Answer to Question #169244 in Mechanics | Relativity for April

Question

A 1-kg ball moving at a velocity of 12 m/s collides head-on with a 2-kg ball moving at 24 m/s in the opposite direction. Calculate the velocity of each ball after collision if (a) e = 2/3, (b) the balls stick together, and (c) the collision is perfectly elastic.

Answer 1

a)

$v_1=u_1-(1+e)\frac{m_2}{m_1+m_2}(u_1-u_2),$

$v_2=u_2+(1+e)\frac{m_1}{m_1+m_2}(u_1-u_2),$

$v_1=12-\frac 53\cdot\frac{2}{3}\cdot(12+24)=-28~\frac ms,$

$v_2=-24+\frac 53\cdot \frac 13\cdot(12+24)=-4~\frac ms.$

b)

$v=\frac{m_1u_1+m_2u_2}{m_1+m_2},$

$v=\frac{1\cdot 12-2\cdot 24}{1+2}=-12~\frac ms.$

c)

$v_1=\frac{2m_2u_2+u_1(m_1-m_2)}{m_1+m_2},$

$v_2=\frac{2m_1u_1+u_2(m_2-m_1)}{m_1+m_2},$

$v_1=\frac{2\cdot 2\cdot(-24)+12\cdot(1-2)}{1+2}=-36~\frac ms,$

$v_2=\frac{2\cdot 1\cdot 12-24\cdot(2-1)}{1+2}=0~\frac ms.$