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svg{background:var(--jp-carousel-bg-color);border-radius:4px;padding:3px 2px}.jp-carousel-pagination-container{flex:1;margin:0 15px 0 35px}.jp-carousel-pagination,.jp-swiper-pagination{color:var(--jp-carousel-primary-color);display:none;font-size:15px;font-weight:400;position:static!important;white-space:nowrap}.jp-carousel-pagination-container .swiper-pagination{line-height:8px;text-align:left}.jp-carousel-pagination{padding-left:5px}.jp-carousel-info-footer .jp-carousel-photo-title-container{flex-basis:50vw;flex:4;justify-content:center;margin:0;overflow:hidden}.jp-carousel-photo-caption,.jp-carousel-photo-title{background:none!important;border:none!important;color:var(--jp-carousel-primary-color);display:inline-block;font:normal 20px/1.3em Helvetica Neue,sans-serif;letter-spacing:0!important;line-height:normal;margin:0 0 10px;overflow:hidden;padding:0;text-shadow:none!important;text-transform:none!important}.jp-carousel-info-footer 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Θεώρημα μεταβολής έργου — ενέργειας | My School Lab | Skip to content Θεώρημα μεταβολής έργου — ενέργειας To Θεώρημα Μεταβολής Έργου Ενέργειας ή όπως συχνά αναφέρεται Θεώρημα Μεταβολής Κινητικής Ενέργειας (Θ.Μ.Κ.Ε.) , είναι ένα από τα βασικά θεωρήματα της μηχανικής και αναφέρεται στη σχέση μεταξύ του έργου που κάνει μια δύναμη σε ένα αντικείμενο και της ενέργειας που μεταφέρεται στο αντικείμενο αυτό. Είναι ένα χρήσιμο εργαλείο για την επίλυση προβλημάτων μηχανικής καθώς με τη βοήθειά του μπορεί εύκολα να υπολογιστεί η ενέργεια που μεταφέρεται σε ένα σύστημα, χωρίς να απαιτείται η επίλυση διαφορικών εξισώσεων. Συγκεκριμένα μας βοηθάει να υπολογίζουμε εύκολα την κινητική ενέργεια ή την ταχύτητα ενός σώματος. Μπορούμε επίσης να υπολογίζουμε το έργο άγνωστης δύναμης που δρα σε ένα σώμα, εφόσον γνωρίζουμε την αρχική και την τελική του ταχύτητα, δηλαδή τη μεταβολή της κινητικής του ενέργειας.
ψηφιακο βιβλιο Διατήρηση της μηχανικής ενέργειας
ΣΤΟΙΧΕΙΑ ΘΕΩΡΙΑΣ Το θεώρημα έργου — ενέργειας ή αλλιώς θεώρημα μεταβολής κινητικής ενέργειας διατυπώνεται ώς εξής:
Η μεταβολή της κινητικής ενέργειας ενός σώματος είναι ίση με το αλγεβρικό άθροισμα των έργων των δυνάμεων που δρουν σε αυτό ή, ισοδύναμα, είναι ίση με το έργο της συνισταμένης δύναμης.
Και στη γλώσσα των μαθηματικών:
$$ \Delta K= ΣW_{F} = W_{ F_{ oλ }} $$
ΠΑΡΟΥΣΙΑΣΗ Στην σύντομη παρουσίαση που ακολουθεί δίνεται η απόδειξη του θεωρήματος της κινητικής ενέργειας στην ειδική περίπτωση ευθύγραμμης ομαλά μεταβαλλόμενης κίνησης.
ΣΗΜΕΙΩΣΕΙΣ ΘΕΩΡΙΑΣ Στο αρχείο που ακολουθεί περιγράφεται η έννοια της κινητικής ενέργειας και αποδεικνύεται το Θεώρημα Μεταβολής της Κινητικής Ενέργειας.
εφαρμογη Ένα κιβώτιο μάζας m = 10 kg είναι αρχικά ακίνητο σε οριζόντιο δάπεδο με συντελεστή τριβής μ = 0,1 . Τη χρονική στιγμή t = 0 δύο παιδιά αρχίζουν να προσπαθούν να το μετακινήσουν προς τα δεξιά. Το ένα ασκεί σταθερή δύναμη μέτρου F1 = 40 N και το άλλο σταθερή δύναμη μέτρου F2 = 60 N , που η κατεύθυνσή της σχηματίζει με την κατεύθυνση της μετατόπισης γωνία φ .
α. Να σχεδιάσεις όλες τις δυνάμεις που ασκούνται στο κιβώτιο και να τις υπολογίσεις.
Τη στιγμή που το σώμα έχει μετατοπιστεί κατά Δx = 5 m , να υπολογίσεις:
β. την κινητική του ενέργεια και
γ. το μέτρο της ταχύτητάς του.
Δίνονται: g = 10 m/s2 , ημφ = 0,8 και συνφ = 0,6 .
Λύση Στο βίντεο που ακολουθεί μπορείς να παρακολουθήσεις τη λύση της άσκησης.
ερωτησεισ — ασκησεισ
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Σχετικά Έργο Δύναμης Θεώρημα Έργου-Ενέργειας Θεώρημα Μεταβολής Κινητικής Ενέργειας
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