Question

9. A child of mas 40kg runs at a speed of 5 m/s and jumps onto a disc shaped merry go round of mass 100 kg and radius 5m. The child lands on the outer edge of the disc when the disc is stationary.. What is the angular speed of the merry go round with the child on it? Was energy lost? If so, how much energy was lost in the process? loo kg 5 he

Answer 1

V = R w w = r/R = 5/5 = 1 rad/s Angular speed = (w) = 1 rad/s from conservation of Angular momentum find Angular momentum w_f = I_cold times w/(I_cold + I_disk) R^2 w_f = 40 times 5^2 (1)^2/(40 times + 00) 5^2 w_f = 0.3 rad/s Initial Energy k_i = 1/2 mv^2 = 1/2 times 40 times 5^2 k = 500 J find energy = 1/4 (40 + 1N) 5^2 times 0.3^2 k_f = 22.5 J loss of energy = -500 + 22.5 lost = 477.5 J