You are holding two carts together that are separated by a compressed spring wit
ID: 1620726 • Letter: Y
Question
You are holding two carts together that are separated by a compressed spring with spring constant 709 N/m, The spring is initially compressed a distance 0.28 m. The carts rest on a nearly frictionless track. The left cart has a mass mL = 54 kg and the right cart has a mass mR = 105 kg. When you release the carts, they move off in opposite directions. After the spring is uncompressed and the carts are moving apart, what is the kinetic energy of the left cart? Give your answer in Joules to two decimal places.
Explanation / Answer
right cart, M = 105 kg
left cart, m = 54 kg
initial velocity of com = final velocity of com ( as no extgernal force is applied to the system)
so, final velocity of mass m be u and thqat of mass M be v
then com mvelocity = (mu + Mv)/(m + M) = 0
105*v = - 54*u
u = -105v/54
total ke = energy in compressed spring ( from conservation of energy)
so, 0.5kx^2 = 0.5mu^2 + 0.5Mv^2
709*0.28^2 = 54(105v/54)^2 + 105v^2
v^2 = 0.179
KE = 0.5Mv^2 = 1.697 J
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