Answer to Question #4191 in Mechanics | Relativity for Nantu

Question

Consider a ball of mass m1 moving with a velocity u1 collides elastically with a ball of mass m2 at rest.Show that the maximum energy transfer takes place when m1=m2.

Answer 1

The Energy transfer equation is
W=E₂ - E₁=m (u₁²)/2 - 0 = m (u₁²)/2.


The Momentum conservation law
m₁u₁ = m₂u₂+m₁ u₁'.


Thus, when masses are equal, the second ball begins to move with the speed u₂=u₁ - u₁' .