Question

# 1.) Starting from rest, a basketball rolls from the top to the bottom of a hill,...

1.) Starting from rest, a basketball rolls from the top to the bottom of a hill, reaching a translational speed of 5.3 m/s. Ignore frictional losses. (a) What is the height of the hill? (b) Released from rest at the same height, a can of frozen juice rolls to the bottom of the same hill. What is the translational speed of the frozen juice can when it reaches the bottom?

2.) A bowling ball encounters a 0.760-m vertical rise on the way back to the ball rack, as the drawing illustrates. Ignore frictional losses and assume that the mass of the ball is distributed uniformly. The translational speed of the ball is 7.86 m/s at the bottom of the rise. Find the translational speed at the top.

3.) Two spheres are each rotating at an angular speed of 24.8 rad/s about axes that pass through their centers. Each has a radius of 0.280 m and a mass of 1.47 kg. However, as the figure shows, one is solid and the other is a thin-walled spherical shell. Suddenly, a net external torque due to friction (magnitude = 0.450 N · m) begins to act on each sphere and slows the motion down. How long does it take (a) the solid sphere and (b) the thin-walled sphere to come to a halt?