lect116_32rev_f11

lect116_32rev_f11 - Friday November 25 Lecture 32...

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Friday, November 25 − Lecture 32 : Applications : Work and energy (Refers to Section 7.4 in your text) Students who have mastered the content of this lecture know : what the “amount of work W performed by F(x) on the mass m over the distance d ” is. Students who have practiced the techniques presented in this lecture will be able to : Compute the amount of work done when a forces F(x) is exerted of an object over a distance d. 32.1 Work performed by a constant force on a mass over a distance d . Suppose a constant force F is exerted on an object providing it with a constant acceleration a over a distance d . Suppose its initial velocity is v i while its final velocity is v f and the force is exerted over the period of time t f t i = t . We will suppose that F is a “net force” in the sense that any force opposing the movement is already taken into account inside F Since the acceleration a ( t ) is constant and that acceleration at time t is the rate of change of the velocity at time t , then we can write The distance d covered by the mass over the period of time t is the “average velocity” × “the time t ”. That is, Recall Newton’s second law of motion states that F = ma . The force will give to the mass m kinetic energy K = (1/2) mv 2 . The energy provided to m by this force is then

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where K f is the final kinetic energy and K i is the kinetic already possessed by the mass when this net force starts acting on it. Then So the net increase in energy K provided to m by this net force F on a distance d is K = Fd The units for Fd must be newtons-meters. We define 1 joule = 1 newton-meter.
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This note was uploaded on 12/28/2011 for the course MATH 116 taught by Professor Robertandre during the Spring '11 term at Waterloo.

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lect116_32rev_f11 - Friday November 25 Lecture 32...

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