Answer to Question #149524 in Mechanics | Relativity for Mikkos Joshua Garcia

Question

Describe a collision in which all kinetic energy is lost.

Answer 1

Suppose a ball with mass m₁ and speed v₁ collide with a ball at rest with mass m₂ and they stuck together

The initial kinetic energy K₁ is:

K₁=0.5m₁v₁²

The conservation of momentum is:

m₁v₁=(m₁+m₂)vf

where v_f is the final velocity.

The final kinetic energy is:

Kf=0.5(m₁+m₂)[$[\tfrac{m_1v_1}{m_1+m_2}]$ ]²

Kf=$0.5[\tfrac{m_1^2v_1^2}{m_1+m_2}]$

If and only if:

m₂→∞

K_f→0

If you throw a sticky ball in a wall the kinetic energy is (roughly speaking!) lost. This because:

earth mass is >> ball mass

However a more simple example are two ball colliding and sticking with the same momentum, in this way v_f will be zero and so K_f.