Answer: M is equal to m.
Explanation:
The question gives us two important informations:
- M is initially at rest
- m finishes at rest after collision.
In any collision, as it is asumed that no external forces can act during the collision, momentum must be conserved.
So, if we call p₁ to the momentum before collision, and p₂ to momentum after it, taking into account the information above, we can write the following:
p₁ = mv₁ + M.0 = p₂ = m.0 + Mv₂ ⇒ mv₁ = Mv₂
From the question, we also know that it was an elastic collision.
In elastic collision, added to the momentum conservation, it must be conserved the kinetic energy also.
So, if we call k₁ to the kinetic energy prior the collision, and k₂ to the one after it, we can write the following:
k₁ = 1/2 m(v₁)² + 1/2 M.0 = k₂ = 1/2m.0 + 1/2M(v₂)² ⇒ m(v₁)² = M(v₂)²
Mathematically, the only way in which both equations be true, should be with v₁ = v₂, which is only possible if m=M too.
In this type of collision, it is said that the energy transfers from one mass to the other.
