Question

Two carts have a compressed spring between them and are initially at rest. One of the carts has total mass, including its contents, of 5.0 kg, and the other has total mass of 3.0 kg. If the 3.0 kg cart is moving at 3.0 m/s after the spring is allowed to push the carts apart, what is the velocity of the 5.0 kg cart after release? The system is closed.

1.8 m/s

5.0 m/s

0.56 m/s

0.0 m/s

Answer 1

Recall the law of conservation of momentum. It says that the total momentum in a given system(closed) is constant.
(Note that momentum is a vector quantity)
You can write this principle down like this :
\[\ \hat{p_{a1}} + \hat{p_{b1}} = \hat{p_{a2}} + \hat{p_{b2}} \]
Where p_a1 and p_b1 are momenta of objects a and b before something happens to them, and p_a2 and p_b2 are momenta of objects a and b after something happens to them.

Since a and b are initially at rest we know that their velocities are 0(momentum is also zero, since p=m*v), which means that their momentum after something happens also needs to be zero.

So from this you can deduce that : \[\ \hat{p_{a2}} = - \hat{p_{b2}}\] and from that, hopefully v_b2 :D