Question

A train car with a mass of 14 kg and speed of 30 m/s is traveling to the right. Another train car with a mass of 26kg is moving with an unknown velocity. After the collision, the 14 kg train car is stuck to the 26 kg train car with a combined velocity of 12 m/s

Answer 1

From the Law of Conservation of Linear Momentum, when two particles get stuck together after a collision, it follows that:

$m_1v_1+m_2v_2=(m_1+m_2)v_f$

In this case, the initial velocity of the second particle is unknown. Isolate it from the equation:

$v_2=\frac{(m_1+m_2)v_f-m_1v_1}{m_2}$

Replace the given data to find the value of v₂:

$\begin{gathered} m_1=14kg \\ v_1=30\frac{m}{s} \\ \\ m_2=26kg \\ v_2=\text{ unknown} \\ \\ v_f=12\frac{m}{s} \\ \\ \Rightarrow v_2=\frac{(14kg+26kg)(12\frac{m}{s})-(14kg)(30\frac{m}{s})}{26kg}=2.3077...\frac{m}{s} \\ \\ \therefore v_2\approx2.3\frac{m}{s} \end{gathered}$

Therefore, the initial velocity of the 26-kg car is approximately 2.3m/s.