Question

An empty freight car of mass $m_1=10,000kg$ rolls at speed $u_1=2m/s$ on a level road and collide with a loaded car of mass $m_2=20,000kg$ standing at rest. If the cars couple together, find their speed $V$ after the collision and also the loss in kinetic energy. What should be speed of the loaded car towards the empty car, in order that both be brought to rest by the collision?

Answer 1

By momentum conservation,

$m_1{u}_1=(m_1+m_2)v$

$v=\frac{2}{3}m{s}^{-1}$

Kinetic Energy loss=$\frac{1}{2}{m}_1{u}_1^2-\frac{1}{2}(m_1+m_2)v^2$

$\frac{1}{2}(10000\times 2^2-\left(30000\right){\left(\frac{2}{3}\right)}^2)$

$=\frac{1}{2}\times 10000(4-\frac{4}{3})$

$=\frac{1}{2}\times \frac{8}{3}\times 10000$

$=13333.34J$