A 2.5-kg cart is rolling along a frictionless, horizontal track towards a 1.3-kg

Question

A 2.5-kg cart is rolling along a frictionless, horizontal track towards a 1.3-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 +4.9 m/s, and the second cart's velocity is -1.7 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

Masses of the carts m = 2.5 kg                               M = 1.3 kg Velocity of first cart v = 4.9 m/ s Velocity of second cart V = -1.7 m / s (a). The total momentum of the system of the two carts at this instant P = mv + MV                                                                                                            = 10.04 kg m/ s (b) Total momentum of the two carts when the second cart is at rest P' = P                                                                                        m v ' + MV' = 10.04 Where V ' = Velocity of the second cart                  = 0 The velocity of the first cart when the second cart was still at rest v ' = 10.04 / m       Since V ' = 0                                                                                                       = 4.016 m/ s

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