9. You tie a cord to a pail of water, and you swing the pail in a vertical circle of radius 0.600m. What minimum speed must you give the pail at the highest point of the circle if no water is to spill from it?

2. A 45.0 kg boy is initially seated on the top of a hemispherical ice mound of radius 20.0 m. He begins to slide down the ice, with a negligible initial speed. Assume the ice is frictionless. a. At what height does the boy lose contact with the ice. b. What is acting as a radial force?

5. When you whirl a ball on a cord in a vertical circle, you find a critical speed at the top for which the tension in the cord is zero. This is because the force of gravity on the object itself supplies the necessary centripetal force. How slowly can you swing a 2.5 kg ball like this so that it will just follow a circle with a radius of 1.5 m?

In 1959, Daytona Speed was added to the NASCAR racing circuit and introduced 31° banked curves for racing. This allowed stock cars to reach much higher speeds (around 200 mph) during a race. Today the steepest banked curves are found at Talladega Motor Speed Way at 33° with a turn radius of 1100 ft. The flattest track in NASCAR is Hew Hampshire Motor Speed Way with banked curves of 7° with a turn radius of 410 ft. a) Assuming no friction, what are the max speeds (in mph) without slipping toward the outer edge of the track at the Talladega and NH Motor Speedways? b) With friction (assume μs of 1.1 between the tires and the track)?