Answer to Question #154182 in Classical Mechanics for Zeke

Question

A loaded wagon, the mass of which is 6000 kg, rolls to the right at

2.0 m / s when it collides with an empty freight car, weighing 3000 kg, rolling to the left on the same track at 3.0 m / s. If the cars remain tied together after the collision, what is the speed and direction of the pair of cars after the collision?

Answer 1

Applying the law of conservation of momentum, we have:

$$m_1v_{1i}-m_2v_{2i}=(m_1+m_2)v_f,$$ $$v_f=\dfrac{m_1v_{1i}-m_2v_{2i}}{(m_1+m_2)},$$ $$v_f=\dfrac{6000\ kg\cdot 2.0\ \dfrac{m}{s}-3000\ kg\cdot 3.0\ \dfrac{m}{s}}{(6000\ kg+3000\ kg)}=0.33\ \dfrac{m}{s}.$$

The sign plus means that the pair of cars after the collision move to the right.

Answer:

$v_f=0.33\ \dfrac{m}{s},$ to the right.