A ball with an initial velocity of 8.00 m/s rolls up a hill without slipping. Treating the ball as a spherical shell, calculate the vertical height it reaches. (b) Repeat the calculation for the same ball if it slides up the hill without rolling.
Step-by-step solution Step 1 of 3 The ball is similar to a spherical shell and the rotational kinetic energy is converted into the potential energy of the ball, which is equated as, Step 2 of 3 (a) Kinetic energy of the ball is, Here, is the moment of inertia of the ball and is the angular velocity of the ball. The moment of inertia of the spherical shell (ball) is, Here is the mass of the ball, is the radius of the shell, The rotational kinetic energy of the ball is equal to the potential energy. Also the linear velocity is given as, The potential energy of the ball after getting the vertical height is, Here is the gravitational acceleration of the ball, is the height of the ball. Substitute, the kinetic energy and potential energy of the ball and 8m/s for v as, So, the height attained by the ball is .