Question

Mazur 9.40: Two identical 0.50 kg carts, each 0.10 m long, are at rest on a low-friction track and are connected by a spring that is initially at its relaxed length of 0.50 m and is of negligible inertia. You give the cart on the left a push to the right (that is, toward the other cart), exerting a constant 5.0-N force. You stop pushing at the instant when the cart has moved 0.40 m. At this instant, the relative velocity of the two carts is zero and the spring is compressed to a length of 0.30 m. A locking mechanism keeps the spring compressed, and the two carts continue moving to the right. (a) What is the work done by you on the two cart system? (b) How far does the system's center of mass move while you are pushing the left cart? (c) By what amount do you change the system's kinetic energy?

Answer 1

Part A)-

Work done by two cart system = W = F*L

W = 5 * 0.4 = 2 J

Part C)-

Xm = ?

Fnet = 5 N = Msystem * a

so, a = 5 / (0.5+0.5) = 5 m/s²

(V )² = U² + 2a*X

V = (2*5*0.40)^0.5

V = 2 m/s

For the change in KE-

initial velocity = 0

KEinitial = 0

KEfinal = 1/2*Mtotal*V²

KEf = 0.5*(0.5+0.5) * 4

KEf = 2 J

Change in KE = KEf - KEi = 2 J = Work done by external force

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