Question

A van of mass 5,000kg travelling at a velocity of 10 m/s collides with a stationary car. The vehicles move together after the impact at a velocity of 6 m/s. Calculate the mass of the car.

Answer 1

Hi there!

We can use the conservation of momentum for an INELASTIC collision:

$m_1v_1 + m_2v_2 = v_f(m_1 + m_2)$

Let:

m1 = mass of van (5000 kg)

m2 = mass of car (? kg)

v1 = initial velocity of van (10 m/s)

v2 = initial velocity of car (0 m/s)

vf = final velocity of BOTH objects (6 m/s)

We can rearrange and plug in values to solve for m2:

$m_1v_1 + m_2(0) = v_f(m_1 + m_2)\\\\m_1v_1 = v_f(m_1 + m_2)\\\\(5000)(10) = 6(5000 + m_2)$

Solve:

$50000 = 30000 + 6m_2\\\\20000 = 6m_2\\\\m_2 = 20000/6 = \boxed{3333.33 kg}$