Conservation of energy Suppose an object with mass m moves in a region R in a conservative force field given by F = -Vọ, where o is a potential function in a region R. The motion of the object is governed by Newton's Second Law of Motion, F = ma, where a is the acceleration. Suppose the object moves from point A to point B in R. dv a. Show that the equation of motion is m - -Vọ. dt 1 d 2 dt c. Take the dot product of both sides of the equation in part (a) with v(t) = r'(t) and integrate along a curve between A and B. Use part (b) and the fact that F is conservative to show that dv b. Show that - dt the total energy (kinetic plus potential) - m|v]² + q is the same at A and B. Conclude that because A and B are arbitrary, energy is conserved in R.

Conservation of energy Suppose an object with mass m moves in a region R in a conservative force field given by F = -Vọ, where o is a potential function in a region R. The motion of the object is governed by Newton's Second Law of Motion, F = ma, where a is the acceleration. Suppose the object moves from point A to point B in R. dv a. Show that the equation of motion is m - -Vọ. dt 1 d 2 dt c. Take the dot product of both sides of the equation in part (a) with v(t) = r'(t) and integrate along a curve between A and B. Use part (b) and the fact that F is conservative to show that dv b. Show that - dt the total energy (kinetic plus potential) - m|v]² + q is the same at A and B. Conclude that because A and B are arbitrary, energy is conserved in R.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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