Problem 5 A bowling ball that has an 10- cm radius and a 7.2- kg mass is rolling

Question

Problem 5A bowling ball that has an 10-cm radius and a 7.2-kg mass is rolling without slipping at 9.0 m/s on a horizontal ball return. It continues to roll without slipping up a hill to a height h before momentarily coming to rest and then rolling back down the hill. Model the bowling ball as a uniform sphere. (a) Find the maximum height h. [Hint: initially it has linear kinetic energy and rotational kinetic energy and no potential energy if reference level is chosen as ground. Finally it only has potential energy]

Explanation / Answer

inertia of the ball = (2/5)*m*r^2 = (2/5)*7.2 * 0.1^2 = 0.0288 kg m^2

initial angular speed = velocity / radius = 9 / 0.1 = 90 rad / sec

intia;l totoal energy = kinetic + rotation

= 0.5 *7.2 * 9^2 + 0.5*0.0288* 90^2 = 408.24 J

so.. 7.2 * 9.8* h = 408.24

so h = 5.7857 m

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