Question

Two asteroids in outer space collide and stick together. The mass of each asteroid, and the velocity of each asteroid before the impact, are known. To find the momentum of the stuck-together asteroids after the impact, what approach would be useful? (1) Use the Energy Principle. (2) Use the Momentum Principle. (3) It depends on whether or not the speed of the asteroids was near the speed of light. (4) Use the relationship among velocity, displacement, and time. (5) It depends on whether the collision was elastic or inelastic.

Short answer

2) Use the momentum principle

Step-by-step solution

Significance of the law of conservation of momentum of a system

This law states that the momentum of a particular system before and after the collision is constant if no external force acts on the system.

The momentum principle gives the momentum of the stuck-together asteroids after the impact.

Determination of the final momentum of the struck-together asteroids

From the law of conservation of momentum, the initial and the final momentum of the asteroids become equal as no external forces are acting on them. Moreover, the momentum also does not depend on the elasticity or inelasticity of the collision. Here, the kinetic energy is also not conserved. So, finding the momentum after the collision, the principle of momentum will be helpful.

Thus, 2) Use the momentum principle is the correct choice for finding the momentum of the stuck-together asteroids after the impact.