Question

a train car has a mass of 10,000 kg and is moving at +3.0 m/s. it strikes an identical train car that is at rest. the train cars combine. what is the magnitude of the final velocity of the combined cars? 0 m/s 1.5 m/s 3.0 m/s 6.0 m/s

Explanation:

Step1: Apply conservation of momentum

The initial momentum of the system is given by the momentum of the moving train - car since the other is at rest. The formula for momentum is $p = mv$. Let $m_1=m_2 = 10000$ kg, $v_1 = 3.0$ m/s and $v_2=0$ m/s. The initial momentum $p_i=m_1v_1 + m_2v_2=m_1v_1=(10000)(3.0)=30000$ kg·m/s.

Step2: Calculate final - mass and final - velocity

After the collision, the two train cars combine, so the final mass $m_f=m_1 + m_2=10000 + 10000=20000$ kg. According to the law of conservation of momentum $p_i = p_f$, and $p_f=m_fv_f$. We know $p_i = 30000$ kg·m/s and $m_f = 20000$ kg. Then $v_f=\frac{p_f}{m_f}=\frac{30000}{20000}=1.5$ m/s.

Answer:

1.5 m/s