Question

On the planet Gizmo, the inhabitants travel by high speed trains that run on air tracks much like the air track you used in lab. A train car with a mass of 8700 kg is traveling at 11.0 m/s when it strikes a second car moving in the same direction at 2.2 m/s. The two stick together and move off with a speed of 4.00 m/s. What is the mass of the second car?

Answer 1

`m_2=33833.33\ kg`

Step-by-step explanation:

It is given that,

Mass of the train car,
`m_1=8700\ kg`

Initial speed of the train car,
`u_1=11\ m/s`

Initial speed of the second car,
`u_2=2.2\ m/s`

After the collision, both cars stick together and move off with a speed of 4.00 m/s, V = 4 m/s

Let
`m_2` is the mass of the second car. It can be calculated using the conservation of momentum. In case of inelastic collision, after collision both objects move with a common speed.

`m_1u_1+m_2u_2=(m_1+m_2)V`

`m_1u_1+m_2u_2=m_1V+m_2V`

`m_1(u_1-V)=m_2(V-u_2)`

`m_2=(m_1(u_1-V))/((V-u_2))`

`m_2=(8700(11-4))/((4-2.2))`

`m_2=33833.33\ kg`

So, the mass of the second car is 33833.33 kg. Hence, this is the required solution.