Answer to Question #144014 in Physics for pixie

Question

You push a cart on an air track which crashes into a smaller cart. The large cart transfers all of it's momentum into the small cart. The large cart has a mass of 8 kg and the small cart has a mass of 2 kg. Before the crash the large cart is going at 6.14 meters per second squared
​What is the velocity of the smaller cart after the crash?

Answer 1

First, calculate the initial momentum of the larger cart:

$$p_L=Mv_L.$$

Then, since the larger one gave all its momentum to the smaller one, we can state that

$$p_S=mv_S=p_L,\\\space\\ v_S=v_L\frac{M}{m}=6.14\frac{8}{2}=24.6\text{ m/s}.$$