; mso-bidi-font-weight: bold;"></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: arial;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXTwAYwe14I77BV5OP3XFQvwv4SSsmMMVvBlKkM85Gt7-nPQHfqPRVXSiezbk8jRyg10SUDfUgD6I5zHz5RrAhyphenhyphen8-eSBg5mWqEp_MnGGXAf4mZ1OdAPhAFMsfEQDX4Tj8Cgdl4aEJ6Iogw/s488/%25CF%2583%25CE%25B9%25CE%25B4%25CE%25B7%25CF%2581%25CE%25BF%25CF%2584%25CF%2581%25CE%25BF%25CF%2587%25CE%25B9%25CE%25B5%25CF%2582+%25CE%25BC%25CE%25B5+%25CF%2581%25CE%25B1%25CE%25B2%25CE%25B4%25CE%25BF.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="198" data-original-width="488" height="163" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXTwAYwe14I77BV5OP3XFQvwv4SSsmMMVvBlKkM85Gt7-nPQHfqPRVXSiezbk8jRyg10SUDfUgD6I5zHz5RrAhyphenhyphen8-eSBg5mWqEp_MnGGXAf4mZ1OdAPhAFMsfEQDX4Tj8Cgdl4aEJ6Iogw/w400-h163/%25CF%2583%25CE%25B9%25CE%25B4%25CE%25B7%25CF%2581%25CE%25BF%25CF%2584%25CF%2581%25CE%25BF%25CF%2587%25CE%25B9%25CE%25B5%25CF%2582+%25CE%25BC%25CE%25B5+%25CF%2581%25CE%25B1%25CE%25B2%25CE%25B4%25CE%25BF.jpg" width="400" /></a></span></div><span style="font-family: arial;"><br /> Η λύση σε λίγες μέρες.</span><br /><p></p>
Panagiotis Stamatiouhttp://www.blogger.com/profile/05743522665371107812noreply@blogger.com0tag:blogger.com,1999:blog-3953680779248074761.post-20832206869566700952020-10-18T14:32:00.004+03:002020-10-18T14:33:30.567+03:00Β΄Λυκείου Νόμος Coulomb Ηλεκτρικό πεδίο<p class="MsoNormal" style="text-align: justify;"><span style="font-family: arial;"><span style="font-size: 12pt; line-height: 115%;"> <b>Νόμος Coulomb Ηλεκτρικό πεδίο</b></span></span></p><p class="MsoNormal" style="text-align: justify;"><span style="font-family: arial;"><span style="font-size: 12pt; line-height: 115%;">Στις κορυφές Β και Γ ενός
ορθογωνίου και ισοσκελούς τριγώνου ΑΒΓ (η γωνία Α είναι η ορθή) βρίσκονται
ακίνητα τα σημειακά φορτία </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">Q</span><sub><span style="font-size: 12pt; line-height: 115%;">Α</span></sub><span style="font-size: 12pt; line-height: 115%;">=</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">Q</span><sub><span style="font-size: 12pt; line-height: 115%;">Β</span></sub><span style="font-size: 12pt; line-height: 115%;">=
–10√2μ</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">C</span><span style="font-size: 12pt; line-height: 115%;">.
Να υπολογίσετε:</span></span></p><span style="font-family: arial;">
</span><p class="MsoNormal" style="text-align: justify;"><span style="font-family: arial;"><span style="font-size: 12pt; line-height: 115%;">Α) <span style="mso-spacerun: yes;"> </span>την απωστική δύναμη μεταξύ των δύο φορτίων </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">Q</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;"> </span><sub><span style="font-size: 12pt; line-height: 115%;">Α</span></sub><span style="font-size: 12pt; line-height: 115%;">
και </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">Q</span><sub><span style="font-size: 12pt; line-height: 115%;">Β</span></sub><span style="font-size: 12pt; line-height: 115%;">
αν οι ίσες πλευρές ΑΒ και ΑΓ του ορθογωνίου τριγώνου είναι 3</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">cm</span><span style="font-size: 12pt; line-height: 115%;"> η καθεμιά,</span></span></p><p class="MsoNormal" style="text-align: justify;"><span style="font-family: arial;"><span style="font-size: 12pt; line-height: 115%;">Β) την ένταση του
ηλεκτροστατικού πεδίου που δημιουργούν τα δύο φορτία στη κορυφή<span style="mso-spacerun: yes;"> </span>Α,</span></span></p><span style="font-family: arial;">
</span><p class="MsoNormal" style="text-align: justify;"><span style="font-family: arial;"><span style="font-size: 12pt; line-height: 115%;">Γ) το μέτρο και το
πρόσημο του σημειακού φορτίου </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">q</span><sub><span style="font-size: 12pt; line-height: 115%;">Μ</span></sub><span style="font-size: 12pt; line-height: 115%;">
που πρέπει να τοποθετήσουμε στο μέσο Μ της ΒΓ έτσι ώστε η ένταση του
ηλεκτροστατικού πεδίου που δημιουργούν τα τρία φορτία στην κορυφή Α να είναι
μηδέν, <br /></span></span></p><span style="font-family: arial;">
</span><p class="MsoNormal" style="text-align: justify;"><span style="font-family: arial;"><span style="font-size: 12pt; line-height: 115%;">Δ) τη συνολική δύναμη
που δέχεται το φορτίο </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">q</span><sub><span style="font-size: 12pt; line-height: 115%;">Μ</span></sub></span></p><p class="MsoNormal" style="text-align: justify;"><span style="font-family: arial;"><sub><span style="font-size: 12pt; line-height: 115%;"></span></sub></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCFLFuiwsmrVrVdaVSjYE39NkH5jEVxoKGl5mNPMBin34Yq_8HHfdq9Ok0qf2Dt4WXM4AE98DotYpcHki4j_jtycRQ5s5imv5RtvLRbPPcofjwZhsBCGe2p0OWLPLv-Ii7b2wDPSgP6w09/s378/%25CE%25BF%25CF%2581%25CE%25B8%25CE%25BF%25CE%25B3%25CF%258E%25CE%25BD%25CE%25B9%25CE%25BF+%25CF%2584%25CF%2581%25CE%25AF%25CE%25B3%25CF%2589%25CE%25BD%25CE%25BF+%25CE%2591%25CE%2592%25CE%2593.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="234" data-original-width="378" height="248" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCFLFuiwsmrVrVdaVSjYE39NkH5jEVxoKGl5mNPMBin34Yq_8HHfdq9Ok0qf2Dt4WXM4AE98DotYpcHki4j_jtycRQ5s5imv5RtvLRbPPcofjwZhsBCGe2p0OWLPLv-Ii7b2wDPSgP6w09/w400-h248/%25CE%25BF%25CF%2581%25CE%25B8%25CE%25BF%25CE%25B3%25CF%258E%25CE%25BD%25CE%25B9%25CE%25BF+%25CF%2584%25CF%2581%25CE%25AF%25CE%25B3%25CF%2589%25CE%25BD%25CE%25BF+%25CE%2591%25CE%2592%25CE%2593.jpg" width="400" /></a></div><br /> <span style="font-size: 12pt; line-height: 115%;">Η λύση σε λίγες μέρες</span>.<p></p>
Panagiotis Stamatiouhttp://www.blogger.com/profile/05743522665371107812noreply@blogger.com0tag:blogger.com,1999:blog-3953680779248074761.post-13898551763805395642020-10-10T14:11:00.001+03:002020-10-10T14:11:03.419+03:00Α΄Λυκείου Κινηματική<p class="MsoNormal" style="text-align: justify;"><span style="font-family: arial;">Ο <span style="font-size: 12pt; line-height: 115%;">Παναγιώτης και ο
Νίκος, θέλουν να μετρήσουν το μήκος του κρουαζιερόπλοιου <span style="mso-spacerun: yes;"> </span>Braemar που εισέρχεται στον Ισθμό της Κορίνθου.
Τα παιδιά στέκονται δίπλα στην ακτογραμμή στα Ίσθμια, και σε απόσταση </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">d</span><span style="font-size: 12pt; line-height: 115%;">=250</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;"> </span><span style="font-size: 12pt; line-height: 115%;">μεταξύ
τους. Όταν η πλώρη του κρουαζιερόπλοιου φτάνει στον Παναγιώτη, τα παιδιά πατάνε
ταυτόχρονα τα χρονόμετρά τους, και αυτή η στιγμή θεωρείται η χρονική στιγμή </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">t</span><sub><span style="font-size: 12pt; line-height: 115%;">0</span></sub><span style="font-size: 12pt; line-height: 115%;">=0</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">s</span><span style="font-size: 12pt; line-height: 115%;">. Τη χρονική στιγμή </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">t</span><sub><span style="font-size: 12pt; line-height: 115%;">1</span></sub><span style="font-size: 12pt; line-height: 115%;">=31,2</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">s</span><span style="font-size: 12pt; line-height: 115%;">,<span style="mso-spacerun: yes;"> </span>περνά ολόκληρο το κρουαζιερόπλοιου από το Παναγιώτη ενώ από το Νίκο
περνά ολόκληρο το<span style="mso-spacerun: yes;"> </span>κρουαζιερόπλοιο, τη
χρονική στιγμή </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">t</span><sub><span style="font-size: 12pt; line-height: 115%;">2</span></sub><span style="font-size: 12pt; line-height: 115%;">=71,2</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">s</span><span style="font-size: 12pt; line-height: 115%;">. Να υπολογίσετε:</span></span></p><span style="font-family: arial;">
</span><p class="MsoNormal" style="text-align: justify;"><span style="font-family: arial;"><span style="font-size: 12pt; line-height: 115%;">Α) τη ταχύτητα του κρουαζιερόπλοιου
<span style="mso-spacerun: yes;"> </span>και</span></span></p><span style="font-family: arial;">
</span><p class="MsoNormal" style="text-align: justify;"><span style="font-family: arial;"><span style="font-size: 12pt; line-height: 115%;">Β) το μήκος του κρουαζιερόπλοιου</span></span></p><p class="MsoNormal" style="text-align: justify;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: arial;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcS5l6T0FIswgkJbAil_K8FfdHD6s8bxVTEdzScUYaFg2fu4ly01SMJ-915-YCLIQOsSxZVxpvr8G8Yn4bgBiP7MhSjoV64LfhgbsvuElfMSsu9afzVm9vn71KWx1X2-LBvo-JR5LfmR6G/s568/%25CF%2580%25CE%25B1%25CE%25B9%25CE%25B4%25CE%25B9%25CE%25AC+%25CE%25BA%25CF%2581%25CE%25BF%25CF%2585%25CE%25B1%25CE%25B6%25CE%25B5%25CF%2581%25CF%258C%25CF%2580%25CE%25BB%25CE%25BF%25CE%25B9%25CE%25BF.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="240" data-original-width="568" height="169" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcS5l6T0FIswgkJbAil_K8FfdHD6s8bxVTEdzScUYaFg2fu4ly01SMJ-915-YCLIQOsSxZVxpvr8G8Yn4bgBiP7MhSjoV64LfhgbsvuElfMSsu9afzVm9vn71KWx1X2-LBvo-JR5LfmR6G/w400-h169/%25CF%2580%25CE%25B1%25CE%25B9%25CE%25B4%25CE%25B9%25CE%25AC+%25CE%25BA%25CF%2581%25CE%25BF%25CF%2585%25CE%25B1%25CE%25B6%25CE%25B5%25CF%2581%25CF%258C%25CF%2580%25CE%25BB%25CE%25BF%25CE%25B9%25CE%25BF.jpg" width="400" /> </a></span></div><div class="separator" style="clear: both; text-align: center;"><span style="font-family: arial;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCHs4fkklKZ1_g9sxQHDy-96T_4AILeFMfFtMFU5mNJX2AnFMWXa3A70YA42WSSPeRzoezaAHFuWjzC8Ex6ekjcS-ObvP0ClnmJdkj1ql9PmGdzLui3owKt5XKcWWc54C5Dr14kGkDOA4g/s715/%25CF%2580%25CE%25B1%25CE%25B9%25CE%25B4%25CE%25B9%25CE%25AC+%25CE%25BA%25CF%2581%25CE%25BF%25CF%2585%25CE%25B1%25CE%25B6%25CE%25B5%25CF%2581%25CF%258C%25CF%2580%25CE%25BB%25CE%25BF%25CE%25B9%25CE%25BF+%25CE%25B1%25CE%25BD%25CE%25B9%25CE%25BC%25CE%25B1%25CF%2584%25CE%25B9%25CE%25BF%25CE%25BDgif.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="308" data-original-width="715" height="173" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCHs4fkklKZ1_g9sxQHDy-96T_4AILeFMfFtMFU5mNJX2AnFMWXa3A70YA42WSSPeRzoezaAHFuWjzC8Ex6ekjcS-ObvP0ClnmJdkj1ql9PmGdzLui3owKt5XKcWWc54C5Dr14kGkDOA4g/w400-h173/%25CF%2580%25CE%25B1%25CE%25B9%25CE%25B4%25CE%25B9%25CE%25AC+%25CE%25BA%25CF%2581%25CE%25BF%25CF%2585%25CE%25B1%25CE%25B6%25CE%25B5%25CF%2581%25CF%258C%25CF%2580%25CE%25BB%25CE%25BF%25CE%25B9%25CE%25BF+%25CE%25B1%25CE%25BD%25CE%25B9%25CE%25BC%25CE%25B1%25CF%2584%25CE%25B9%25CE%25BF%25CE%25BDgif.gif" width="400" /></a></div></span></div><span style="font-family: arial;"> Η λύση σε λίγες μέρες.</span><br /><p></p>
Panagiotis Stamatiouhttp://www.blogger.com/profile/05743522665371107812noreply@blogger.com0tag:blogger.com,1999:blog-3953680779248074761.post-67716953062979699292020-10-03T14:19:00.004+03:002020-10-05T13:19:06.945+03:00 Β Λυκείου Γενικής Παιδείας Νόμος Coulomb<p align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: arial;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 12pt; line-height: 115%;"> Νόμος </span></b><b style="mso-bidi-font-weight: normal;"><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">Coulomb</span></b></span></p><span style="font-family: arial;">
</span><p align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: arial;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 12pt; line-height: 115%;"></span></b></span></p><span style="font-family: arial;">
</span><p class="MsoNormal" style="text-align: justify;"><span style="font-family: arial;"><span style="font-size: 12pt; line-height: 115%;">Στην κορυφή Α ενός ορθογωνίου
τριγώνου ΑΒΓ, βρίσκεται το φορτίο </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">q</span><sub><span style="font-size: 12pt; line-height: 115%;">Α</span></sub><span style="font-size: 12pt; line-height: 115%;">=+2μ</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">C</span><span style="font-size: 12pt; line-height: 115%;">. Στις κορυφές Β και Γ, βρίσκονται
τα φορτία │</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">q</span><sub><span style="font-size: 12pt; line-height: 115%;">Β</span></sub><span style="font-size: 12pt; line-height: 115%;">│=
4μ</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">C</span><span style="font-size: 12pt; line-height: 115%;">
και </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">q</span><sub><span style="font-size: 12pt; line-height: 115%;">Γ</span></sub><span style="font-size: 12pt; line-height: 115%;">
αντίστοιχα. Αν το φορτίο στη κορυφή Α δέχεται συνολική δύναμη </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">F</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;"> </span><span style="font-size: 12pt; line-height: 115%;">από
τα άλλα φορτία κάθετη προς την υποτείνουσα του ορθογωνίου τριγώνου ΑΒΓ και με φορά
προς αυτήν, όπως φαίνεται στο σχήμα, να υπολογίσετε:</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;"></span></span></p><span style="font-family: arial;">
</span><p class="MsoNormal" style="text-align: justify;"><span style="font-family: arial;"><span style="font-size: 12pt; line-height: 115%;">Α) τα πρόσημα των
φορτίων </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">q</span><sub><span style="font-size: 12pt; line-height: 115%;">Β
</span></sub><span style="font-size: 12pt; line-height: 115%;">και
</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">q</span><sub><span style="font-size: 12pt; line-height: 115%;">Γ,
</span></sub><span style="font-size: 12pt; line-height: 115%;">και
την τιμή του φορτίου </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">q</span><sub><span style="font-size: 12pt; line-height: 115%;">Γ</span></sub><span style="font-size: 12pt; line-height: 115%;"></span></span></p><span style="font-family: arial;">
</span><p class="MsoNormal" style="text-align: justify;"><span style="font-family: arial;"><span style="font-size: 12pt; line-height: 115%;">Β) τη δύναμη </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">F</span><sub><span style="font-size: 12pt; line-height: 115%;">ΑΒ</span></sub><span style="font-size: 12pt; line-height: 115%;">
μεταξύ των φορτιών Α και Β, όπως και τη δύναμη </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">F</span><sub><span style="font-size: 12pt; line-height: 115%;">ΑΓ</span></sub><span style="font-size: 12pt; line-height: 115%;">
μεταξύ των φορτίων Α και Γ.</span></span></p><span style="font-family: arial;">
</span><p class="MsoNormal" style="text-align: justify;"><span style="font-family: arial;"><span style="font-size: 12pt; line-height: 115%;">Γ) την συνισταμένη
δύναμη </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">F</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">
</span><span style="font-size: 12pt; line-height: 115%;">που
δέχεται το φορτίο </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">q</span><sub><span style="font-size: 12pt; line-height: 115%;">Α
</span></sub><span style="font-size: 12pt; line-height: 115%;"></span></span></p><span style="font-family: arial;">
</span><p class="MsoNormal" style="text-align: justify;"><span style="font-family: arial;"><span style="font-size: 12pt; line-height: 115%;">Δ) Αν στο ίχνος της καθέτου
Κ από την κορυφή Α στην υποτείνουσα του ορθογωνίου τριγώνου ΑΒΓ, τοποθετήσουμε φορτίο
</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">q</span><sub><span style="font-size: 12pt; line-height: 115%;">Κ
</span></sub><span style="font-size: 12pt; line-height: 115%;">=
+1μ</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">C</span><span style="font-size: 12pt; line-height: 115%;">,
να υπολογίσετε τη συνισταμένη δύναμη </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">F</span><span style="font-size: 12pt; line-height: 115%;">΄
που δέχεται από τα άλλα φορτία.</span></span></p><span style="font-family: arial;">
</span><p class="MsoNormal" style="text-align: justify;"><span style="font-family: arial;"><span style="font-size: 12pt; line-height: 115%;">Τα φορτία θεωρούνται
σημειακά και τα μήκη των πλευρών του ορθογωνίου τριγώνου είναι: (ΑΓ)=3</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">cm</span><span style="font-size: 12pt; line-height: 115%;"> και (ΑΒ)=4</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">cm</span><span style="font-size: 12pt; line-height: 115%;">. Δίνεται επίσης η σταθερά </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">k</span><span style="font-size: 12pt; line-height: 115%;">=9<sup>.</sup>10<sup>9</sup></span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">N</span><sup><span style="font-size: 12pt; line-height: 115%;">.</span></sup><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><sup><span style="font-size: 12pt; line-height: 115%;">2</span></sup><span style="font-size: 12pt; line-height: 115%;">/</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">C</span><sup><span style="font-size: 12pt; line-height: 115%;">2</span></sup><span style="font-size: 12pt; line-height: 115%;">.</span></span></p><p class="MsoNormal" style="text-align: justify;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: arial;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6AziPOHDdeqNN3cGkho8AAcE89D2y5EVEa3l9tiHIdnf8oIOooj4anMOB2AezLiQfW2bX5dXGjbCgwTNbw-yAtuqU2-W6X-0Q-_0FKTr8ry3C6mE3yS2fCKXKH-plM12Z52uoHuN6Fot6/s532/%25CE%25BD%25CF%258C%25CE%25BC%25CE%25BF%25CF%2582+Coulomb.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="308" data-original-width="532" height="231" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6AziPOHDdeqNN3cGkho8AAcE89D2y5EVEa3l9tiHIdnf8oIOooj4anMOB2AezLiQfW2bX5dXGjbCgwTNbw-yAtuqU2-W6X-0Q-_0FKTr8ry3C6mE3yS2fCKXKH-plM12Z52uoHuN6Fot6/w400-h231/%25CE%25BD%25CF%258C%25CE%25BC%25CE%25BF%25CF%2582+Coulomb.jpg" width="400" /></a></span></div><span style="font-family: arial;"><br /> Η λύση σε λίγες μέρες.</span><br /><p></p>
Panagiotis Stamatiouhttp://www.blogger.com/profile/05743522665371107812noreply@blogger.com0tag:blogger.com,1999:blog-3953680779248074761.post-75944002296100586882020-09-11T08:46:00.007+03:002020-09-13T18:39:52.064+03:00ΕΠΑΝΑΛΗΠΤΙΚΕΣ ΠΑΝΕΛΛΑΔΙΚΕΣ ΕΞΕΤΑΣΕΙΣ ΓΕΛ ΚΑΙ ΟΜΟΓΕΝΩΝ ΜΕ ΠΑΛΑΙΟ ΚΑΙ ΝΕΟ ΣΥΣΤΗΜΑ<p><!--[if gte mso 9]><xml>
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</p><p align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: arial;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 12pt; line-height: 115%;">ΑΝΑΚΟΙΝΩΘΗΚΑΝ
ΟΙ ΒΑΣΕΙΣ ΕΙΣΑΓΩΓΗΣ ΣΤΗΝ ΤΡΙΤΟΒΑΘΜΙΑ ΕΚΠΑΙΔΕΥΣΗ ΓΙΑ ΤΟ 2020</span></b></span></p><span style="font-family: arial;">
</span><p align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: arial;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 12pt; line-height: 115%;"> </span></b></span></p><span style="font-family: arial;">
</span><p class="MsoNormal" style="text-align: justify;"><span style="font-family: arial;"><span style="font-size: 12pt; line-height: 115%;">Οι βάσεις των <strong><span style="font-weight: normal; mso-bidi-font-weight: bold;">Πανελλαδικών</span></strong>
<strong><span style="font-weight: normal; mso-bidi-font-weight: bold;">Εξετάσεων</span></strong>
του έτους 2020 ανακοινώθηκαν περί τις 9:00πμ την Παρασκευή 28-08-2020, βάζοντας
τέλος στην αγωνία χιλιάδων υποψηφίων για μια θέση στην τριτοβάθμια εκπαίδευση. </span></span></p><span style="font-family: arial;">
</span><p class="MsoNormal" style="text-align: justify;"><span style="font-family: arial;"><span style="font-size: 12pt; line-height: 115%;">Οι φετινές <strong><span style="color: black; font-weight: normal; mso-bidi-font-weight: bold; mso-themecolor: text1;">Πανελλήνιες Εξετάσεις</span></strong><span style="color: black; mso-themecolor: text1;">,</span> πραγματοποιήθηκαν υπό ιδιαίτερα δύσκολες συνθήκες λόγω της <strong><span style="font-weight: normal; mso-bidi-font-weight: bold;">πανδημίας</span></strong>
του <strong><span style="font-weight: normal; mso-bidi-font-weight: bold;">κορωνοϊού</span></strong>
και μετά από παρατεταμένη απουσία των <strong><span style="font-weight: normal; mso-bidi-font-weight: bold;">μαθητών</span></strong> από τα <strong><span style="font-weight: normal; mso-bidi-font-weight: bold;">σχολεία. </span></strong></span></span></p><span style="font-family: arial;">
</span><p class="MsoNormal" style="text-align: justify;"><span style="font-family: arial;"><span style="font-size: 12pt; line-height: 115%;">Στο <strong>1ο
επιστημονικό πεδίο</strong> για όσους διαγωνίστηκαν με το <strong><span style="font-weight: normal; mso-bidi-font-weight: bold;">νέο σύστημα,</span></strong>
παρατηρήθηκε <strong><span style="font-weight: normal; mso-bidi-font-weight: bold;">οριακή
άνοδος</span></strong> στις νομικές σχολές και μεγαλύτερη η οποία έφτασε τα 265
μόρια στις σχολές της ψυχολογίας. Πολλά περιφερειακά τμήματα φιλοσοφίας,
φιλολογίας, ιστορίας και αρχαιολογιας καθώς και τμήματα κοινωνικής πολιτικής
είναι κάτω από τα 10.000 μόρια.</span></span></p><span style="font-family: arial;">
</span><p style="text-align: justify;"><span style="font-family: arial;">Στο <strong>2ο επιστημονικό</strong> <strong>πεδίο</strong>
υπάρχουν <strong><span style="font-weight: normal; mso-bidi-font-weight: bold;">συνθήκες
ελεύθερης πρόσβασης</span></strong>.</span></p><span style="font-family: arial;">
</span><p style="text-align: justify;"><span style="font-family: arial;"><strong><span style="font-weight: normal; mso-bidi-font-weight: bold;">Στο </span>3ο επιστημονικό</strong> <strong>πεδίο</strong>
ι<strong><span style="font-weight: normal; mso-bidi-font-weight: bold;">στορική</span></strong>
είναι φέτος η <strong><span style="font-weight: normal; mso-bidi-font-weight: bold;">πτώση</span></strong> των βάσεων στις <span style="mso-bidi-font-weight: bold;">ιατρικές σχολές</span>. Στην <strong><span style="font-weight: normal; mso-bidi-font-weight: bold;">Αθήνα</span></strong> ήταν περίπου <strong><span style="font-weight: normal; mso-bidi-font-weight: bold;">500</span></strong> <strong><span style="font-weight: normal; mso-bidi-font-weight: bold;">μόρια</span></strong> και ξεπέρασε
τα <strong><span style="font-weight: normal; mso-bidi-font-weight: bold;">700</span></strong>
στην Ιατρική της <strong><span style="font-weight: normal; mso-bidi-font-weight: bold;">Αλεξανδρούπολης</span></strong>. <strong><span style="font-weight: normal; mso-bidi-font-weight: bold;">Ελεύθερη πτώση</span></strong> έκαναν επίσης και τα
τμήματα της νοσηλευτικής (άγγιξαν τα <strong><span style="font-weight: normal; mso-bidi-font-weight: bold;">3.000 μόρια)</span></strong></span></p><span style="font-family: arial;">
</span><p style="text-align: justify;"><span style="font-family: arial;">Στο <b style="mso-bidi-font-weight: normal;">4ο
επιστημονικό πεδίο</b> των σχολών <strong><span style="font-weight: normal; mso-bidi-font-weight: bold;">οικονομίας</span></strong> και <strong><span style="font-weight: normal; mso-bidi-font-weight: bold;">πληροφορικής</span></strong>,
παρατηρήθηκαν αυξήσεις στα τμήματα των κεντρικών πανεπιστημίων αλλά και
μειώσεις σε πολλά περιφερειακά τμήματα</span></p><span style="font-family: arial;">
</span><p class="MsoNormal" style="text-align: justify;"><span style="font-family: arial;"><span style="font-size: 12pt; line-height: 115%;">Εντυπωσιακό είναι το
γεγονός ότι <b style="mso-bidi-font-weight: normal;">στο τμήμα δασολογί</b><b>ας</b> και
διαχείρισης φυσικού περιβάλλοντος στο Καρπενήσι εισάγεται υποψήφιος με μόλις… <b style="mso-bidi-font-weight: normal;">625 μόρια</b></span></span></p><span style="font-family: arial;">
</span><p class="MsoNormal" style="text-align: justify;"><span style="font-family: arial;"><span style="font-size: 12pt; line-height: 115%;">Για εκείνους που
διαγωνίστηκαν με το παλαιό σύστημα, διαπιστώθηκε άνοδος στις ιατρικές σχολές
που ξεκινούσε από τα 200 και έφτανε στα 300 μόρια και εντυπωσιακή πτώση στις
νομικές σχολές.</span></span></p><span style="font-family: arial;">
</span><p class="MsoNormal" style="text-align: justify;"><b><span style="font-family: arial;"><span style="font-size: 12pt; line-height: 115%;">Για να δείτε τις βάσεις
εισαγωγής μεταβείτε στη σελίδα Βάσεις ΑΕΙ- ΤΕΙ</span></span></b></p><span style="font-family: arial;">
</span><p><span style="font-family: arial;"> </span></p>Panagiotis Stamatiouhttp://www.blogger.com/profile/05743522665371107812noreply@blogger.com0tag:blogger.com,1999:blog-3953680779248074761.post-82840281183654948782020-07-05T12:33:00.001+03:002020-07-05T12:37:36.687+03:00ΚΑΛΟ ΚΑΛΟΚΑΙΡΙ - ΤΕΛΟΣ ΣΧΟΛΙΚΗΣ ΧΡΟΝΙΑ 2019-2020<div dir="ltr" style="text-align: left;" trbidi="on">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span>
<br />
<div align="center" style="text-align: center;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: red;"><b><u><span style="font-family: "arial" , "sans-serif";">ΤΕΛΟΣ ΣΧΟΛΙΚΗΣ ΧΡΟΝΙΑΣ 2019-2020</span></u></b></span></span></div>
<div align="center" style="text-align: center;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><b><u><span style="color: blue; font-family: "arial" , "sans-serif";"><br /></span></u></b></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><b><u><span style="color: blue; font-family: "arial" , "sans-serif";">ΚΑΛΟ ΚΑΛΟΚΑΙΡΙ</span></u></b></span></div>
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</span></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "sans-serif";">Στο
καλό αγαπημένα μας παιδιά……</span></span></div>
<div style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span></div>
<div style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "sans-serif";">Έπεσε
η αυλαία και αυτής της σχολικής χρονιάς μέσα στη γόνιμη σιωπή, όπως ορίζει ο
δάσκαλος - καθηγητής. Σιωπή, για να ευδοκιμήσει η περιπλάνηση στη γνώση, για να
αφουγκραστούμε τον απόηχο της εκπαιδευτικής πράξης, για να ψάξουμε κάτω από τις
λέξεις, για να ετοιμαστούν οι απόφοιτοι για τη μεγάλη βόλτα στο σεργιάνι της
ζωής. Οι προβολείς θα ανάψουν εκτυφλωτικά, σχεδόν παραμορφωτικά στις
πανελλαδικές εξετάσεις που ακολουθούν. Εκεί που υπάρχουν μόνο μόρια και
αριθμοί, βάσεις ….. </span></span></div>
<div style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span></div>
<div style="text-align: justify;">
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "sans-serif";">Για
να δείτε τη συνέχεια πατήστε <a href="https://drive.google.com/file/d/1sepdLF0d9lafF6e5CqXNgz-2ChreL4gS/view?usp=sharing" target="_blank">εδώ</a>.</span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><b><u><span style="color: blue; font-size: 12pt;">ΘΕΜΑΤΑ ΦΥΣΙΚΗΣ ΠΑΝΕΛΛΗΝΙΩΝ Γ.Ε.Λ. <span style="mso-spacerun: yes;"> </span>2020 ΜΕ ΤΟ ΝΕΟ ΣΥΣΤΗΜΑ</span></u></b><span style="font-size: 12pt;"></span></span></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
<span style="font-size: 12pt; line-height: 115%;"><br />
Δείτε τα θέματα <a href="https://drive.google.com/file/d/198vVQSp23LaPWWHCqHJsODmYM0ROa5Uh/view?usp=sharing" target="_blank">εδώ</a>.</span></span><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"></span></span>
<br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Για να δείτε τις λύσεις πατήστε <a href="https://drive.google.com/file/d/1fXoqDFR8M9DbFPRJTqpMy1jDb9xzngWm/view?usp=sharing" target="_blank">εδώ</a>.</span></span></span></span><br />
<br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;"> </span></span></span></span>
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<div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><b><u><span style="color: red; font-size: 12pt;">ΘΕΜΑΤΑ ΦΥΣΙΚΗΣ ΠΑΝΕΛΛΗΝΙΩΝ Γ.Ε.Λ. <span style="mso-spacerun: yes;"> </span>2020 ΜΕ ΤΟ ΠΑΛΑΙΟ ΣΥΣΤΗΜΑ</span></u></b><span style="font-size: 12pt;"></span></span></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><br />
Δείτε τα θέματα <a href="https://drive.google.com/file/d/1bvf-qtNJ2V8l7X4fnOYtQtDKwUP3nTo_/view?usp=sharing" target="_blank">εδώ</a>.</span></span><span style="font-family: "arial" , "helvetica" , sans-serif;"></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"></span><br />
<br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Για να δείτε τις λύσεις πατήστε <a href="https://drive.google.com/file/d/1Gyb8Sg2uNJN2VPLlOOAP2XifHPVlrQYc/view?usp=sharing" target="_blank">εδώ</a>.</span></span></span></span><br />
<br /></div>
Panagiotis Stamatiouhttp://www.blogger.com/profile/05743522665371107812noreply@blogger.com0tag:blogger.com,1999:blog-3953680779248074761.post-12936014183549660482020-06-10T20:11:00.001+03:002020-06-14T12:54:13.810+03:00Γ΄Λυκείου Στερεό-Ταλάντωση<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="MsoNormal" style="tab-stops: 69.0pt; text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Ομογενής
και ισοπαχής ράβδος ΑΒ μήκους<span style="mso-spacerun: yes;"> </span></span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">L</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;"> </span><span style="font-size: 12pt; line-height: 115%;">και
μάζας </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">M</span><span style="font-size: 12pt; line-height: 115%;">=4</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">Kg</span><span style="font-size: 12pt; line-height: 115%;"> ισορροπεί ακίνητη με τη βοήθεια
άρθρωσης στο άκρο της Α και οριζοντίου τεντωμένου νήματος, το ένα άκρο του
οποίου είναι δεμένο στο άκρο Β της ράβδου, και το άλλο άκρο δεμένο σε
κατακόρυφο τοίχο στο σημείο Γ. Η ράβδος σχηματίζει γωνία φ με τον κατακόρυφο τοίχο
που βρίσκεται η άρθρωση όπως φαίνεται στο σχήμα. Στο άκρο Β υπάρχει στερεωμένο
ιδανικό ελατήριο σταθεράς </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">k</span><span style="font-size: 12pt; line-height: 115%;">=100Ν/</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span style="font-size: 12pt; line-height: 115%;">, στο άλλο άκρο του οποίου
ισορροπεί σώμα Σ<sub>1</sub> μάζας <span style="mso-spacerun: yes;"> </span></span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><sub><span style="font-size: 12pt; line-height: 115%;">1</span></sub><span style="font-size: 12pt; line-height: 115%;">=2</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">Kg</span><span style="font-size: 12pt; line-height: 115%;">.</span></span></div>
<div class="MsoNormal" style="tab-stops: 69.0pt; text-align: justify;">
<br /></div>
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/* Style Definitions */
table.MsoNormalTable
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mso-tstyle-rowband-size:0;
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</span></span></div>
<div class="MsoNormal" style="tab-stops: 69.0pt; text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Α)
Να υπολογίσετε τα μέτρα των δυνάμεων που δέχεται η ράβδος</span></span></div>
<div class="MsoNormal" style="tab-stops: 69.0pt; text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span></div>
<div class="MsoListParagraphCxSpFirst" style="margin-left: 39pt; text-align: justify; text-indent: -39pt;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;"><span style="mso-list: Ignore;"><span style="font-feature-settings: normal; font-kerning: auto; font-language-override: normal; font-optical-sizing: auto; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-variation-settings: normal; font-weight: normal; line-height: normal;">
</span>I.<span style="font-feature-settings: normal; font-kerning: auto; font-language-override: normal; font-optical-sizing: auto; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-variation-settings: normal; font-weight: normal; line-height: normal;">
</span></span></span><span style="font-size: 12pt; line-height: 115%;">από το νήμα και </span></span></div>
<div class="MsoListParagraphCxSpFirst" style="margin-left: 39pt; text-align: justify; text-indent: -39pt;">
<br /></div>
<div style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 39pt; text-align: justify; text-indent: -39pt;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;"><span style="mso-list: Ignore;"><span style="font-feature-settings: normal; font-kerning: auto; font-language-override: normal; font-optical-sizing: auto; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-variation-settings: normal; font-weight: normal; line-height: normal;">
</span>II.<span style="font-feature-settings: normal; font-kerning: auto; font-language-override: normal; font-optical-sizing: auto; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-variation-settings: normal; font-weight: normal; line-height: normal;">
</span></span></span><span style="font-size: 12pt; line-height: 115%;">από την άρθρωση.</span></span></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 39pt; text-align: justify; text-indent: -39pt;">
<br /></div>
<div style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span></div>
<div class="MsoNormal" style="tab-stops: 69.0pt; text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Απομακρύνουμε
το σώμα Σ<sub>1</sub> μάζας </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><sub><span style="font-size: 12pt; line-height: 115%;">1</span></sub><span style="font-size: 12pt; line-height: 115%;">
κατακόρυφα προς τα κάτω κατά </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">d</span><span style="font-size: 12pt; line-height: 115%;">=0,1</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;"> </span><span style="font-size: 12pt; line-height: 115%;">και
τη χρονική στιγμή </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">t</span><span style="font-size: 12pt; line-height: 115%;">=0</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">s</span><span style="font-size: 12pt; line-height: 115%;">, το αφήνουμε να κινηθεί. Η ράβδος
στη διάρκεια της ταλάντωσης ισορροπεί συνεχώς στην ίδια θέση.</span></span></div>
<div class="MsoNormal" style="tab-stops: 69.0pt; text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span></div>
<div class="MsoNormal" style="tab-stops: 69.0pt; text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Β)
Να γράψετε τη χρονική εξίσωση της κινητικής και της δυναμικής ενέργειας
ταλάντωσης του σώματος Σ<sub>1</sub>. </span></span></div>
<div class="MsoNormal" style="tab-stops: 69.0pt; text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span></div>
<div class="MsoNormal" style="tab-stops: 69.0pt; text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Γ)
Να υπολογίσετε τη συνάρτηση της τάσης του νήματος σε συνάρτηση με την
απομάκρυνση </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">x</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">
</span><span style="font-size: 12pt; line-height: 115%;">του
σώματος Σ<sub>1 </sub>από τη θέση ισορροπίας του.</span></span></div>
<div class="MsoNormal" style="tab-stops: 69.0pt; text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span></div>
<div class="MsoNormal" style="tab-stops: 69.0pt; text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Κάποια
στιγμή που το σώμα Σ<sub>1</sub> βρίσκεται στην άνω ακραία θέση του,
τοποθετούμε πάνω του χωρίς αρχική ταχύτητα ένα σώμα Σ<sub>2 </sub>μάζας </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><sub><span style="font-size: 12pt; line-height: 115%;">2</span></sub><span style="font-size: 12pt; line-height: 115%;">.
Το σώμα Σ<sub>2</sub> κολλά στο σώμα Σ<sub>1</sub> οπότε δεν χάνεται<span style="mso-spacerun: yes;"> </span>η επαφή των δυο σωμάτων σε καμία στιγμή. Αν
το όριο θραύσης του νήματος είναι Τθρ=67,5Ν τότε, </span></span></div>
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<br /></div>
<div style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span></div>
<div class="MsoNormal" style="tab-stops: 69.0pt; text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Δ)
να υπολογίσετε τη μέγιστη τιμή της μάζας </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><sub><span style="font-size: 12pt; line-height: 115%;">2</span></sub><span style="font-size: 12pt; line-height: 115%;">
του σώματος Σ<sub>2</sub>, ώστε να μην κόβεται το νήμα στη διάρκεια της νέας
ταλάντωσης του συστήματος των Σ<sub>1</sub> και Σ<sub>2</sub>. </span></span></div>
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<br /></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Να θεωρήσετε ότι:</span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">γ) η επιτάχυνση της
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Για να δείτε τη λύση πατήστε <a href="https://drive.google.com/file/d/1bNWEoy860aRbrUFsMtrI8EPx7DZUTqLB/view?usp=sharing" target="_blank">εδώ</a>.</span></span></div>
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Panagiotis Stamatiouhttp://www.blogger.com/profile/05743522665371107812noreply@blogger.com0tag:blogger.com,1999:blog-3953680779248074761.post-66119874937203422032020-06-02T12:52:00.000+03:002020-06-02T13:09:24.222+03:00ΕΠΑΝΑΛΗΠΤΙΚΟ ΔΙΑΓΩΝΙΣΜΑ 2019-20<div dir="ltr" style="text-align: left;" trbidi="on">
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<b style="mso-bidi-font-weight: normal;"><span style="color: #0070c0; font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 115%;">Επαναληπτικό Διαγώνισμα
Φυσικής Προσανατολισμού για το σχολ.έτος 2019-2020 απο ΨΕΒ</span></b></div>
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<b style="mso-bidi-font-weight: normal;"><span style="color: red; font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 115%;">6ο ΔΙΑΓΩΝΙΣΜΑ (ΕΠΑΝΑΛΗΠΤΙΚΟ) –
ΘΕΜΑΤΑ - ΛΥΣΕΙΣ</span></b></div>
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<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 115%;">Για να δείτε τα θέματα
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Panagiotis Stamatiouhttp://www.blogger.com/profile/05743522665371107812noreply@blogger.com0tag:blogger.com,1999:blog-3953680779248074761.post-52399762767794479802020-05-28T12:13:00.000+03:002020-06-06T17:30:51.041+03:00Γ΄Λυκείου Στερεό - ισορροπία - Ταλάντωση<div dir="ltr" style="text-align: left;" trbidi="on">
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 112%;">Μια οµογενής ράβδος ΑΒ μήκους L=1m και
µάζας m=4kg είναι αρθρωµένη στο άκρο της Α και µε την βοήθεια ενός αβαρούς µη εκτατού
νήµατος που είναι δεµένο στο σημείο Β, ισορροπεί οριζόντια, µε το νήµα να σχηµατίζει
γωνία φ=30<sup>o</sup> µε την ράβδο. Στο σημείο Κ της ράβδου με ΒΚ=0,25m, έχουµε
αναρτήσει ένα ιδανικό ελατήριο σταθεράς k που στο κάτω άκρο του ισορροπεί ακλόνητα
στερεωμένο ένα σώµα µάζας m<sub>1</sub>=2kg.</span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 117%;">Α) Να<span style="letter-spacing: -.4pt;"> β</span>ρεθεί<span style="letter-spacing: -.45pt;"> </span>το<span style="letter-spacing: -.45pt;"> </span>µέτρο<span style="letter-spacing: -.45pt;">
</span>της<span style="letter-spacing: -.4pt;"> </span>δύναµης<span style="letter-spacing: -.45pt;"> </span>που<span style="letter-spacing: -.45pt;"> </span>δέχεται<span style="letter-spacing: -.5pt;"> </span>η<span style="letter-spacing: -.4pt;"> </span>ράβδος<span style="letter-spacing: -.45pt;"> </span>από<span style="letter-spacing: -.45pt;"> </span>το<span style="letter-spacing: -.45pt;"> </span>νήµα,<span style="letter-spacing: -.4pt;"> </span>και</span><span style="font-size: 12pt; line-height: 117%;"> </span><span style="font-size: 12pt; line-height: 117%;">η<span style="letter-spacing: -.25pt;"> </span>δύναµη<span style="letter-spacing: -.2pt;"> </span>που<span style="letter-spacing: -.25pt;"> </span>δέχεται<span style="letter-spacing: -.2pt;"> </span>η<span style="letter-spacing: -.25pt;"> </span>άρθρωση<span style="letter-spacing: -.2pt;"> </span>από<span style="letter-spacing: -.25pt;"> </span>την<span style="letter-spacing: -.2pt;"> </span>ράβδο.</span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 112%;">Στο<span style="letter-spacing: -.95pt;">
</span>έδαφος<span style="letter-spacing: -1.0pt;"> </span>και<span style="letter-spacing: -.95pt;"> </span>στην<span style="letter-spacing: -1.0pt;"> </span>ίδια<span style="letter-spacing: -.9pt;"> </span>κατακόρυφο<span style="letter-spacing: -.95pt;"> </span>µε<span style="letter-spacing: -1.0pt;"> </span>τον<span style="letter-spacing: -.95pt;"> </span>άξονα<span style="letter-spacing: -.9pt;"> </span>του<span style="letter-spacing: -1.0pt;"> </span>ελατηρίου<span style="letter-spacing: -.95pt;"> </span>βρίσκεται<span style="letter-spacing: -.25pt;"> </span>δεύτερο<span style="letter-spacing: -.25pt;"> </span>σώμα<span style="letter-spacing: -.25pt;"> </span>µάζας<span style="letter-spacing: -.25pt;"> </span></span><span lang="EN-US" style="font-size: 12pt; line-height: 112%;">m</span><sub><span style="font-size: 12pt; line-height: 112%;">2</span></sub><span style="font-size: 12pt; line-height: 112%;">=2</span><span lang="EN-US" style="font-size: 12pt; line-height: 112%;">Kg</span><span lang="EN-US" style="font-size: 12pt; letter-spacing: -0.8pt; line-height: 112%;"> </span><span style="font-size: 12pt; line-height: 112%;">το<span style="letter-spacing: -.25pt;">
</span>οποίο<span style="letter-spacing: -.25pt;"> </span>εκτοξεύεται<span style="letter-spacing: -.25pt;"> </span>κατακόρυφα<span style="letter-spacing: -.2pt;"> </span>προς<span style="letter-spacing: -.25pt;"> </span>τα<span style="letter-spacing: -.25pt;"> </span>πάνω </span><span style="font-size: 12pt; line-height: 112%;">µε<span style="letter-spacing: -.6pt;"> </span>ταχύτητα<span style="letter-spacing: -.6pt;"> </span>μέτρου<span style="letter-spacing: -.6pt;"> </span>υ<sub><span style="mso-text-raise: -1.5pt; position: relative; top: 1.5pt;">0</span></sub>=4</span><span lang="EN-US" style="font-size: 12pt; line-height: 112%;">m</span><span style="font-size: 12pt; line-height: 112%;">/</span><span lang="EN-US" style="font-size: 12pt; line-height: 112%;">s</span><span lang="EN-US" style="font-size: 12pt; letter-spacing: -1.25pt; line-height: 112%;"> </span><span style="font-size: 12pt; line-height: 112%;">και<span style="letter-spacing: -.55pt;">
</span>την<span style="letter-spacing: -.6pt;"> </span>χρονική<span style="letter-spacing: -.6pt;"> </span>στιγμή<span style="letter-spacing: -.6pt;"> </span></span><span lang="EN-US" style="font-size: 12pt; line-height: 112%;">t</span><sub><span style="font-size: 12pt; line-height: 112%;">0</span></sub><span style="font-size: 12pt; line-height: 112%;">=0</span><span lang="EN-US" style="font-size: 12pt; line-height: 112%;">s</span><span lang="EN-US" style="font-size: 12pt; letter-spacing: -0.9pt; line-height: 112%;"> </span><span style="font-size: 12pt; line-height: 112%;">σφηνώνεται</span><span style="font-size: 12pt; line-height: 112%;"> </span><span style="font-size: 12pt; line-height: 112%;">στο<span style="letter-spacing: -.85pt;"> </span>σώµα που είναι αναρτημένο<span style="letter-spacing: -.8pt;"> </span>στο<span style="letter-spacing: -.8pt;"> </span>ελατήριο.
Το<span style="letter-spacing: -.4pt;"> </span>συσσωµάτωµα<span style="letter-spacing: -.35pt;"> </span>που<span style="letter-spacing: -.4pt;"> </span>δηµιουργείται<span style="letter-spacing: -.35pt;"> </span>σταµατά<span style="letter-spacing: -.35pt;">
</span>στιγµιαία<span style="letter-spacing: -.4pt;"> </span>την<span style="letter-spacing: -.35pt;"> </span>χρονική<span style="letter-spacing: -.35pt;">
</span>στιγμ</span><span style="font-size: 12pt; line-height: 112%;">ή<span style="letter-spacing: .8pt;"> </span></span><span lang="EN-US" style="font-size: 12pt; line-height: 112%;">t</span><sub><span style="font-size: 12pt; line-height: 112%; position: relative; top: 1.5pt;">1</span></sub><span style="font-size: 12pt; line-height: 112%;">=π/15 </span><span lang="EN-US" style="font-size: 12pt; line-height: 112%;">s</span><span lang="EN-US" style="font-size: 12pt; line-height: 112%;"> </span><span style="font-size: 12pt; line-height: 112%;">όταν<span style="letter-spacing: 1.05pt;"> </span>ϕτάσει<span style="letter-spacing: 1.1pt;"> </span>στην<span style="letter-spacing: 1.05pt;"> </span>ϑέση<span style="letter-spacing: 1.05pt;"> </span>που<span style="letter-spacing: 1.1pt;"> </span>µηδενίζεται<span style="letter-spacing: 1.05pt;"> </span>η<span style="letter-spacing: 1.05pt;"> </span>δύναµη<span style="letter-spacing: 1.1pt;"> </span>παραμόρφωσης του ελατηρίου.</span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 117%;">Β) <span style="mso-spacerun: yes;"> </span>Να βρεθεί η ταχύτητα υ με την οποία θα
συγκρουστεί το σώμα μάζας<span style="mso-spacerun: yes;"> </span>m<sub>2</sub> <span style="mso-spacerun: yes;"> </span>με το σώμα μάζας m<sub>1</sub> και η αρχική
απόσταση h ανάµεσα στα δύο σώµατα.</span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt;">Γ) Να<span style="letter-spacing: .1pt;"> </span>γράψετε<span style="letter-spacing: .05pt;"> </span>την<span style="letter-spacing: .05pt;"> </span>χρονική<span style="letter-spacing: .1pt;"> </span>εξίσωση<span style="letter-spacing: .05pt;"> </span>του<span style="letter-spacing: .05pt;"> </span>ρυθµού<span style="letter-spacing: .1pt;"> </span>µεταβολής<span style="letter-spacing: .05pt;"> </span>της<span style="letter-spacing: .05pt;"> </span>ορµής<span style="letter-spacing: .1pt;"> </span>του</span><span style="font-size: 12pt;"> </span><span style="font-size: 12pt;">συσσωµατώµατος<span style="letter-spacing: -1.95pt;"> </span>ϑεωρώντας<span style="letter-spacing: -1.9pt;"> </span>ως<span style="letter-spacing: -1.95pt;"> </span>ϑετική<span style="letter-spacing: -1.9pt;">
</span>την<span style="letter-spacing: -1.9pt;"> </span>ϕορά<span style="letter-spacing: -1.95pt;"> </span>της<span style="letter-spacing: -1.9pt;"> </span>ταχύτητας<span style="letter-spacing: -1.95pt;"> </span>µετά<span style="letter-spacing: -1.9pt;">
</span>την κρούση.<span style="letter-spacing: .65pt;"> </span></span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;">
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 118%;">Δ) Να γράψετε την εξίσωση της δύναµης
που δέχεται η ράβδος από το νήµα σε συνάρτηση με την απομάκρυνση του συσσωµατώµατος
από την ϑέση ισορροπίας του, και να εξετάσετε αν το νήµα θα κοπεί κατά την
διάρκεια της ταλάντωσης του συσσωµατώµατος, αν σας είναι γνωστό ότι το όριο ϑραύσης
του νήµατος είναι 82Ν.</span></span></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 118%;">Δίνεται: </span><span lang="EN-US" style="font-size: 12pt; line-height: 118%;">g=10m/s<sup>2</sup>.</span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuWBCbiHWh9USI1OENHT2NpHqeEbFa7zKAh2q6mdz8o43AvhSrylMbqIsXWAYzmimNd7-26S0SIDtss9yRLvPx0WUqV5vxOXQ-ckEKhRIAna8mXnaOXU0v-gieESBbMH4Dekc8lwPujjFJ/s1600/%25CF%2581%25CE%25AC%25CE%25B2%25CE%25B4%25CE%25BF%25CF%2582+%25CE%25BD%25CE%25AE%25CE%25BC%25CE%25B1+%25CE%25B5%25CE%25BB%25CE%25B1%25CF%2584%25CE%25AE%25CF%2581%25CE%25B9%25CE%25BF.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="506" data-original-width="568" height="356" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuWBCbiHWh9USI1OENHT2NpHqeEbFa7zKAh2q6mdz8o43AvhSrylMbqIsXWAYzmimNd7-26S0SIDtss9yRLvPx0WUqV5vxOXQ-ckEKhRIAna8mXnaOXU0v-gieESBbMH4Dekc8lwPujjFJ/s400/%25CF%2581%25CE%25AC%25CE%25B2%25CE%25B4%25CE%25BF%25CF%2582+%25CE%25BD%25CE%25AE%25CE%25BC%25CE%25B1+%25CE%25B5%25CE%25BB%25CE%25B1%25CF%2584%25CE%25AE%25CF%2581%25CE%25B9%25CE%25BF.jpg" width="400" /></a></span></div>
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<span lang="EN-US" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 118%;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> Για να δείτε τη λύση πατήστε <a href="https://drive.google.com/file/d/1IxjMkO0ZvPTeqIicTUqn6Tq1np0rCXua/view?usp=sharing" target="_blank">εδώ</a>.</span></span></div>
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Panagiotis Stamatiouhttp://www.blogger.com/profile/05743522665371107812noreply@blogger.com0tag:blogger.com,1999:blog-3953680779248074761.post-76626622807527103172020-05-22T11:09:00.000+03:002020-06-20T18:45:02.336+03:00Γ΄Λυκείου Στερεό ισορροπία - Ταλάντωση<div dir="ltr" style="text-align: left;" trbidi="on">
<br />
<div class="MsoNormal" style="tab-stops: 62.25pt; text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Η
λεπτή και ομογενής ράβδος ΑΒ μήκους<span style="mso-spacerun: yes;"> </span></span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">L</span><span style="font-size: 12pt; line-height: 115%;">=4</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;"> </span><span style="font-size: 12pt; line-height: 115%;">και μάζας </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span style="font-size: 12pt; line-height: 115%;">=7</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">Kg</span><span style="font-size: 12pt; line-height: 115%;"> συνδέεται μέσω άρθρωσης με
κατακόρυφο τοίχο. Η ράβδος ισορροπεί σε οριζόντια θέση με τη βοήθεια αβαρούς
και μη εκτατού νήματος, το ένα άκρο του οποίου δένεται στο σημείο Κ της ράβδου
με ΒΚ=1</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">
</span><span style="font-size: 12pt; line-height: 115%;">ενώ
το άλλο του άκρο σε σταθερό και ακλόνητο σημείο Ο. Το νήμα έχει κατακόρυφη
διεύθυνση και είναι τεντωμένο. Στο μέσο Μ της ράβδου βρίσκεται σημειακό σώμα Σ<sub>2</sub>
μάζας </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><sub><span style="font-size: 12pt; line-height: 115%;">2</span></sub><span style="font-size: 12pt; line-height: 115%;">=1</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">Kg</span><span style="font-size: 12pt; line-height: 115%;"> που είναι στερεωμένο στο ένα άκρο
κατακόρυφου ελατηρίου σταθεράς </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">k</span><span style="font-size: 12pt; line-height: 115%;">=100Ν/</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span style="font-size: 12pt; line-height: 115%;">. Στο άλλο άκρο του ελατηρίου είναι
στερεωμένο και ισορροπεί σώμα Σ<sub>1</sub> μάζας </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><sub><span style="font-size: 12pt; line-height: 115%;">1</span></sub><span style="font-size: 12pt; line-height: 115%;">=1</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">Kg</span><span style="font-size: 12pt; line-height: 115%;">.</span></span></div>
<div class="MsoNormal" style="tab-stops: 62.25pt; text-align: justify;">
<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="tab-stops: 62.25pt; text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Α)
Να υπολογίσετε το μέτρο της τάσης Τ του νήματος.</span></span></div>
<div class="MsoNormal" style="tab-stops: 62.25pt; text-align: justify;">
<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="tab-stops: 62.25pt; text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Β)
Να υπολογίσετε το μέτρο της δύναμης </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">F</span><sub><span style="font-size: 12pt; line-height: 115%;">αρθρ</span></sub><span style="font-size: 12pt; line-height: 115%;"> που δέχεται η ράβδος
από την άρθρωση.</span></span></div>
<div class="MsoNormal" style="tab-stops: 62.25pt; text-align: justify;">
<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="tab-stops: 62.25pt; text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Μετακινούμε
το σώμα Σ<sub>1</sub> σε τέτοιο σημείο ώστε το ελατήριο να είναι συσπειρωμένο
κατά </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">d</span><span style="font-size: 12pt; line-height: 115%;">=0,3</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span style="font-size: 12pt; line-height: 115%;"> και τη χρονική στιγμή </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">t</span><sub><span style="font-size: 12pt; line-height: 115%;">0</span></sub><span style="font-size: 12pt; line-height: 115%;">=0</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">s</span><span style="font-size: 12pt; line-height: 115%;"> το αφήνουμε ελεύθερο ναι κινηθεί.,
οπότε αυτό εκτελεί απλή αρμονική ταλάντωση με </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">D</span><span style="font-size: 12pt; line-height: 115%;"> = </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">k</span><span style="font-size: 12pt; line-height: 115%;">.</span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Γ)
Να γράψετε την εξίσωση της απομάκρυνσης του σώματος <span style="mso-spacerun: yes;"> </span>Σ<sub>1</sub> με το χρόνο.</span></span></div>
<div class="MsoNormal" style="tab-stops: 62.25pt; text-align: justify;">
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<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Δ)
Να γράψετε την εξίσωση του μέτρου της δύναμης που δέχεται η ράβδος στο σημείο Κ
από το σώμα Σ<sub>2</sub> σε συνάρτηση με το χρόνο, και να εξετάσετε αν υπάρχει
περίπτωση να κοπεί το νήμα κατά τη διάρκεια της ταλάντωσης του σώματος Σ<sub>1 </sub>αν
το όριο <span style="mso-spacerun: yes;"> </span>θραύσης του νήματος είναι Τ<sub>θρ</sub>=47Ν.</span></span></div>
<div class="MsoNormal" style="tab-stops: 62.25pt; text-align: justify;">
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<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Ε)
Να υπολογίσετε το μέτρο της δύναμης </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">F</span><span style="font-size: 12pt; line-height: 115%;">΄<sub>αρθρ</sub>
που δέχεται η ράβδος από την άρθρωση όταν η ταχύτητα του σώματος Σ<sub>1 </sub>μηδενίζεται
για πρώτη φορά.</span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUA5tWKFk9qhGmWBYKde7zcuzDQU5r_eKQchxfuXvuO2nRU28WkScoqfxMgaEASHpQZ-GwDsyBQBQpUm_bx_SC1tpQ61MuDzTS_yu4aayLQMus4smIzovaKR4Sn-QarfQAfTqQUhEpZbWE/s1600/%25CE%25A1%25CE%25AC%25CE%25B2%25CE%25B4%25CE%25BF%25CF%2582+%25CF%2583%25CE%25B5+%25CE%25B9%25CF%2583%25CE%25BF%25CF%2581%25CF%2581%25CE%25BF%25CF%2580%25CE%25AF%25CE%25B1+%25CE%25BC%25CE%25B5+%25CE%25B4%25CF%2585%25CE%25BF+%25CF%2583%25CF%258E%25CE%25BC%25CE%25B1%25CF%2584%25CE%25B1+%25CE%25B4%25CE%25B5%25CE%25BC%25CE%25AD%25CE%25BD%25CE%25B1+%25CF%2583%25CE%25B5+%25CE%25B5%25CE%25BB%25CE%25B1%25CF%2584%25CE%25AE%25CF%2581%25CE%25B9%25CE%25BF.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="398" data-original-width="408" height="390" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUA5tWKFk9qhGmWBYKde7zcuzDQU5r_eKQchxfuXvuO2nRU28WkScoqfxMgaEASHpQZ-GwDsyBQBQpUm_bx_SC1tpQ61MuDzTS_yu4aayLQMus4smIzovaKR4Sn-QarfQAfTqQUhEpZbWE/s400/%25CE%25A1%25CE%25AC%25CE%25B2%25CE%25B4%25CE%25BF%25CF%2582+%25CF%2583%25CE%25B5+%25CE%25B9%25CF%2583%25CE%25BF%25CF%2581%25CF%2581%25CE%25BF%25CF%2580%25CE%25AF%25CE%25B1+%25CE%25BC%25CE%25B5+%25CE%25B4%25CF%2585%25CE%25BF+%25CF%2583%25CF%258E%25CE%25BC%25CE%25B1%25CF%2584%25CE%25B1+%25CE%25B4%25CE%25B5%25CE%25BC%25CE%25AD%25CE%25BD%25CE%25B1+%25CF%2583%25CE%25B5+%25CE%25B5%25CE%25BB%25CE%25B1%25CF%2584%25CE%25AE%25CF%2581%25CE%25B9%25CE%25BF.jpg" width="400" /></a></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> Για να δείτε τη λύση πατήστε <a href="https://drive.google.com/file/d/1gAETbfMo_R0e8nOPCaeGTEsboqknbgOg/view?usp=sharing" target="_blank">εδώ</a>.</span></span></div>
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Panagiotis Stamatiouhttp://www.blogger.com/profile/05743522665371107812noreply@blogger.com0tag:blogger.com,1999:blog-3953680779248074761.post-15874940205778942562020-05-15T19:20:00.000+03:002020-06-20T18:49:37.018+03:00Γ΄λυκείου Επαγωγή<div dir="ltr" style="text-align: left;" trbidi="on">
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">Δύο παράλληλοι οριζόντιοι αγωγοί Γx και Δx'
με αμελητέα αντίσταση απέχουν μεταξύ τους </span><span lang="EN-US" style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">l</span><span style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">=0,5</span><span lang="EN-US" style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">m</span><span lang="EN-US" style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;"> </span><span style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">και τα άκρα τους Γ και Δ συνδέονται με αντιστάτη <span style="mso-spacerun: yes;"> </span>αντίστασης </span><span lang="EN-US" style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">R</span><span style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">=5Ω. Ένας άλλος αγωγός ΚΛ, με μήκος </span><span lang="EN-US" style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">l</span><span style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">=0,5</span><span lang="EN-US" style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">m</span><span lang="EN-US" style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;"> </span><span style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">και μάζα </span><span lang="EN-US" style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">m</span><span style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">=1</span><span lang="EN-US" style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">Kg</span><span style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">, χωρίς αντίσταση, μπορεί και ολισθαίνει χωρίς τριβές
μένοντας κάθετος και σε επαφή με τους παράλληλους αγωγούς Γx και Δx΄. Το σύστημα
των τεσσάρων αγωγών βρίσκεται μέσα σε ομογενές μαγνητικό πεδίο έντασης Β=2Τ
κάθετο στο επίπεδό τους και με φορά όπως φαίνεται στο σχήμα. Ο αγωγός ΚΛ είναι
αρχικά ακίνητος και τη χρονική στιγμή t=0</span><span lang="EN-US" style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">s</span><span lang="EN-US" style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;"> </span><span style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">του ασκείται δύναμη F, της ίδιας διεύθυνσης με αυτή των
παράλληλων αγωγών, η οποία τον εξαναγκάζει να κινηθεί με σταθερή επιτάχυνση α=2</span><span lang="EN-US" style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">m</span><span style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">/</span><span lang="EN-US" style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">s</span><sup><span style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">2</span></sup><span style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">. Ζητείτε: </span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">Α) </span><span lang="EN-US" style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">N</span><span style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">α υπολογίσετε τη συνάρτηση </span><span lang="EN-US" style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">I</span><span style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">=</span><span lang="EN-US" style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">f</span><span style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">(</span><span lang="EN-US" style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">t</span><span style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">) της έντασης του ηλεκτρικού ρεύματος με
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">Β) </span><span lang="EN-US" style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">N</span><span style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">α υπολογίσετε το επαγωγικό φορτίο που
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">Γ) </span><span lang="EN-US" style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">N</span><span style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">α προσδιοριστεί η συνάρτηση </span><span lang="EN-US" style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">F</span><span style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">=</span><span lang="EN-US" style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">f</span><span style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">(</span><span lang="EN-US" style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">t</span><span style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">) της εξωτερικής δύναμης σε<span style="mso-spacerun: yes;"> </span>συνάρτηση με το χρόνο.</span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">Αν το έργο που παράγει η<span style="mso-spacerun: yes;"> </span>δύναμη<span style="mso-spacerun: yes;">
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">Δ) να υπολογιστεί η θερμότητα που
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με τον οποίο αυξάνεται η κινητική ενέργεια του αγωγού τη χρονική στιγμή </span><span lang="EN-US" style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">t</span><span style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">=5</span><span lang="EN-US" style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">s.</span></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span lang="EN-US" style="font-size: 12pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;">Για να δείτε τη λύση πατήστε <a href="https://drive.google.com/file/d/1utyOzlw68kLjWJXJly0lPbosvAvF1kDp/view?usp=sharing" target="_blank">εδώ</a>. </span></span><span lang="EN-US" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; font-weight: normal; letter-spacing: 0pt; line-height: 150%;"> </span></div>
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Panagiotis Stamatiouhttp://www.blogger.com/profile/05743522665371107812noreply@blogger.com0tag:blogger.com,1999:blog-3953680779248074761.post-1973734683198506582020-05-08T11:56:00.001+03:002020-05-08T12:07:45.320+03:00Πρόγραμμα πανελλαδικών εξετάσεων ΓΕΛ και ΕΠΑΛ 2020.<div dir="ltr" style="text-align: left;" trbidi="on">
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ</span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">ΥΠΟΥΡΓΕΙΟ ΠΑΙΔΕΙΑΣ ΚΑΙ ΘΡΗΣΚΕΥΜΑΤΩΝ</span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Ταχ. Δ/νση: Α. Παπανδρέου 37</span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Τ.Κ. – Πόλη: 15180 - Μαρούσι</span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Ιστοσελίδα: <a href="http://www.minedu.gov.gr/"><span style="mso-fareast-font-family: "Arial Unicode MS";">www.minedu.gov.gr</span></a></span></span></div>
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30 Απριλίου 2020</span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 12pt; line-height: 120%;"><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-tab-count: 4;"> </span></span></b></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 12pt; line-height: 120%;"><span style="mso-tab-count: 4;"> </span><span style="text-shadow: auto;">Δελτίο
Τύπου</span></span></b></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 12pt; line-height: 150%;">ΘΕΜΑ:
Πρόγραμμα πανελλαδικών εξετάσεων ΓΕΛ και ΕΠΑΛ 2020.</span></b></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 150%;">Από το Υπουργείο
Παιδείας και Θρησκευμάτων ανακοινώνεται ότι με Υπουργικές Αποφάσεις καθορίστηκε
το πρόγραμμα των πανελλαδικών εξετάσεων των Γενικών Λυκείων (με το Νέο και με
το Παλαιό σύστημα) και των Επαγγελματικών Λυκείων 2020. </span></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGe3R8aYHby3W0WnO6_M26p4nLDt5tjhJuchx2QiP5oyAprTyM2pu_RPtdtj-xgDCtuN7pkuaoc5Z0VgWuWZLJaAJKgOWpOmLPBKyEqSBJS8VSHw9emM1QzjeM_ZLH38Ky6h1m6-Fwei2T/s1600/%25CE%25A0%25CE%25A1%25CE%259F%25CE%2593%25CE%25A1%25CE%2591%25CE%259C%25CE%259C%25CE%2591+%25CE%25A0%25CE%2591%25CE%259D%25CE%2595%25CE%259B%25CE%259B%25CE%2591%25CE%2594%25CE%2599%25CE%259A%25CE%25A9%25CE%259D+%25CE%2595%25CE%259E%25CE%2595%25CE%25A4%25CE%2591%25CE%25A3%25CE%2595%25CE%25A9%25CE%259D+2020+%25CE%2593%25CE%2595%25CE%259B+%25CE%259C%25CE%2595+%25CE%25A4%25CE%259F+%25CE%259D%25CE%2595%25CE%259F+%25CE%25A3%25CE%25A5%25CE%25A3%25CE%25A4%25CE%2597%25CE%259C%25CE%2591.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="514" data-original-width="710" height="288" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGe3R8aYHby3W0WnO6_M26p4nLDt5tjhJuchx2QiP5oyAprTyM2pu_RPtdtj-xgDCtuN7pkuaoc5Z0VgWuWZLJaAJKgOWpOmLPBKyEqSBJS8VSHw9emM1QzjeM_ZLH38Ky6h1m6-Fwei2T/s400/%25CE%25A0%25CE%25A1%25CE%259F%25CE%2593%25CE%25A1%25CE%2591%25CE%259C%25CE%259C%25CE%2591+%25CE%25A0%25CE%2591%25CE%259D%25CE%2595%25CE%259B%25CE%259B%25CE%2591%25CE%2594%25CE%2599%25CE%259A%25CE%25A9%25CE%259D+%25CE%2595%25CE%259E%25CE%2595%25CE%25A4%25CE%2591%25CE%25A3%25CE%2595%25CE%25A9%25CE%259D+2020+%25CE%2593%25CE%2595%25CE%259B+%25CE%259C%25CE%2595+%25CE%25A4%25CE%259F+%25CE%259D%25CE%2595%25CE%259F+%25CE%25A3%25CE%25A5%25CE%25A3%25CE%25A4%25CE%2597%25CE%259C%25CE%2591.jpg" width="400" /></a></div>
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<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Για να δείτε το πρόγραμμα των πανελλαδικών εξετάσεων ΓΕΛ και ΕΠΑΛ με το παλαιό και το νέο σύστημα μεταβείτε στη σελίδα Νέα για τους υποψήφιους.</span></span></div>
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Panagiotis Stamatiouhttp://www.blogger.com/profile/05743522665371107812noreply@blogger.com0tag:blogger.com,1999:blog-3953680779248074761.post-48232401846204614182020-05-06T18:10:00.001+03:002020-05-17T12:40:15.951+03:00Γ΄Λυκείου Κρούσεις - Ταλαντώσεις<div dir="ltr" style="text-align: left;" trbidi="on">
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<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Σώμα Σ<sub>1</sub>
μάζας </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><sub><span style="font-size: 12pt; line-height: 115%;">1</span></sub><span style="font-size: 12pt; line-height: 115%;">=2</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">Kg</span><span style="font-size: 12pt; line-height: 115%;">, είναι δεμένο στην άκρη νήματος
μήκους </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">l</span><span style="font-size: 12pt; line-height: 115%;">=1,6</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span style="font-size: 12pt; line-height: 115%;"> το άλλο άκρο του οποίου είναι
στερεωμένο σε ακλόνητο σημείο Ο. Εκτρέπουμε το σώμα Σ<sub>1 </sub>από τη θέση
ισορροπίας στη θέση που το νήμα να σχηματίζει γωνία φ=60<sup>0</sup> με την
κατακόρυφη και το αφήνουμε ελεύθερο να κινηθεί. Τη στιγμή που το σώμα Σ<sub>1</sub>
φθάνει στο κατώτατο σημείο, κόβεται το νήμα και το σώμα συγκρούεται κεντρικά
και ελαστικά με αρχικά ακίνητη σφαίρα Σ<sub>2</sub>, μάζας </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><sub><span style="font-size: 12pt; line-height: 115%;">2</span></sub><span style="font-size: 12pt; line-height: 115%;">=6</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">Kg</span><span style="font-size: 12pt; line-height: 115%;"> που βρίσκεται σε λείο οριζόντιο
επίπεδο. Στο ίδιο επίπεδο βρίσκεται οριζόντιο ιδανικό ελατήριο σταθεράς </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">k</span><span style="font-size: 12pt; line-height: 115%;">=100Ν/</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;"> </span><span style="font-size: 12pt; line-height: 115%;">στο
ελεύθερο άκρο του οποίου είναι δεμένη και ισορροπεί σφαίρα Σ<sub>3</sub> μάζας </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><sub><span style="font-size: 12pt; line-height: 115%;">3</span></sub><span style="font-size: 12pt; line-height: 115%;">=2</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">Kg</span><span style="font-size: 12pt; line-height: 115%;"> που απέχει απόσταση </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">d</span><span style="font-size: 12pt; line-height: 115%;">=π/2</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span style="font-size: 12pt; line-height: 115%;"> από την σφαίρα Σ<sub>2</sub>. Μετά
την κρούση μεταξύ των σφαιρών Σ<sub>1 </sub>και Σ<sub>2</sub>, η σφαίρα Σ<sub>1</sub>
συγκρούεται κεντρικά και πλαστικά με την σφαίρα Σ<sub>3</sub>. </span></span></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Για την ταλάντωση του
συσσωματώματος, χρονική στιγμή </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">t</span><sub><span style="font-size: 12pt; line-height: 115%;">0</span></sub><span style="font-size: 12pt; line-height: 115%;">=0</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">s</span><span style="font-size: 12pt; line-height: 115%;">, θεωρείται η στιγμή αμέσως μετά
την κρούση και θετική φορά η προς τα δεξιά. Να υπολογίσετε:</span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Α) τις ταχύτητες υ<sub>1</sub>΄και
υ<sub>2</sub>΄των σφαιρών Σ<sub>1</sub> και Σ<sub>2</sub> αμέσως μετά την
μεταξύ τους κρούση και το ποσοστό επί τοις εκατό % της αρχικής κινητικής
ενέργειας που διατήρησε η σφαίρα Σ<sub>1</sub> κατά τη διάρκεια της κρούσης με
τη σφαίρα Σ<sub>2</sub></span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Β) την ταχύτητα υκ, του
συσσωματώματος των σφαιρών Σ<sub>1</sub> και Σ<sub>3</sub>, το πλάτος της
ταλάντωσης που θα εκτελέσει το συσσωμάτωμα, καθώς<sub> </sub>και την εξίσωση της
απομάκρυνσης της ταλάντωσης σε συνάρτηση με το χρόνο </span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Γ) τη δύναμη του
ελατηρίου και τη δυναμική ενέργεια της ταλάντωσης τη χρονική στιγμή </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">t</span><span style="font-size: 12pt; line-height: 115%;">=π/15 </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">s</span></span></div>
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<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Δ) την απόσταση </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">x</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;"> </span><span style="font-size: 12pt; line-height: 115%;">μεταξύ
της σφαίρας Σ<sub>2</sub> και του συσσωματώματος των σφαιρών Σ<sub>1</sub> και
Σ<sub>3</sub>, όταν μηδενίζεται για δεύτερη φορά η κινητική ενέργεια του
συσσωματώματος.</span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="height: 243px; left: 0px; margin-left: 31px; margin-top: 84px; mso-ignore: vglayout; position: absolute; width: 449px; z-index: 2;"> </span><span style="height: 243px; left: 0px; margin-left: 31px; margin-top: 84px; mso-ignore: vglayout; position: absolute; width: 449px; z-index: 2;"> </span><span style="height: 243px; left: 0px; margin-left: 31px; margin-top: 84px; mso-ignore: vglayout; position: absolute; width: 449px; z-index: 2;"> </span><span style="height: 243px; left: 0px; margin-left: 31px; margin-top: 84px; mso-ignore: vglayout; position: absolute; width: 449px; z-index: 2;"> </span><span style="height: 243px; left: 0px; margin-left: 31px; margin-top: 84px; mso-ignore: vglayout; position: absolute; width: 449px; z-index: 2;"> </span><span style="height: 243px; left: 0px; margin-left: 31px; margin-top: 84px; mso-ignore: vglayout; position: absolute; width: 449px; z-index: 2;"> </span><span style="height: 243px; left: 0px; margin-left: 31px; margin-top: 84px; mso-ignore: vglayout; position: absolute; width: 449px; z-index: 2;"> </span><span style="height: 243px; left: 0px; margin-left: 31px; margin-top: 84px; mso-ignore: vglayout; position: absolute; width: 449px; z-index: 2;"> </span><span style="height: 243px; left: 0px; margin-left: 31px; margin-top: 84px; mso-ignore: vglayout; position: absolute; width: 449px; z-index: 2;"> </span><span style="height: 243px; left: 0px; margin-left: 31px; margin-top: 84px; mso-ignore: vglayout; position: absolute; width: 449px; z-index: 2;"> </span><span style="height: 243px; left: 0px; margin-left: 31px; margin-top: 84px; mso-ignore: vglayout; position: absolute; width: 449px; z-index: 2;"> </span><span style="font-size: 12pt; line-height: 115%;">Δίνεται:
η επιτάχυνση της βαρύτητας </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">g</span><span style="font-size: 12pt; line-height: 115%;">=10</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span style="font-size: 12pt; line-height: 115%;">/</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">s</span><sup><span style="font-size: 12pt; line-height: 115%;">2</span></sup><span style="font-size: 12pt; line-height: 115%;">.</span></span><br />
<br /></div>
<br />
<br />
<div class="MsoNormal" style="text-align: justify;">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIsnsZUnqJKmdIPC5VhCwW2itDIppiwX-41ODkufYvc1NY_CUgPKJS4FxEGnIM6fWNbB_NoY0BPW-W7NmMmJ2PK67DA6v3amqXMA1jep2_e6FXnhIZRnRNYnv6xwrRG1oX5f0DFxg1Iq5G/s1600/%25CE%25A3%25CF%258E%25CE%25BC%25CE%25B1+%25CE%25A31%252C+%25CE%25A32+%25CE%25BA%25CE%25B1%25CE%25B9+%25CE%25A33+%25CF%2583%25CE%25B5+%25CE%25B5%25CE%25BB%25CE%25B1%25CF%2584%25CE%25AE%25CF%2581%25CE%25B9%25CE%25BF.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="294" data-original-width="482" height="243" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIsnsZUnqJKmdIPC5VhCwW2itDIppiwX-41ODkufYvc1NY_CUgPKJS4FxEGnIM6fWNbB_NoY0BPW-W7NmMmJ2PK67DA6v3amqXMA1jep2_e6FXnhIZRnRNYnv6xwrRG1oX5f0DFxg1Iq5G/s400/%25CE%25A3%25CF%258E%25CE%25BC%25CE%25B1+%25CE%25A31%252C+%25CE%25A32+%25CE%25BA%25CE%25B1%25CE%25B9+%25CE%25A33+%25CF%2583%25CE%25B5+%25CE%25B5%25CE%25BB%25CE%25B1%25CF%2584%25CE%25AE%25CF%2581%25CE%25B9%25CE%25BF.jpg" width="400" /></a></div>
<br />
<br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Για να δείτε τη λύση πατήστε <a href="https://drive.google.com/file/d/1D4g-sRJHv_WFbU9qUAJw-gi01PdNZHvp/view?usp=sharing" target="_blank">εδώ</a>.</span></span></div>
</div>
Panagiotis Stamatiouhttp://www.blogger.com/profile/05743522665371107812noreply@blogger.com0tag:blogger.com,1999:blog-3953680779248074761.post-66613520728899403742020-05-01T12:30:00.001+03:002020-06-02T10:52:11.297+03:00Γ΄Λυκείου Διαγωνισματα <div dir="ltr" style="text-align: left;" trbidi="on">
<h3 class="post-title entry-title" itemprop="name" style="text-align: center;">
<span style="color: red;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><u><span style="font-size: 12pt; line-height: 115%;">ΔΙΑΓΩΝΙΣΜΑΤΑ</span></u></span></span></span></span></h3>
<h3 class="post-title entry-title" itemprop="name" style="text-align: center;">
<span style="color: red;"><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: small;"><span style="color: blue;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> </span></span></span></span></h3>
<h3 class="post-title entry-title" itemprop="name">
<span style="font-family: "arial" , "helvetica" , sans-serif; font-size: small;"><span style="color: blue;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Διαγωνίσματα Φυσικής Προσανατολισμού για το σχολ.έτος 2019-2020 απο ΨΕΒ</span></span></span></h3>
<h3 class="post-title entry-title" itemprop="name">
<span style="font-family: "arial" , "helvetica" , sans-serif; font-size: small;"><span style="color: blue;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> </span></span></span></h3>
<h3 class="post-title entry-title" itemprop="name">
<span style="color: red;"> <span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><u><span style="font-size: 12pt; line-height: 115%;">1ο ΔΙΑΓΩΝΙΣΜΑ (ΗΛΕΚΤΡΟΜΑΓΝΗΤΙΣΜΟΣ)
– ΘΕΜΑΤΑ - ΛΥΣΕΙΣ</span></u></span></span></span></span></h3>
<div style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span>
<span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Για να δείτε τα θέματα πατήστε <a href="https://drive.google.com/file/d/1jY5X6Lax0PUvEe18Bw-4Rs3C6ADz9idh/view?usp=sharing" target="_blank">εδώ</a>.</span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span>
<span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span>
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Για να δείτε τις λύσεις πατήστε <a href="https://drive.google.com/file/d/1_yGEtrt3Rk7_9W3wickWPMeA-RERZgvG/view?usp=sharing" target="_blank">εδώ</a>.</span></span><br />
<br />
<br />
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<![endif]--><u><span style="color: #00b050; font-size: 12pt; line-height: 115%;">2ο ΔΙΑΓΩΝΙΣΜΑ (ΚΡΟΥΣΕΙΣ)
– ΘΕΜΑΤΑ - ΛΥΣΕΙΣ</span></u><span style="font-size: 12pt; line-height: 115%;"><br />
<br />
<br />
Για να δείτε τα θέματα πατήστε <a href="https://drive.google.com/file/d/1Y-6axWoKCCou_dZbvSY5-yVQZGRKXutm/view?usp=sharing" target="_blank">εδώ</a>.<br />
<br />
<br />
Για να δείτε τις λύσεις πατήστε <a href="https://drive.google.com/file/d/1UTLbn-ifJAMYo5P8_VYfpVg3jql3mdcx/view?usp=sharing" target="_blank">εδώ</a>.</span> </span></span></span><br />
<br />
<br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: lime;"><u><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;">3ο ΔΙΑΓΩΝΙΣΜΑ (ΤΑΛΑΝΤΩΣΕΙΣ) – ΘΕΜΑΤΑ - ΛΥΣΕΙΣ</span></span></span></u></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><br />
<br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Για να δείτε τα θέματα πατήστε</span> <a href="https://drive.google.com/file/d/11wG61gD9JDdjW3On7HkhTfJdksrPw_j3/view?usp=sharing" target="_blank">εδώ</a>.</span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> </span></span></span><br />
<br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Για να δείτε τις λύσεις πατήστε</span> <a href="https://drive.google.com/file/d/1Fdo2milob2dPoXCG1EeIg6xhJ2RKYFpU/view?usp=sharing" target="_blank">εδώ</a>.</span></span></span></span><br />
<br />
<br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><br />
<span style="color: blue;"><u><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;">4ο ΔΙΑΓΩΝΙΣΜΑ (ΡΕΥΣΤΑ) – ΘΕΜΑΤΑ - ΛΥΣΕΙΣ</span></span></span></u></span></span><br />
<br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Για να δείτε τα θέματα πατήστε</span> <a href="https://drive.google.com/file/d/19DzXyEbh1jRMb_R4hKGA-mk-ywW6nDxE/view?usp=sharing" target="_blank">εδώ</a>.</span></span></span></span><br />
<br />
<br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Για να δείτε τις λύσεις πατήστε</span> <a href="https://drive.google.com/file/d/1PSjwFCOPLDtEg-ercWkifvLmnJqgeIRX/view?usp=sharing" target="_blank">εδώ</a>.</span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> </span></span></span><br />
<br />
<span style="color: #0b5394;"><u><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;">5ο ΔΙΑΓΩΝΙΣΜΑ (ΣΤΕΡΕΟ) - ΘΕΜΑΤΑ - ΛΥΣΕΙΣ</span></span></span></u></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><br />
<br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Για να δείτε τα θέματα πατήστε</span> <a href="https://drive.google.com/file/d/1_odCTD7hmjcnRPgZD31cPzxPW-NxJ-lZ/view?usp=sharing" target="_blank">εδώ</a>.</span></span></span></span></span></span></span></span><br />
<br />
<br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Για να δείτε τις λύσεις πατήστε</span> <a href="https://drive.google.com/file/d/1VMOUcwWSFUJhIksGsmgfMQ2ThLqZ9ebO/view?usp=sharing" target="_blank">εδώ</a>.</span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span></span></span></span></span></span></span></span></div>
Panagiotis Stamatiouhttp://www.blogger.com/profile/05743522665371107812noreply@blogger.com0tag:blogger.com,1999:blog-3953680779248074761.post-20019468557435389862020-04-30T13:21:00.000+03:002020-06-20T18:52:16.309+03:00Γ΄λυκείου Επαγωγή<div dir="ltr" style="text-align: left;" trbidi="on">
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<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Τα άκρα </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">A</span><span style="font-size: 12pt; line-height: 115%;"> και Γ δυο παραλλήλων οριζόντιων χάλκινων
αγωγών Α</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">x</span><span style="font-size: 12pt; line-height: 115%;">
και Γ</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">x</span><span style="font-size: 12pt; line-height: 115%;">΄
μεγάλου μήκους, οι οποίοι δεν έχουν ωμική αντίσταση, συνδέονται μέσω αντιστάτη
αντίστασης </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">r</span><span style="font-size: 12pt; line-height: 115%;">=1Ω.
Πάνω στο επίπεδο των δυο αγωγών είναι τοποθετημένος, κάθετα προς τη διεύθυνση
τους, άλλος ευθύγραμμος αγωγός ΚΛ μήκους </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">L</span><span style="font-size: 12pt; line-height: 115%;">=1</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span style="font-size: 12pt; line-height: 115%;"> ο οποίος μπορεί να ολισθαίνει
στους αγωγούς Α</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">x</span><span style="font-size: 12pt; line-height: 115%;">
και Γ</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">x</span><span style="font-size: 12pt; line-height: 115%;">΄
με σταθερή ταχύτητα υ=8</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span style="font-size: 12pt; line-height: 115%;">/</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">s</span><span style="font-size: 12pt; line-height: 115%;"> με την επίδραση σταθερής
εξωτερικής δύναμης </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">F</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">
</span><span style="font-size: 12pt; line-height: 115%;">μέτρου
</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">F</span><span style="font-size: 12pt; line-height: 115%;">=6Ν
ομόρροπης της ταχύτητας και κάθετης στον άξονα του αγωγού. Η αντίστασή του αγωγού
ΚΛ είναι </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">R</span><span style="font-size: 12pt; line-height: 115%;">=7Ω.
Ολόκληρη η διάταξη των τριών αγωγών βρίσκεται μέσα σε ομογενές μαγνητικό πεδίο
του οποίου η ένταση Β=2Τ είναι κάθετη στο επίπεδο των δυο αγωγών. </span></span></div>
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<br /></div>
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</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Α) Να υπολογίσετε την ηλεκτρεγερτική
δύναμη ΗΕΔ από επαγωγή που αναπτύσσεται στον αγωγό ΚΛ και την διαφορά δυναμικού
</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">V</span><sub><span style="font-size: 12pt; line-height: 115%;">ΚΛ</span></sub></span></div>
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<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Β) Να εξετάσετε αν
εκτός από τη δύναμη<span style="mso-spacerun: yes;"> </span></span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">F</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;"> </span><span style="font-size: 12pt; line-height: 115%;">ενεργούν
και άλλες δυνάμεις στον αγωγό ΚΛ κατά τη διεύθυνση της κίνησης, και αν ναι, να
βρείτε το μέτρο της καθεμίας </span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Γ) Να υπολογίσετε το
ρυθμό με τον οποίο μεταφέρεται ενέργεια στον αγωγό ΚΛ μέσω του έργου της δύναμης
</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">F</span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span lang="EN-US" style="font-size: 12pt; line-height: 115%;"> </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">
</span><span style="font-size: 12pt; line-height: 115%;"></span></span></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Δ) Να υπολογίσετε το
ρυθμό με τον οποίο μετατρέπεται ενέργεια σε θερμική (λόγω φαινομένου </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">Joule</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;"> </span><span style="font-size: 12pt; line-height: 115%;">και
λόγω της τριβής αν υπάρχει)</span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHb7YhUMc7PvCBE-jk6sUFrmfe9SeOmQRsQcvPQc8aap2EcYXSJUfuYDSLJjWNIQDoS_3f6UINWLN-pkEQe1sFlogOM18YtVwYS0faWcXMvHUFclBjOOrSR0OsYlewmS1UZZlKrQKr7vqG/s1600/%25CE%2595%25CE%25A0%25CE%2591%25CE%2593%25CE%25A9%25CE%2593%25CE%2597.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="234" data-original-width="534" height="175" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHb7YhUMc7PvCBE-jk6sUFrmfe9SeOmQRsQcvPQc8aap2EcYXSJUfuYDSLJjWNIQDoS_3f6UINWLN-pkEQe1sFlogOM18YtVwYS0faWcXMvHUFclBjOOrSR0OsYlewmS1UZZlKrQKr7vqG/s400/%25CE%2595%25CE%25A0%25CE%2591%25CE%2593%25CE%25A9%25CE%2593%25CE%2597.jpg" width="400" /></a></span></div>
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<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> Για να δείτε τη λύση πατήστε <a href="https://drive.google.com/file/d/1wmlgq-OsZTv0xNv6puj_SU0hEVSSGZ4k/view?usp=sharing" target="_blank">εδώ</a>.</span></span></div>
</div>
Panagiotis Stamatiouhttp://www.blogger.com/profile/05743522665371107812noreply@blogger.com0tag:blogger.com,1999:blog-3953680779248074761.post-82841951703111925412020-04-24T19:16:00.000+03:002020-04-28T13:03:45.199+03:00Γ΄Λυκείου Μηχανική ρευστών - Φθίνουσα Ταλάντωση<div dir="ltr" style="text-align: left;" trbidi="on">
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Ένα ανοικτό κυλινδρικό δοχείο
βρίσκεται σε λείο οριζόντιο επίπεδο και περιέχει νερό πυκνότητας ρ=10<sup>3</sup></span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">Kg</span><span style="font-size: 12pt; line-height: 115%;">/</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><sup><span style="font-size: 12pt; line-height: 115%;">3</span></sup><span style="font-size: 12pt; line-height: 115%;">
μέχρι ύψος </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">H</span><span style="font-size: 12pt; line-height: 115%;">.
Το δοχείο είναι ενωμένο στο σημείο του Β με τη μια άκρη οριζοντίου και μη
ελαστικού νήματος η άλλη άκρη του οποίου είναι στερεωμένη σε κατακόρυφο τοίχο
στο σημείο Γ. Παράλληλα με το οριζόντιο δάπεδο υπάρχει λείο οριζόντιο επίπεδο
πάνω στο οποίο βρίσκεται ιδανικό ελατήριο σταθεράς </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">k</span><span style="font-size: 12pt; line-height: 115%;">=625π<sup>2</sup>Ν/</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;"> </span><span style="font-size: 12pt; line-height: 115%;">το
ένα άκρο του οποίου είναι στερεωμένο σε σταθερό ακλόνητο σημείο </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">K</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;"> </span><span style="font-size: 12pt; line-height: 115%;">ενώ
στο άλλο άκρο του είναι δεμένο σώμα Σ<sub>1</sub> μάζας </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span style="font-size: 12pt; line-height: 115%;">. Σε σημείο Δ του πλευρικού
τοιχώματος του δοχείου που απέχει απόσταση </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">h</span><span style="font-size: 12pt; line-height: 115%;">=0,2</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span style="font-size: 12pt; line-height: 115%;"> από τον πυθμένα του δοχείου,
υπάρχει μικρή οπή εμβαδού Α=10<sup>-3</sup></span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><sup><span style="font-size: 12pt; line-height: 115%;">2</span></sup><span style="font-size: 12pt; line-height: 115%;">
που αρχικά είναι κλειστή. Εκτρέπουμε το σώμα Σ<sub>1</sub> κατά </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">d</span><span style="font-size: 12pt; line-height: 115%;">=0,8</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;"> </span><span style="font-size: 12pt; line-height: 115%;">προς
τη θετική κατεύθυνση από τη θέση φυσικού μήκους του ελατηρίου. Ανοίγουμε την
οπή στο σημείο Δ τη χρονική στιγμή </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">t</span><sub><span style="font-size: 12pt; line-height: 115%;">0</span></sub><span style="font-size: 12pt; line-height: 115%;">=0</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">s</span><span style="font-size: 12pt; line-height: 115%;">, οπότε αρχίζει να εκρέει το νερό
με ταχύτητα υ=5</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span style="font-size: 12pt; line-height: 115%;">/</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">s</span><span style="font-size: 12pt; line-height: 115%;"> και, ταυτόχρονα αφήνουμε το σώμα Σ<sub>1</sub>
να κινηθεί. Το σώμα Σ<sub>1</sub> κατά την κίνηση του δέχεται δύναμη </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">F</span><span style="font-size: 12pt; line-height: 115%;">= - </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">b</span><span style="font-size: 12pt; line-height: 115%;">υ. Τη χρονική στιγμή κατά την οποία
η πρώτη στοιχειώδης ποσότητα Δ</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">
</span><span style="font-size: 12pt; line-height: 115%;">του
νερού φθάνει στο οριζόντιο δάπεδο, το σώμα Σ<sub>1</sub> έχει εκτελέσει τρεις πλήρεις
ταλαντώσεις και βρίσκεται σε απόσταση </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">l</span><span style="font-size: 12pt; line-height: 115%;">=0,7</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span style="font-size: 12pt; line-height: 115%;"> από την αρχική θέση εκτροπής του
σώματος. Με κατάλληλο μηχανισμό, η στάθμη του νερού στο δοχείο διατηρείται
σταθερή. Ζητείτε να υπολογίσετε:</span></span></div>
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<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Α) τη παροχή της οπής και </span></span><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">τη μάζα<span style="mso-spacerun: yes;"> </span>του σώματος Σ<sub>1</sub></span></span></span></span></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
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</div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Β) τη σταθερά Λ</span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Γ) τη συνολική πίεση
στον πυθμένα του δοχείου</span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Δ) την τάση Τ του
νήματος ώστε το δοχείο να ισορροπεί.</span></span></div>
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<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Να θεωρήσετε το εμβαδόν
τομής της οπής στο σημείο Δ, αμελητέο σε σχέση με το εμβαδόν διατομής του
δοχείου, η επιτάχυνση της βαρύτητας είναι </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">g</span><span style="font-size: 12pt; line-height: 115%;">=10</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span style="font-size: 12pt; line-height: 115%;">/</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">s</span><sup><span style="font-size: 12pt; line-height: 115%;">2</span></sup><span style="font-size: 12pt; line-height: 115%;">,
η ατμοσφαιρική πίεση είναι </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">p<sub>atm</sub></span><span style="font-size: 12pt; line-height: 115%;">=10<sup>5</sup>Ν/</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><sup><span style="font-size: 12pt; line-height: 115%;">2</span></sup><span style="font-size: 12pt; line-height: 115%;">
και ότι το νήμα είναι συνεχώς τεντωμένο.</span></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfBwom-Lq2MfpIbdxD6SdYWtfbedNAS0pGALgCq5qxgg2qdv4qjVI6Ri6eW5LI94YZRr1F74MTsdVlV-dUY1Wm8IcaeDHcK71kL37B1T8V_rhecvsnLAM8YCR_S7oFu_HhKBKYmaP9lRPV/s1600/%25CE%2594%25CE%25BF%25CF%2587%25CE%25B5%25CE%25AF%25CE%25BF+-+%25CE%25BD%25CE%25AE%25CE%25BC%25CE%25B1+-+%25CE%25B5%25CE%25BB%25CE%25B1%25CF%2584%25CE%25AE%25CF%2581%25CE%25B9%25CE%25BF.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="290" data-original-width="568" height="202" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfBwom-Lq2MfpIbdxD6SdYWtfbedNAS0pGALgCq5qxgg2qdv4qjVI6Ri6eW5LI94YZRr1F74MTsdVlV-dUY1Wm8IcaeDHcK71kL37B1T8V_rhecvsnLAM8YCR_S7oFu_HhKBKYmaP9lRPV/s400/%25CE%2594%25CE%25BF%25CF%2587%25CE%25B5%25CE%25AF%25CE%25BF+-+%25CE%25BD%25CE%25AE%25CE%25BC%25CE%25B1+-+%25CE%25B5%25CE%25BB%25CE%25B1%25CF%2584%25CE%25AE%25CF%2581%25CE%25B9%25CE%25BF.jpg" width="400" /></a></div>
<br />
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<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Για να δείτε τη λύση πατήστε <a href="https://drive.google.com/file/d/1CaOb7UuLdMpBxjgqlhhhIzq2UkvIyKI2/view?usp=sharing" target="_blank">εδώ</a>.</span><br /> </span></div>
</div>
Panagiotis Stamatiouhttp://www.blogger.com/profile/05743522665371107812noreply@blogger.com0tag:blogger.com,1999:blog-3953680779248074761.post-86896370077943733822020-04-21T12:59:00.001+03:002020-04-27T10:49:51.262+03:00Β΄Λυκείου Ορμή-Κρούση<div dir="ltr" style="text-align: left;" trbidi="on">
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<br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Βλήμα μάζας </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span style="font-size: 12pt; line-height: 115%;">=0,1</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">Kg</span><span style="font-size: 12pt; line-height: 115%;"> κινείται οριζόντια με ταχύτητα υ<sub>0</sub>.
Δύο ξύλινα σώματα με μάζες </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><sub><span style="font-size: 12pt; line-height: 115%;">1</span></sub><span style="font-size: 12pt; line-height: 115%;">=1</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">Kg</span><span style="font-size: 12pt; line-height: 115%;"> και </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><sub><span style="font-size: 12pt; line-height: 115%;">2</span></sub><span style="font-size: 12pt; line-height: 115%;">=0,9</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">Kg</span><span style="font-size: 12pt; line-height: 115%;"> είναι κρεμασμένα από αβαρή και μη
εκτατά νήματα ίσου μήκους </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">L</span><span style="font-size: 12pt; line-height: 115%;">=3,6</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span style="font-size: 12pt; line-height: 115%;"> το καθένα, όπως φαίνεται στο
σχήμα. Το βλήμα διαπερνά το σώμα μάζας </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><sub><span style="font-size: 12pt; line-height: 115%;">1 </span></sub><span style="font-size: 12pt; line-height: 115%;">και
στη συνέχεια σφηνώνεται στο σώμα μάζας </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><sub><span style="font-size: 12pt; line-height: 115%;">2</span></sub><span style="font-size: 12pt; line-height: 115%;">.
Το μέγιστο ύψος στο οποίο φθάνει το σώμα μάζας </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><sub><span style="font-size: 12pt; line-height: 115%;">1 </span></sub><span style="font-size: 12pt; line-height: 115%;">αμέσως
μετά την κρούση είναι </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">h</span><sub><span style="font-size: 12pt; line-height: 115%;">1</span></sub><span style="font-size: 12pt; line-height: 115%;">=3,2</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span style="font-size: 12pt; line-height: 115%;"> ενώ το συσσωμάτωμα, μάζας<span style="mso-spacerun: yes;"> </span>(</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><sub><span style="font-size: 12pt; line-height: 115%;">2</span></sub><span style="font-size: 12pt; line-height: 115%;">+</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span style="font-size: 12pt; line-height: 115%;">)<sub> </sub>φθάνει σε τέτοια θέση ώστε
το νήμα να σχηματίζει με την κατακόρυφο γωνία φ=60<sup>0</sup><sub>. <span style="mso-spacerun: yes;"> </span></sub>Αν οι κρούσεις είναι κεντρικές και η
διάρκεια τους αμελητέα, ζητείτε να υπολογίσετε:</span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Α) την ταχύτητα υ<sub>1</sub>
του σώματος μάζας </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><sub><span style="font-size: 12pt; line-height: 115%;">1
</span></sub><span style="font-size: 12pt; line-height: 115%;">αμέσως
μετά την πρώτη κρούση, καθώς<span style="mso-spacerun: yes;"> </span>και την
ταχύτητα του συσσωματώματος </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">V</span><span style="font-size: 12pt; line-height: 115%;">κ
μετά την ενσφήνωση του βλήματος στο σώμα μάζας<span style="mso-spacerun: yes;">
</span></span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><sub><span style="font-size: 12pt; line-height: 115%;">2</span></sub></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Β) την ταχύτητα του βλήματος
υ μετά την πρώτη κρούση καθώς και την αρχική ταχύτητα υ<sub>0</sub> του
βλήματος</span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Γ) την ελάττωση της
κινητικής ενέργειας του συστήματος σε κάθε κρούση</span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Δ) τη μέση οριζόντια
δύναμη που δέχτηκε το βλήμα από το σώμα μάζας </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><sub><span style="font-size: 12pt; line-height: 115%;">1</span></sub><span style="font-size: 12pt; line-height: 115%;">,
αν το χρονικό διάστημα που απαιτείται για να το διαπεράσει είναι Δ</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">t</span><span style="font-size: 12pt; line-height: 115%;">=10<sup>-4</sup> </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">s</span><span style="font-size: 12pt; line-height: 115%;">.</span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Δίνεται ότι η
επιτάχυνση της βαρύτητας είναι: </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">g</span><span style="font-size: 12pt; line-height: 115%;">=10</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span style="font-size: 12pt; line-height: 115%;">/</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">s</span><sup><span style="font-size: 12pt; line-height: 115%;">2</span></sup><span style="font-size: 12pt; line-height: 115%;">.</span></span></div>
<div class="MsoNormal" style="text-align: justify;">
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Για να δείτε τη λύση πατήστε <a href="https://drive.google.com/file/d/11fCPzajKaiqkH9BWtfShW8xPgTlh21ci/view?usp=sharing" target="_blank">εδώ</a>. </span></span></div>
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Panagiotis Stamatiouhttp://www.blogger.com/profile/05743522665371107812noreply@blogger.com0tag:blogger.com,1999:blog-3953680779248074761.post-44992016931875439012020-04-18T16:45:00.005+03:002020-04-18T16:50:47.116+03:00ΕΥΧΕΣ ΓΙΑ ΤΟ ΠΑΣΧΑ<div dir="ltr" style="text-align: left;" trbidi="on">
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><u><b style="mso-bidi-font-weight: normal;"><span style="font-size: 12pt; line-height: 115%;">ΚΑΛΟ ΠΑΣΧΑ….</span></b></u></span></span></div>
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Panagiotis Stamatiouhttp://www.blogger.com/profile/05743522665371107812noreply@blogger.com0tag:blogger.com,1999:blog-3953680779248074761.post-58542776592501732422020-04-13T18:38:00.002+03:002020-04-20T13:08:07.900+03:00Γ΄Λυκείου Στερεό σώμα Ισορροπία<div dir="ltr" style="text-align: left;" trbidi="on">
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<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 12pt; line-height: 115%;">ΣΤΕΡΕΟ
ΣΩΜΑ - ΙΣΟΡΡΟΠΙΑ</span></b></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Ομογενής και ισοπαχής
ράβδος ΑΒ μάζας </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span style="font-size: 12pt; line-height: 115%;">=6Κ</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">g</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;"> </span><span style="font-size: 12pt; line-height: 115%;">και
μήκους </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">L</span><span style="font-size: 12pt; line-height: 115%;">=4</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span style="font-size: 12pt; line-height: 115%;"> ισορροπεί σε οριζόντια<span style="mso-spacerun: yes;"> </span>θέση με τη βοήθεια υποστηριγμάτων που
βρίσκονται στα σημεία Γ και Δ<span style="mso-spacerun: yes;"> </span>και οι
αποστάσεις<span style="mso-spacerun: yes;"> </span>ΑΓ και ΔΒ είναι τέτοιες ώστε
ΑΓ=1</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span style="font-size: 12pt; line-height: 115%;">
και ΔΒ=1</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span style="font-size: 12pt; line-height: 115%;">.
Σε σημείο Κ που απέχει από το άκρο Α της ράβδου απόσταση ΑΚ=0,75</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span style="font-size: 12pt; line-height: 115%;"> βρίσκεται σώμα Σ<sub>2</sub> μάζας
</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><sub><span style="font-size: 12pt; line-height: 115%;">2</span></sub><span style="font-size: 12pt; line-height: 115%;">=8</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">Kg</span><span style="font-size: 12pt; line-height: 115%;">. Ένα άλλο σώμα Σ<sub>1</sub> μάζας
</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><sub><span style="font-size: 12pt; line-height: 115%;">1</span></sub><span style="font-size: 12pt; line-height: 115%;">=4,8</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">Kg</span><span style="font-size: 12pt; line-height: 115%;"> είναι δεμένο στο ελεύθερο άκρο
νήματος μήκους </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">l</span><span style="font-size: 12pt; line-height: 115%;">=0,2</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;"> </span><span style="font-size: 12pt; line-height: 115%;">το
άλλο άκρο του οποίου είναι ακλόνητα στερεωμένο σε σημείο Ο, και συγκρατείται
ακίνητο σε οριζόντια θέση όπως φαίνεται στο σχήμα. Να υπολογίσετε:</span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Α) Τα μέτρα των
δυνάμεων </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">F</span><sub><span style="font-size: 12pt; line-height: 115%;">Γ</span></sub><span style="font-size: 12pt; line-height: 115%;">
και </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">F</span><sub><span style="font-size: 12pt; line-height: 115%;">Δ
</span></sub><span style="font-size: 12pt; line-height: 115%;">που
δέχεται η ράβδος από τα στηρίγματα Γ και Δ αντίστοιχα. (Η ράβδος ισορροπεί).</span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Κάποια στιγμή αφήνουμε
το σώμα Σ<sub>1</sub> ελεύθερο να κινηθεί οπότε αυτό, τη χρονική στιγμή </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">t</span><sub><span style="font-size: 12pt; line-height: 115%;">0</span></sub><span style="font-size: 12pt; line-height: 115%;">=0</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">s</span><span style="font-size: 12pt; line-height: 115%;"> συγκρούεται κεντρικά και ελαστικά με
το σώμα Σ<sub>2</sub>. Η διάρκεια της κρούσης είναι αμελητέα. Τη χρονική στιγμή
</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">t</span><sub><span style="font-size: 12pt; line-height: 115%;">1</span></sub><span style="font-size: 12pt; line-height: 115%;">=2</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">s</span><span style="font-size: 12pt; line-height: 115%;"> το σώμα Σ<sub>2</sub> φθάνει σε
θέση στην οποία η ράβδος είναι έτοιμη να ανατραπεί.</span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Β) Να βρεθεί η θέση του
σώματος Σ<sub>2</sub> τη χρονική στιγμή </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">t</span><sub><span style="font-size: 12pt; line-height: 115%;">1</span></sub><span style="font-size: 12pt; line-height: 115%;">=2</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">s</span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Γ) Να υπολογίσετε τα
μέτρα των ταχυτήτων των σωμάτων Σ<sub>1 </sub><span style="mso-spacerun: yes;"> </span>και Σ<sub>2 </sub>μετά τη κρούση. </span></span></div>
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<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Δ) Να υπολογισθεί το
ύψος στο οποίο το σώμα Σ<sub>1 </sub>θα σταματήσει στιγμιαία</span></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Για να δείτε τη λύση πατήστε <a href="https://drive.google.com/file/d/1x571uQ_QOxfddFRUQBXBMzqp-gtjSP9R/view?usp=sharing" target="_blank">εδώ</a>.</span></span></div>
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Panagiotis Stamatiouhttp://www.blogger.com/profile/05743522665371107812noreply@blogger.com0tag:blogger.com,1999:blog-3953680779248074761.post-81599876872935972902020-04-10T18:24:00.000+03:002020-04-10T18:24:49.403+03:00Ανακοίνωση Εξεταστέα ύλη 2020<div dir="ltr" style="text-align: left;" trbidi="on">
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<br />
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-align: justify; text-autospace: none;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b style="mso-bidi-font-weight: normal;"><u><span style="color: #0070c0; font-size: 12pt;">Εξεταστέα ύλη για το έτος
2020 για τα μαθήματα που εξετάζονται πανελλαδικά για την εισαγωγή στην Τριτοβάθμια
Εκπαίδευση αποφοίτων Γ΄ τάξης Ημερησίου Γενικού Λυκείου.</span></u></b></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-align: justify; text-autospace: none;">
<br /></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-align: justify; text-autospace: none;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: 12pt;">Τροποποίηση της με
αρ. πρωτ. 106428/Δ2/02-07-2019 Υ.Α. (Β΄ 2875) με θέμα: «Καθορισμός εξεταστέας ύλης
για το έτος 2020 για τα μαθήματα που εξετάζονται πανελλαδικά για την εισαγωγή στην
Τριτοβάθμια Εκπαίδευση αποφοίτων Γ΄ τάξης Ημερησίου Γενικού Λυκείου, Γ΄ τάξης Εσπερινού
Γενικού Λυκείου και Δ΄ τάξης Εσπερινού Γενικού Λυκείου», η οποία τροποποιήθηκε με
την με αρ. πρωτ. 124893/Δ2/02-08-2019 Υ.Α. (Β΄ 3226) και συμπληρώθηκε με την με
αρ. πρωτ. 172155/Δ2/05-11-2019 Υ.Α (Β΄ 4266)</span><span lang="EN-US" style="font-size: 12pt;"></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-align: justify; text-autospace: none;">
<br /></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><u><span style="color: #0070c0; font-size: 12pt;">ΦΥΣΙΚΗ</span></u></b><b><u><span lang="EN-US" style="color: #0070c0; font-size: 12pt;"></span></u></b></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<br /></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="color: red; font-size: 12pt;">Δεν αποτελούν
εξεταστέα ύλη για το έτος 2020 τα κάτωθι:</span></b><b><span lang="EN-US" style="color: red; font-size: 12pt;"></span></b></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<br /></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="font-size: 12pt;">Από το βιβλίο ΦΥΣΙΚΗ
- ΤΕΥΧΟΣ Γ':</span></b><b><span lang="EN-US" style="font-size: 12pt;"></span></b></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<br /></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="font-size: 12pt;">Από το Κεφ. 4. ΜΗΧΑΝΙΚΗ
ΣΤΕΡΕΟΥ ΣΩΜΑΤΟΣ οι παράγραφοι:</span></b><b><span lang="EN-US" style="font-size: 12pt;"></span></b></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<br /></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="font-size: 12pt;">4.5.</span></b><span style="font-size: 12pt;">Ροπή αδράνειας.</span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="font-size: 12pt;">4.6 </span></b><span style="font-size: 12pt;">Θεμελιώδης νόμος
της στροφικής κίνησης.</span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="font-size: 12pt;">4.7 </span></b><span style="font-size: 12pt;">Στροφορμή.</span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="font-size: 12pt;">4.8 </span></b><span style="font-size: 12pt;">Διατήρηση της στροφορμής.</span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="font-size: 12pt;">4.9 </span></b><span style="font-size: 12pt;">Κινητική ενέργεια
λόγω περιστροφής.</span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="font-size: 12pt;">4.10 </span></b><span style="font-size: 12pt;">Έργο κατά τη στροφική
κίνηση.</span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-align: justify; text-autospace: none;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="font-size: 12pt;">Oι ασκήσεις 25,
70</span></b><span lang="EN-US" style="font-size: 12pt;"></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-align: justify; text-autospace: none;">
<br /></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-align: justify; text-autospace: none;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 12pt;">Δείτε </span></b><span style="font-size: 12pt;">την εξεταστέα ύλη σε όλα τα μαθήματα για
κάθε προσανατολισμό <a href="https://drive.google.com/file/d/1vkrkKSPDHrLwDXlxLSgX-Gd3a7LFHPeu/view?usp=sharing" target="_blank"><b style="mso-bidi-font-weight: normal;">εδώ</b></a>. </span><span lang="EN-US" style="font-size: 12pt;"></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-align: justify; text-autospace: none;">
<br /></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-align: justify; text-autospace: none;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: 12pt;">Για τη Φυσική θα
ανατρέξετε στη σελίδα 10-11 του </span><span lang="EN-US" style="font-size: 12pt;">pdf</span><span style="font-size: 12pt;">.</span></span></div>
</div>
Panagiotis Stamatiouhttp://www.blogger.com/profile/05743522665371107812noreply@blogger.com0tag:blogger.com,1999:blog-3953680779248074761.post-60801419899360807332020-04-08T11:34:00.000+03:002020-04-18T16:11:45.356+03:00Γ΄Λυκείου Στερεό σώμα-Μηχανική ρευστών<div dir="ltr" style="text-align: left;" trbidi="on">
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<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Η διπλή τροχαλία
έχει<span style="mso-spacerun: yes;"> </span>ροπή αδράνειας Ι=0,54</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">Kgm</span><sup><span style="font-size: 12pt; line-height: 115%;">2</span></sup><span style="font-size: 12pt; line-height: 115%;">
και οι δίσκοι της έχουν ακτίνες </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">r</span><span style="font-size: 12pt; line-height: 115%;">=0,1</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span style="font-size: 12pt; line-height: 115%;"> και </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">R</span><span style="font-size: 12pt; line-height: 115%;">=0,2</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span style="font-size: 12pt; line-height: 115%;">. Στις περιφέρειες του μεγάλου και
μικρού δίσκου είναι τυλιγμένα αβαρή και εκτατά νήματα (1) και (2) αντίστοιχα.
Το νήμα (1) είναι ενωμένο με σώμα Σ<sub>1</sub> μάζας </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><sub><span style="font-size: 12pt; line-height: 115%;">1</span></sub><span style="font-size: 12pt; line-height: 115%;">=2</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">Kg</span><span style="font-size: 12pt; line-height: 115%;"> που βρίσκεται πάνω σε οριζόντιο
επίπεδο και πάνω από αυτό βρίσκεται στερεωμένο, σώμα Σ<sub>2</sub> μάζας </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><sub><span style="font-size: 12pt; line-height: 115%;">2</span></sub><span style="font-size: 12pt; line-height: 115%;">.
Ο συντελεστής τριβής ολίσθησης και ο συντελεστής οριακής τριβής μεταξύ του
σώματος Σ<sub>1</sub> και του οριζοντίου επιπέδου είναι μ</span><sub><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">s</span></sub><span style="font-size: 12pt; line-height: 115%;">=μ=0,2. Το νήμα (2)
συνδέεται με δοχείο αμελητέου βάρους και διατομής Α=2<sup>.</sup>10<sup>-3</sup></span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><sup><span style="font-size: 12pt; line-height: 115%;">2</span></sup><span style="font-size: 12pt; line-height: 115%;">,
το οποίο περιέχει μέχρι ύψος </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">h</span><span style="font-size: 12pt; line-height: 115%;">
νερό μάζας </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span style="font-size: 12pt; line-height: 115%;">=2</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">Kg</span><span style="font-size: 12pt; line-height: 115%;"> και πυκνότητας ρ=10<sup>3</sup></span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">Kg</span><span style="font-size: 12pt; line-height: 115%;">/</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><sup><span style="font-size: 12pt; line-height: 115%;">3</span></sup><span style="font-size: 12pt; line-height: 115%;">.
Το σύστημα τροχαλία σώμα Σ<sub>1</sub> σώμα Σ<sub>2</sub> δοχείο ισορροπεί. Να υπολογίσετε:</span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Α) τη μάζα </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><sub><span style="font-size: 12pt; line-height: 115%;">2</span></sub><span style="font-size: 12pt; line-height: 115%;">του
σώματος Σ<sub>2</sub></span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Β) την συνολική πίεση </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">p</span><span style="font-size: 12pt; line-height: 115%;"> στον πυθμένα του δοχείου</span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;"><span style="mso-spacerun: yes;"></span>Τη χρονική στιγμή </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">t</span><sub><span style="font-size: 12pt; line-height: 115%;">0</span></sub><span style="font-size: 12pt; line-height: 115%;">=0</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">s</span><span style="font-size: 12pt; line-height: 115%;">, με κάποιο μηχανισμό απομακρύνουμε
το σώμα Σ<sub>2</sub> από το σώμα Σ<sub>1</sub> και το σύστημα αρχίζει να
κινείται. Να υπολογίσετε:</span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Γ) τη γωνιακή
επιτάχυνση της τροχαλίας</span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Δ) τη κινητική ενέργεια
του συστήματος τη χρονική στιγμή κατά την οποία το δοχείο έχει μετατοπισθεί
κατά </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">x</span><span style="font-size: 12pt; line-height: 115%;">=1</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Ε) την υδροστατική
πίεση </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">p</span><span style="font-size: 12pt; line-height: 115%;">΄
στον πυθμένα του δοχείου</span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Κάποια στιγμή το νήμα
(2) κόβεται</span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Ζ) Να υπολογίσετε την
υδροστατική πίεση </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">p</span><span style="font-size: 12pt; line-height: 115%;">΄΄
στον πυθμένα του δοχείου.</span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;">Για να δείτε τη λύση πατήστε <a href="https://drive.google.com/file/d/1zYUKnfWFnbdrBRLsaVEBDQzBmRtWbqeo/view?usp=sharing" target="_blank">εδώ</a>.</span></div>
</div>
Panagiotis Stamatiouhttp://www.blogger.com/profile/05743522665371107812noreply@blogger.com0tag:blogger.com,1999:blog-3953680779248074761.post-79398681054947680732020-04-05T11:46:00.002+03:002020-04-05T12:34:32.784+03:00Β΄ Λυκείου Τράπεζα Θεμάτων Γενικής Παιδείας <div dir="ltr" style="text-align: left;" trbidi="on">
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<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Ένα σώμα Σ<sub>1 </sub>μάζας
</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><sub><span style="font-size: 12pt; line-height: 115%;">1</span></sub><span style="font-size: 12pt; line-height: 115%;">=2</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">Kg</span><span style="font-size: 12pt; line-height: 115%;"> είναι δεμένο στο ελεύθερο άκρο
αβαρούς και μη εκτατού νήματος μήκους<span style="mso-spacerun: yes;"> </span></span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">L</span><span style="font-size: 12pt; line-height: 115%;">=2√3/3</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span style="font-size: 12pt; line-height: 115%;">, το άλλο άκρο του οποίου είναι
στερεωμένο σε σταθερό σημείο Κ. Φέρνουμε το σώμα Σ<sub>1</sub> στην οριζόντια
θέση, με το νήμα τεντωμένο και του προσδίδουμε ταχύτητα με μέτρο υ<sub>0</sub>=4</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span style="font-size: 12pt; line-height: 115%;">/</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">s</span><span style="font-size: 12pt; line-height: 115%;"> και κατακόρυφη διεύθυνση με φορά
προς τα κάτω. Όταν το σώμα Σ<sub>1 </sub>βρίσκεται σε θέση όπου το νήμα
σχηματίζει γωνία θ=30<sup>0</sup> με την κατακόρυφη, το νήμα κόβεται και το
σώμα Σ<sub>1</sub> τη χρονική στιγμή </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">t</span><sub><span style="font-size: 12pt; line-height: 115%;">0</span></sub><span style="font-size: 12pt; line-height: 115%;">=0</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">s</span><span style="font-size: 12pt; line-height: 115%;">, συγκρούεται κεντρικά και ελαστικά
με το ακίνητο σώμα Σ<sub>2</sub> μάζας<span style="mso-spacerun: yes;"> </span></span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><sub><span style="font-size: 12pt; line-height: 115%;">2</span></sub><span style="font-size: 12pt; line-height: 115%;">=6</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">Kg</span><span style="font-size: 12pt; line-height: 115%;"> που βρίσκεται ακίνητο στο άκρο </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">A</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;"> λείου </span><span style="font-size: 12pt; line-height: 115%;">κεκλιμένου
επιπέδου γωνίας κλίσης φ=30<sup>0</sup> και μήκους </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">s</span><span style="font-size: 12pt; line-height: 115%;">=ΑΒ=5,5</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span style="font-size: 12pt; line-height: 115%;">, όπως φαίνεται στο σχήμα. Το σώμα
Σ<sub>1</sub> έχει ταχύτητα παράλληλη στο κεκλιμένο επίπεδο τη στιγμή της
σύγκρουσης. Μετά τη κρούση, το σώμα Σ<sub>2</sub> κινείται, φθάνει στο άκρο Β του
κεκλιμένου επιπέδου που βρίσκεται σε ύψος </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">h</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;"> </span><span style="font-size: 12pt; line-height: 115%;">από
το έδαφος, στη συνέχεια πέφτει και φθάνει στο έδαφος τη χρονική στιγμή </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">t</span><sub><span style="font-size: 12pt; line-height: 115%;">2</span></sub><span style="font-size: 12pt; line-height: 115%;">=2</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">s</span><span style="font-size: 12pt; line-height: 115%;">. Να υπολογιστούν:</span></span></div>
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<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Α) το μέτρο της
ταχύτητας του σώματος Σ<sub>1</sub> τη χρονική στιγμή που κόβεται το νήμα</span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Β) οι ταχύτητες των
σωμάτων Σ<sub>1</sub> και Σ<sub>2</sub> αμέσως μετά τη κρούση</span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Γ) το ποσοστό επί τοις
εκατό της κινητικής ενέργειας του σώματος Σ<sub>1</sub> που μεταφέρθηκε στο
σώμα Σ<sub>2</sub> κατά τη διάρκεια της κρούσης</span></span></div>
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<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;"><span style="mso-spacerun: yes;"> </span>Δ) το ύψος </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">h</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;"> </span><span style="font-size: 12pt; line-height: 115%;">και
την ταχύτητα του σώματος Σ<sub>2</sub> όταν φθάνει στο έδαφος</span></span></div>
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<br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">
</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Δίνεται<span style="mso-spacerun: yes;"> </span>ότι η επιτάχυνση της βαρύτητας είναι: </span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">g</span><span style="font-size: 12pt; line-height: 115%;">=10</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">m</span><span style="font-size: 12pt; line-height: 115%;">/</span><span lang="EN-US" style="font-size: 12pt; line-height: 115%;">s</span><sup><span style="font-size: 12pt; line-height: 115%;">2</span></sup><span style="font-size: 12pt; line-height: 115%;">και
η χρονική διάρκεια της κρούσης θεωρείται αμελητέα.</span></span></div>
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<style>
/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Κανονικός πίνακας";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
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<div class="MsoNormal">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: 12pt; line-height: 115%;">Για να δείτε τη λύση πατήστε <a href="https://drive.google.com/file/d/1byQLSZRdwwYRw34rYrT5LHoFVy28-Tgc/view?usp=sharing" target="_blank">εδώ</a>.</span></span></div>
</div>
Panagiotis Stamatiouhttp://www.blogger.com/profile/05743522665371107812noreply@blogger.com0