Question

A train car with a mass of 10 kg and speed of 10 m/s is traveling to the right. Another train car with an unknown mass is stationary. After the collision, the 10 kg train car is now moving at 5 m/s and the second train is movingat 25 m/s.Find the unknown mass.

Answer 1

From the Law of Conservation of Linear Momentum, we know that:

`m_1v_1+m_2v_2=m_1v_1^(\prime)+m_2v_2^(\prime)`

Where v₁, v₂ are the initial velocities of masses m₁ and m₂ respectively, and v₁', v₂' are their final velocities.

In the given problem, the mass of the second particle is unknown. Isolate m₂ from the equation:

`m_2=(m_1(v_1^(\prime)-v_1))/((v_2-v_2^(\prime)))`

Replace the data into the equation to find m₂:

`\begin{gathered} m_1=10kg \\ v_1=10(m)/(s) \\ v_1^(\prime)=5(m)/(s) \\ \\ m_2=\text{ unknown} \\ v_2=0 \\ v_2^(\prime)=25(m)/(s) \end{gathered}`

The initial velocity of the second particle is 0 because the problem says it is stationary.

`m_2=((10kg)(5(m)/(s)-10(m)/(s)))/((0-25(m)/(s)))=2kg`

Therefore, the mass of the second train car is 2kg.