Conservation of Momentum: Solving a Collision Problem

[Cheesy74]

Homework Statement

If an object with momentum n going right collides with an object with momentum 2n going left, will the right-moving object go left at momentum n while the left-moving object stops, or will both objects move left at momentum n/2?

The Attempt at a Solution

Obviously, the opposing forces are going to cancel out, but I'm not sure if the remaining n momentum is going to be distributed between both objects or not. Could someone give me a quick solution here?

 

[LowlyPion]

Presumably this is an elastic collision.

What else needs to be conserved?

 

[nlightner]

I can provide a solution to this collision problem by applying the principle of conservation of momentum. According to this principle, the total momentum of a system remains constant before and after a collision. In this case, the total momentum of the system before the collision is n + 2n = 3n. Therefore, after the collision, the total momentum of the system must also be 3n.

Now, let's consider two scenarios:

1. The right-moving object goes left at momentum n while the left-moving object stops: In this scenario, the final momentum of the system is n + 0 = n. However, this does not satisfy the conservation of momentum principle as the total momentum of the system before and after the collision is not the same (3n ≠ n).

2. Both objects move left at momentum n/2: In this scenario, the final momentum of the system is n/2 + n/2 = n. This satisfies the conservation of momentum principle as the total momentum of the system remains the same before and after the collision (3n = n).

Therefore, the correct solution is that both objects will move left at momentum n/2 after the collision, in order to satisfy the conservation of momentum principle. This means that the remaining momentum of n will be distributed equally between the two objects.