Answer to Question #299642 in Classical Mechanics for mafydre

Question

A railway truck of 100 kg mass travelling with a velocity of 7 ms collides with a second truck of 200 kg mass and the two couple automatically and move off together. Calculate the velocity of the coupled trucks, and the energy lost to the system, if the second truck has a speed of 5 ms (al in the same direction, (b) in the opposite direction and ic) is initially stationary

Answer 1

Given:

$m_1=100\:\rm kg$

$v_1=7\:\rm m/s$

$m_2=200\:\rm kg$

$v_2=5\:\rm m/s$

(a) The law of conservation of momentum

$$m_1v_1+m_2v_2=(m_1+m_2)v$$ $$v=\frac{m_1v_1+m_2v_2}{m_1+m_2}=\frac{100*7+200*5}{100+200}=5.7\:\rm m/s$$

(b) The law of conservation of momentum

$$m_1v_1-m_2v_2=(m_1+m_2)v$$ $$v=\frac{m_1v_1-m_2v_2}{m_1+m_2}=\frac{100*7-200*5}{100+200}=-1.0\:\rm m/s$$