Question

11. A rubber ball is dropped from an initial height h=2m. After each bounce the ball returns to 75% of its previous height. What percent of its maximum potential energy, maximum kinetic energy and maximum speed is lost as the result of the first bounce? 12. A 20 kg rock slides across a rough horizontal surface and eventually stops. Initial velocity of the rock is 10m/s, coefficient of kinetic friction is 0.1. What average thermal power is produced as the rock move? What instantaneous thermal power is produced when rock is 10m away from starting point? Explain why the power is not constant.

Answer 1

Let the ball have mass = 1Kg Initial potential energy = mgh = 1 times 9.8 times 2J = 19.6 J Final potential energy = mg times 0.75h = 1 times 9.8 times 0.75 times 2J = 14.7J change, Delta PE = (19.6 - 14.7) J = 4.9J 4.9/19.6 times 100 = 25% i.e. 25% of its maximum potential energy is lost. This much is also lost from its maximum kinetic energy. Now, 1/2 mv^2 = mgh = > V = squareroot 2gh Initial velocity, V_i = squareroot 2 times 9.8 times 2 m/s = 6.26 m/s Final velocity, V_f = squareroot 2 times 9.8 times 0.75 times 2 m/s = 5.42 m/s \r\n change, Delta V = (6.26 - 5.42) m/s = 0.84 m/s 0.84/6.26 times 100 = 13.41% i.e 13.41% of its maximum velocity is lost.