Ch 8 Conservation of Energy

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©1997 by Eric Mazur Published by Pearson Prentice Hall Upper Saddle River, NJ ISBN No portion of the file may be distributed, transmitted.

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©1997 by Eric Mazur Published by Pearson Prentice Hall

Presentation transcript:

Ch 8 Conservation of Energy 8-1 The Nonisolated System: Conservation of Energy Mechanical Energy E = K + U Esystem = T (T stands for energy transfer) 8-2 The Isolated System: Conservation of Energy W = K For a conservative force WC = -U -U = K K + U = 0 = Esystem If several potential energies: E = K + U1 + U2 + U3 + …… Esystem = K + U1 + U2 + U3 + … E is constant or conserved

Method for Energy Approach Draw a picture Write down equations for the energies and works involved E = K + U K = mv2/2 Ug = mgy (near surface of Earth – pick zero for Ug) Us = kx2/2 (Us =0 for x=0) Pick before (B) and after (A) and label on the picture Set EA = EB or E = 0

P8.6 (p.219) P8.57 (p.224)

CT1: A block initially at rest is allowed to slide down a frictionless ramp and attains a speed v at the bottom. To achieve a speed 2v at the bottom, how many times as high must a new ramp be? A. 1 B. 2 C. 3 D. 4 E. 5 F. 6

CT2: A spring-loaded toy dart gun is used to shoot a dart straight up in the air, and the dart reaches a maximum height of 24 m. The same dart is shot straight up a second time from the same gun, but this time the spring is compressed only half as far before firing. How far up does the dart go this time, neglecting friction and assuming an ideal spring? A. 96 m B. 48 m C. 24 m D. 12 m E. 6 m F. 3 m G. impossible to determine

8.3,4 Changes in Mechanical Energy for Nonconservative Forces WTOT = WC + WNC = K -U + WNC = K WNC = K + U WNC = E Friction is just another nonconservative force! The work of friction is always negative.

Method for Energy Approach Draw a picture Write down equations for the energies and works involved E = K + U K = mv2/2 Ug = mgy (near surface of Earth – pick zero for Ug) Us = kx2/2 (Us =0 for x=0) Work of non-conservative forces Pick before (B) and after (A) and label on the picture Set Wnc = E (If Wnc = 0, then EA = EB or E = 0 and mechanical energy is conserved)

P8.21 (p.220) P8.55 (p.224)

P = dE/dt Units: J/s = Watt PAV = W/t P = lim F·r/t = F·v 8.5 Power P = dE/dt Units: J/s = Watt PAV = W/t P = lim F·r/t = F·v     t0

P8.32 (p.221)

CT3 A. B. C. D. E.

P8.44 (p.223)