Question

A 0.36-kg cart and a 0.11-kg cart are held together with a compressed spring between them. When they are released, the 0.36-kg cart moves at 1.1 m/s to the right.

.How much elastic potential energy was stored in the spring before the release?

Answer 1

Let m₁=0.36 kg and m₂=0.11 kg

Let x be the compression in the spring, and V₁ abd V₂ be the velocities of m₁ and m₂ respectively

Since the spring is at rest initially the velocity of the center of mass (V_cm) of the system is zero. Velocity of center of mass is given by the following expression

Since V_cm=0

and It is said that the mass m₁ moves to the right with velocity V₁=1.1 m/s

(-ve because m2 moves towards left side)

Since m₁and m₂were at rest initially their initial velocities are zero. If x is the initial compression in the spring according to conservation of energy this energy must be transfered to m₁and m₂in the form of kinetic energy. Due to this they move with velocities V₁ and V₂. Now, using conservation of energy, we can calculate initial elastic energy U stored in the spring. Which is as follows

is the elastic energy stored in the spring initially (before the release).