Question

A 5kg ball moving to the right at a velocity of 2m/s on a frictionless table , collides head on with a stationary 7.50kg ball. Find the final velocities of the balls if the conclusion is ;elastic, or completely inelastic., and also how much energy was lost in the inelastic collision?​

Answer 1

To determine the final velocities in both an elastic and a completely inelastic collision, conservation of momentum is used. For an elastic collision, kinetic energy is also conserved, while for a completely inelastic collision, the objects stick together, and energy is lost.

Step-by-step explanation:

To find the final velocities of the balls after an elastic collision, we use the conservation of momentum and kinetic energy. For a completely inelastic collision, only momentum is conserved and the objects stick together post-collision.

Let the 5kg ball be ball 1 and the 7.50kg ball be ball 2.
Initially, ball 1 has a velocity of 2m/s and ball 2 is stationary. Using the conservation of momentum and kinetic energy, the final velocities (v1' and v2')

Solving these equations simultaneously gives the final velocities.

For completely inelastic collisions, the two objects stick together, so they have a common final velocity (v').
Using momentum conservation, (5kg × 2m/s) = (5kg + 7.50kg) × v'.
Solving for v' gives the final velocity of the combined mass.

The energy lost in the inelastic collision is the difference between the initial and final kinetic energies of the system.