Question

A ball with a mass of `5 kg` moving at `8 m/s` hits a still ball with a mass of `21 kg`. If the first ball stops moving, how fast is the second ball moving? How much kinetic energy was lost as heat in the collision?

Answer 1

The velocity of the second ball is `=1.905ms^-1` and the energy lost is `=121.9J`

Explanation:

We have conservation of momentum

`m_1u_1+m_2u_2=m_1v_1+m_2v_2`

The mass `m_1=5kg`

The mass `m_2=21kg`

The velocity of the first ball is `u_1=8ms^-1`

The velocity of the second ball is `=v_1ms^-1`

Therefore,

`5*8+21*0=5*0+21*v_2`

`40+0=0+21v_2`

`v_2=40/21=1.905ms^-1`

The kinetic energy before the collision is

`KE_1=1/2m_1u_1^2=1/2*5*8^2=160J`

The kinetic energy after the collision is

`KE_2=1/2m_2v_2^2=1/2*21*(40/21)^2=38.1J`

The energy lost as heat is

`DeltaKE=KE_1-KE_2=160-38.1=121.9J`