Question

Boyong and Boyet is conducting their experiments on a frictionless surface. They observed that Boyet’s 5-kg ball travelling to the right at 2 m/s collides head-on with the stationary 7.50-kg ball of Boyong. If the collision is (a) elastic and (b) perfectly inelastic, calculate the final velocities of the balls. 

Answer 1

Momentum conservation

$m_1u_1+m_2u_2=m_1v_1+m_2v_2$

Put value

$5\times2+7.50\times0=5v_1+7.50v_2$

$5v_1+7.50v_2=10$

Restitution cofficient

$e=\frac{v_2-v_1}{u_1-u_2}$

Part(a)

For elastic collision

e=1

$v_1-v_2=u_1-u_2$

$v_2-v_1=2$

Equation (1) and (2) we can solve it

$12.20v_2=20\\v_2=1.6m/sec$

Put

value in equation (2)

$v_1=0.4m/sec$

Part(b)

Perfect inelastic

e=0

$v_2-v_1=0$

Momentum conservation

$m_1u_1+m_2u_2=m_1v_1+m_2v_2$

$$5\times2+7.50\times0=5\times v_1+7.50v_2$$

$5v_1+7.50v_2=10$

$v_1=v_2$

$12.50v_1=10$

$v_1=v_2=\frac{10}{12.50}=0.8m/sec$

$v_1=v_2=0.8m/sec$