Physics Conservation of Momentum

Question

1. A red ball with a mass of 5 kg sits at rest on the gym floor. YOU roll a blue ball, with a mass of 20 kg, into the red ball. This blue ball is moving at 2 m/s before the collision. After the collision, the blue ball stops moving, and the red ball begins rolling. At what velocity would the red ball be rolling?

In this ignore friction and assume a completely elastic Collison.

Answer 1

This is a conservation of momentum problem.

Recall that Momentum = Mass x Velocity, and that the momentum of a system is the TOTAL momentum of all bodies within the system. We are also given that the collision is elastic, which means there is no loss in kinetic energy, and that we can ignore friction entirely.

Using this information we can set up an equation for the momentum of the red and blue ball system before and after the collision:

m_b = mass of blue ball = 20kg

m_r = mass of red ball = 5kg

V_b1 = initial velocity of the blue ball = 2 m/s

V_b2 = final velocity of the blue ball = 0 m/s

Vr₁ = initial velocity of the red ball = 0 m/s

V_r2 = final velocity of the red ball = ?

The equation:

m_bV_b1 + m_rVr_{1 =} m_bV_b2 + m_rV_r2

Plug in our values:

(20kg * 2 m/s) + (5kg * 0 m/s) = (20kg * 0 m/s) + (5kg * V_r2)

Simplify and solve for V_r2:

V_r2 = (40 kg*m/s)/5kg = 8 m/s

The red ball will have a velocity of 8 m/s after the elastic collision