Question

A ball with a mass of `14 kg` moving at `15 m/s` hits a still ball with a mass of `17 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

`12.353m//s and 278J`

Explanation:

The Principle of Conservation of Linear Momentum states that total linear momentum is always conserved in each direction.

Application of the principle of conservation of linear momentum :

`vecp_i=vecp_f`, where `vecp=mvecv`.

`therefore (m_1v_1+m_2v_2)_i=(m_1v_1+m_2v_2)_f`

`therefore(14xx15)+(17xx0)=(14xx0)+(17v)`

`thereforev=12.353m//s`.

Total `(E_k)_i=1/2mv^2`

`=1/2xx14xx15^2=1575J`.

Total `(E_k)_f=1/2xx17xx12.353^2=1297J`.

`therefore E_k` lost in collision is `1575-1297=278J`.

This energy is lost from t he mechanical system and converted into other forms of energy like heat. Hence the collision is termed to be inelastic since kinetic energy is not conserved.