Answer to Question #299244 in Classical Mechanics for Mafydre

Question

A body of 4kg mass travelling at 8m/s² collides with a stationary body of mass 12kg, both being constrainted in their motion by the same frictionless guides. Find their velocities and loss of kinetic energy, if coefficient of restitution is 1 and (b) if it is 0.5

Answer 1

Given:

$v_1=8\:\rm m/s$

$m_1=4.0\:\rm kg$

$v_2=0$

$m_2=12\:\rm kg$

(a) $e=1$

$|v_1'-v_2'|=|v_1-v_2|=8$

Hence

$$m_1v_1=m_1v_1'+m_2(8-v_1')$$

$$4*8=4v_1'+12(8-v_1')$$

$v_1'=8\:\rm m/s$

$v_2'=0$

The loss of kinetic energy is zero.

(b) $e=0.5$

$|v_1'-v_2'|=0.5|v_1-v_2|=4$

Hence

$$m_1v_1=m_1v_1'+m_2(v_1'-0.5v_1)$$

$$4*8=4v_1'+12(v_1'-4)$$

$v_1'=5\:\rm m/s$

$v_2'=1\:\rm m/s$

The loss of kinetic energy

$$\Delta E=4*8^2/2-(4*5^2/2+12*1^2/2)$$

$\Delta E=72\:\rm J$