Question

A proton undergoes a head on elastic collision with a particle of unknown mass which is initially at rest and rebounds with 16/25 of its initial kinetic energy. Calculate the ratio of the unknown mass with respect to the mass of the proton.

Answer 1

masses of two particles:  m1 , m2.

u1,  u2=0

1/2 m1 * v1^2 = 16/25 * 1/2 m1 * u1^2    =>  v1 = 4 u1 /5

Assuming that there is no effect due to the particle being electrically charged. We assume that the collision is elastic.

Conservation of linear momentum:

      m1 u1 + m2 u2 = m1 v1 + m2 v2

      m1 u1 = m1 *4 u1 / 5 + m2  v2

      m2 v2 = m1 u1 /5         --- (1)

Conservation of energy:

      1/2 m1 u1^2 + 1/2 m2 u2^2 = 1/2 m1 v1^2 + 1/2 m2 v2^2

      m2 v2^2 = 9/25 m1  u1^2      -- (2)

(2) / (1)  =>   v2 = 9/5 * u1

Substitute in (1) to get:    m2/m1 = 1/9