Answer to Question #170217 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

Answer

Given data

$u_1=24m/s$

$u_1=-12m/s$

$m_1=2kg\\m_2=1kg$

Initial momentum

$P_i=m_1u_1+m_2u_2=48-12\\=36kg-m/sec.$

Velocitu after collosion

$v_1=\frac{P_i+em_2(u_2-u_1) }{m_1+m_2}$

$v_2=\frac{P_i+em_2(u_1-u_2) }{m_2+m_1}$

a)putting all value

e=2/3

$v_1=\frac{36+2/3\times1(-12-24) }{2+1}=4m/s$

$v_2=\frac{36+2/3\times1(24+12) }{2+1}=16m/s$

b) balls stick together

$P_i=(m_1+m_2) v$

$36=(2+1) v$

$v=12m/sec$

c) perfectly elastic e=1

$v_1=\frac{36+2/3(-12-24) }{2+1}=0m/s$

$v_2=\frac{36+(24+12) }{2+1}=24m/s$