Question

If the projectile rebounds upon impact instead of sticking to the pendulum, how would the vertical rise of the pendulum compare to the value obtained when the two move together? Give an explanation.

Answer 1

Consider a projectile of mass m moving with a velocity v strikes the pendulum and rebounds with same velocity in the opposite direction.

Let us consider the mass of pendulum be m moves with velocity v' after collision

By conservation of momentum

mv=mv'+(-mv) {As it changes direction after collision}

v'=2v

When the pendulum rises to height h it's kinetic energy is converted in potential energy

Applying conservation of energy,

1/2mv'²=mgh

h= 1/2v'²/g=2v²/g

Condition 2: If projectile sticks to it

Let us consider the mass of pendulum be m moves with velocity v' with projectile sticked to it after collision

By conservation of momentum

mv= (m+m)v'

v'= v/2

When the pendulum rises to height h it's kinetic energy is converted in potential energy

Applying conservation of energy,

1/2(m+m)v'²=(m+m)gh

h= v'²/2g= v²/8g

By comparing both the heights we can conclude that the vertical rise of the pendulum is more when a projectile rebounds.