What fraction of its mechanical energy is lost in each bounce, if a ball bounces to 80% of its original height?
Let the ball fall from height h then, Kinetic energy of ball at the time of just striking the ground = Potential energy of ball at height h, K = mgh Similarly, on rebounding the ball moves to a maximum height h’, then kinetic energy will be K’ = mgh’ Loss of kinetic energy K – K’ = mgh – mgh’ = mg (h –h’) = mg (h – 80/100h) = mgh x (0.2) Fractional loss in K.E. of ball in each re = mgh x (0.2)/mgh = 0.2 = 0.2 x 100% = 20%
kinetigh energy
