Derive the final velocity equation in a 1D perfectly inelastic two body collision.

Expert Solution

Inelastic Collisions in One Dimension

In an inelastic collision, two (or sometimes more, but let's not get carried away) objects collide and stick together. We generally ignore any outside forces on the colliding objects, so the two-object system is an isolated system. This is reasonable in practice if we examine the objects during the time interval immediately before the collision and then immediately after - before friction, gravity, etc., have time to exert any appreciable impulses on our system.

An Inelastic Collision

The standard method for handling inelastic collisions in one dimension is to invoke the Law of Conservation of Momentum. After all, if no external forces act on a system, its total momentum will be conserved.

Total momentum of the system (the two objects) before the collision is:

p_before = m₁v₁ - m₂v₂

Total momentum of the system after the collision:

p_after = (m₁ + m₂)v

If momentum is conserved, then:

p_after = p_before

so that:

(m₁ + m₂)v = m₁v₁ - m₂v₂

Solving for v gives:

genius_generous answered 2 years ago

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