Question

A green cart is less massive than a red cart. Both carts are on a frictionless horizontal track where they can only travel along the same straight line. The green cart bumps into the stationary red cart. As a result of the collision, the red cart moves forward in the direction of the green cart's original velocity. The green cart bounces off the red cart and moves backward. How does the magnitude of the red cart's momentum after the collision compare with the magnitude of the green cart's momentum before the collision?
A. The magnitude of the red carts momentum after Collision is greater than the magnitude of the green cart’s momentum before collision
B. The magnitude of the red carts momentum after collision is less than the magnitude of green carts momentum before the collision
C. The magnitude of the red carts momentum after collision is same as the magnitude of green carts momentum before the collision
D. Nothing can be determined about the magnitude of the red cart momentum after the collision unless we know that the collision is perfectly elastic.

Answer 1

In the question, we can observe there’s no amount of force acting on the system. If no external force is acting on the system, the net momentum along any axis for the system is conserved. Therefore, conserve the momentum by assuming the momentums of the red and green cart before and after the collision happened.

Formulas used:
${{P}_{initial}}={{P}_{final}}$

Complete step by step answer:
Let us now assume the momentums of green cart and red cart before collision as ${{P}_{red}}, {{P}_{green}}$ and the momentums of the red and green carts after the collision as ${{P}^{1}}_{red}, {{P}^{1}}_{green}$ respectively.
Now, before the collision, the momentum of the red cart is zero.
As there’s no net force acting along the axis, the momentum is conserved,
That means, ${{P}_{red}}+0={{P}^{1}}_{red}+{{P}^{1}}_{green}$
Clearly, we can say from the above equation that,
The magnitude of the red carts momentum after the collision is greater than the magnitude of green carts momentum before the collision.
Therefore, the correct option is option a.

Additional information:
The linear momentum of any system given is considered as conserved only when the mass of the system throughout the system remains constant during the entire interaction and when there’s no external force acting on the system during the interaction. If we consider our universe, our universe is an isolated system. It doesn’t have any external forces. Therefore, we can say in our universe, momentum is always considered.

Note:
If there’s any resisting force like friction, gravity or any net force acting on the system from outside the system, the momentum will not be conserved. If we are applying any external force, we are changing the internal velocity of the body by adding or taking some amount of it. Therefore, momentum will not be conserved.