You can think of the work?kinetic energy theorem as a second theory of motion, p

Question

You can think of the work?kinetic energy theorem as a second theory of motion, parallel to Newton's laws in describing how outside influences affect the motion of an object. In this problem, solve parts (a), (b), and (c) separately from parts (d) and (e) so you can compare the predictions of the two theories. A 15.9-g bullet is accelerated from rest to a speed of 758 m/s in a rifle barrel of length 78.1 cm. (a) Find the kinetic energy of the bullet as it bullet as it leaves the barrel.
kJ

(b) Use the work-kinetic energy theorem to find the net work that is done on the bullet.
kJ

(c) Use the result to part (b) to find the magnitude of the average net force that acted on the bullet while it was in the barrel.
kN

(d) Now model the bullet as a particle under constant acceleration. Find the constant acceleration of the bullet that starts from rest and gains a speed of 758 m/s over a distance of 78.1 cm.
km/s2

(e) Modeling the bullet as a particle under a net force, find the net force that acted on it during its acceleration.
kN

(f) What conclusion can you draw from comparing your results of parts (c) and (e)

Explanation / Answer

1) KE = 1/2 m v^2 = (.0159 / 2) * 758^2 = 4568 J
2) F d = W  = KE    Kinetic Energy = Work done on bullet   
3) F = KE / d = 4568 / .781 = 5849 N
4) 2 a s = v^2
      a = 758^2 / (2 * .781) = = 3.68 * 10E5 m/s^2
5) F = m a = .0159 * 3.68 * 10E5 = 5849 N
6)    The work-energy theorem is consistant with Newton's Second Law

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