Impulse Physics

Question

As shown in the figure below, two blocks (m₁ and m₂) are each released from rest at a height of h = 3.73 m

 on a frictionless track and when they meet on the horizontal section of the track they undergo an elastic collision.

If m₁ = 2.50 kg

 and m₂ = 4.45 kg,

 determine the maximum heights (in m) to which they rise after the collision. Use the coordinate system shown in the figure.

Answer 1

The steps:

1. find the potential energy for each block. PE = force of gravity times height
2. The PE is converted to kinetic energy (KE) after the blocks are moving horizontally. KE = 1/2 * m *v² . Use the KE for each block to find the velocity
3. Since there is an elastic collision, both momentum and energy will be conserved. Based on this, find the velocity of each block after the collision. Use the velocity to find the kinetic energy.
4. Recognize that the KE of each block is converted back to Potential Energy (PE) by the time the blocks stop moving. From the PE, get the final height of each block

I have a hunch that there may be a shortcut--just based on the ratio of the masses. But, I have not worked through the numbers