Question

Two balls of masses m and 2m travelling in a vacuum with initial velocities 2v and v respectively collide with each other head on as shown. After the collision, the ball of mass m rebounds to the left with velocity v. What is the loss of kinetic energy in the collision

Answer 1

answer : 9/4 mv²

from law of conservation of linear momentum,

initial momentum = final momentum

or, m × 2v + 2m × -v = m × (-v) + 2m × vf

or, 0 = - mv + 2mvf

or, vf = v/2

hence, final velocity of the ball of mass 2m = v/2

now, initial kinetic energy = 1/2 m(2v)² + 1/2 (2m)v² = 2mv² + mv² = 3mv²

final kinetic energy = 1/2 mv² + 1/2 (2m)(v/2)²

= 1/2 mv² + 1/4 mv²

= 3/4 mv²

so, lose in kinetic energy = initial kinetic energy - final kinetic energy

= 3mv² - 3/4 mv²

= 9/4 mv²

hence, lose in kinetic energy in the collision is 9/4 mv² .