A projectile of mass m makes a one-dimensional head-on elastic collision with a stationary atom of mass M. Which expression gives the maximum fraction of the projectile's initial kinetic energy that can be transferred to the stationary atom?
Options

Question

A projectile of mass m makes a one-dimensional head-on elastic collision with a stationary atom of mass M. Which expression gives the maximum fraction of the projectile's initial kinetic energy that can be transferred to the stationary atom?

Options

G1 Physics · Accepted Answer

For a head-on elastic collision with the target initially at rest, V = 2mu ÷ (m+M), where u is the projectile's initial speed and V is the target speed after collision. The transferred-energy fraction is K_T ÷ K_i = 4mM ÷ (m+M)². The fraction becomes 1 when m = M, so equal masses can transfer all projectile kinetic energy in a head-on elastic collision. Correct option: B.