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Two trolleys are moving in the same direction along a track. Trolley 1 has a momentum of 2 kg m/s and Trolley 2 has a momentum of 6 kg m/s. Trolley 2 catches up to Trolley 1. They collide, stick together and move off with a velocity of 2 m/s. Use the principle of conservation of momentum to work out the combined mass of the trolleys.

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leena

Hi there!

Recall the conservation of momentum:

[tex]\large\boxed{m_1v_1 + m_2v_2 = m_1v_1' + m_2v_2'}}[/tex]

For this type of inelastic collision:

[tex]\large\boxed{m_1v_1 + m_2v_2 = v_f(m_1 + m_2)}}[/tex]

Thus, the initial momentum equal the final momentum if there are no external forces.

We can begin by writing out this problem:

[tex]2 + 6 = v_f(m_1 + m_2)[/tex]

[tex]8 = 2(m_1 + m_2)\\\\m_1 + m_2 = \boxed{4 kg}[/tex]

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