A 2.6-kg cart is rolling along a frictionless, horizontal track towards a 1.2-kg

Question

A 2.6-kg cart is rolling along a frictionless, horizontal track towards a 1.2-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 +5.0 m/s, and the second cart's velocity is -1.1 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

The idea is that since they only apply forces to each other (through the magnets) their total momentum is always the same. So...

(a) total momentum = mass * velocity for each =

= 2.6 * 5.9 + 1.7 * -1.1 =

= 13.47 kg-m/s is the total momentum

(b) Initially the second cart has zero momentum... so the total momentum must be entirely with the first cart!

So... momentum = mass * velocity

13.47 = 2.6 * v

v = 5.18 m/s

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