When two carts having the same mass and the same speed collide and stick togethe

Question

When two carts having the same mass and the same speed collide and stick together, they stop. What happened to each cart's momentum? Is momentum conserved? Explain. When two carts having the same mass and the same speed collide and bounce off of each other elastically, what is the final total momentum of the carts? Is momentum conserved in explosions? Write an equation for the total impulse in the unequal mass explosion and an expression for the impulse on each individual cart. Explain in terms of conservation.

Explanation / Answer

8. An inelastic collision has taken place between the carts. Since the velocities of the two carts are in opposite directions, their momentum after collision adds up to zero, hence the total momentum of the system is conserved. However, some of energy is converted into heat, sound etc, energy conservation doesn't takes place.

9. This refers to elastic collision. The momentum of both the carts before the collision are equal in magnitude and oppsite in direction, thereby cancelling each other. The final momentum of the system after collision is the vector sum of the individual momentum of the carts and hence is equal to zero. Thus, momentum is conserved.

10. In both the collisions, momentum is conserved, that is, momentum before and after the collision is same. The impulse of the system is defined as the change in the momentum, and thus the impulse acting on the two carts is also zero.

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