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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?

Respuesta :

Answer:

[tex]m_2=33833.33\ kg[/tex]                                                            

Explanation:

It is given that,

Mass of the train car, [tex]m_1=8700\ kg[/tex]

Initial speed of the train car, [tex]u_1=11\ m/s[/tex]

Initial speed of the second car, [tex]u_2=2.2\ m/s[/tex]

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

Let [tex]m_2[/tex] 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.

[tex]m_1u_1+m_2u_2=(m_1+m_2)V[/tex]

[tex]m_1u_1+m_2u_2=m_1V+m_2V[/tex]

[tex]m_1(u_1-V)=m_2(V-u_2)[/tex]

[tex]m_2=\dfrac{m_1(u_1-V)}{(V-u_2)}[/tex]

[tex]m_2=\dfrac{8700(11-4)}{(4-2.2)}[/tex]

[tex]m_2=33833.33\ kg[/tex]

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

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