A 2.4-kg cart is rolling along a frictionless, horizontal track towards a 1.4-kg

Question

A 2.4-kg cart is rolling along a frictionless, horizontal track towards a 1.4-kg cart that is held initially at rest. The carts are loaded with strong magnets that cause them to attract one another. Thus, the speed of each cart increases. At a certain instant before the carts collide, the first cart's velocity is +4.8 m/s, and the second cart's velocity is -1.2 m/s. (a) What is the total momentum of the system of the two carts at this instant? (b) What was the velocity of the first cart when the second cart was still at rest?

Explanation / Answer

m1 = 2.4 kg , m2 = 1.4 kg , v1 = 4.8 m/s , v2 = -1.2 m/s

(a) Total momentum is given by

m1v1 + m2v2 = 4.8 x 2.4 - 1.4 x 1.2 = 9.84 kgm/s

(b) Let V1 be the velocity of the mass m1 while m2 was still at rest.

when m2 was at rest , all the momentum the system had was due to the mass m1

m1V1 = 9.84 kgm/s (because of conservation of momentum)

=> V1 = 4.1 m/s

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