A 2.3 kg cart is rolling across a frictionless, horizontal track toward a 1.5 kg

Question

A 2.3 kg cart is rolling across a frictionless, horizontal track toward a 1.5 kg cart that is held initially at rest. The cars are loaded with strong magnets that cause them to attract one another. Thus, the speed of each car increases. At a certain instant before the cars collide, the first car's velocity is 4.5 m/s and the second car's velocity is -1.9 m/s. (A) what is the total momentum of the system of the two cars at this instant? (B) What was the velocity of the first cart when the second cart was still at rest?

Explanation / Answer

mass of 1 st cart m = 2.3 kg mass of 2nd cart m ' = 1.5 kg velocity of the 1 st cart before collision v = 4.5 m /s velocity of the 2 nd cart before collision v ' = -1.9 m/s Total momentum of the system of the two carts P = m v +m ' v' = 10.35 - 2.85 = 7.5 kg m / s from law of conservation of momentum ,momentum beforecollision =momentum after collision P = m V + M V ' = 2.3 * V + ( 1.5 * 0 ) the velocity of the forst cart when the secondcart was still atrest V = P / 2.3 = 3.26 m / s

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