The kinetic energy KE of an object of mass m moving with velocity v is defined as KE 1 2

Chapter 6, Problem 31

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The kinetic energy KE of an object of mass m moving with velocity v is defined as KE 1 2 mv 2 . If a force fsxd acts on the object, moving it along the x-axis from x1 to x2, the Work-Energy Theorem states that the net work done is equal to the change in kinetic energy: 1 2 mv 2 2 2 1 2 mv 2 1 , where v1 is the velocity at x1 and v2 is the velocity at x2. (a) Let x sstd be the position function of the object at time t and vstd, astd the velocity and acceleration functions. Prove the Work-Energy Theorem by first using the Substitution Rule for Definite Integrals (5.5.6) to show that W y x2 x1 fsxd dx y t2 t1 fssstdd vstd dt Then use Newtons Second Law of Motion (force mass 3 acceleration) and the substitution u vstd to evaluate the integral. (b) How much work (in ft-lb) is required to hurl a 12-lb bowling ball at 20 miyh? (Note: Divide the weight in pounds by 32 ftys 2 , the acceleration due to gravity, to find the mass, measured in slugs.)