Question

The coefficient of the restitution of an object is defined as the ratio of its outgoing to incoming speed when the object collides with a rigid surface. For an object with a coefficient of 0.72, what fraction of the object's kinetic energy is lost during a single collision?

Answer 1

Answer:

48.16 %

Explanation:

coefficient of restitution = 0.72

let the incoming speed be = u

let the outgoing speed be = v

kinetic energy = 0.5 x mass x $x velocity^{2}$

• incoming kinetic energy = 0.5 x m x $x u^{2}$

     

•  coefficient of restitution =$\frac{v}{u}$

       0.72 =$\frac{v}{u}$

       v = 0.72u

        therefore the outgoing kinetic energy = 0.5 x m x $(0.72u)^{2}$

        outgoing kinetic energy = 0.5 x m x $0.5184 x u^{2}$

        outgoing kinetic energy = 0.5184 (0.5 x m x $x u^{2}$)

recall that 0.5 x m x $x u^{2}$ is our incoming kinetic energy, therefore

outgoing kinetic energy = 0.5184 x (incoming kinetic energy)

from the above we can see that the outgoing kinetic energy is 51.84 % of the incoming kinetic energy.

The energy lost would be 100 - 51.84 = 48.16 %