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

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