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problem 1: A curve of radius 120 m is banked at an angle of 18°. At what speed can it be negotiated beneath icy conditions where friction is negligible?

problem 2: The condition of apparent weightlessness can be made for a brief instant when a plane flies over the top of a vertical circle. At a speed of 215 m/s, then find out the radius of the vertical circle that the pilot should use?

problem 3: A motorcycle has a constant speed of 25.0 m/s as it passes over the top of a hill whose radius of curvature is 126 m. The mass of motorcycle and driver is 342 kg. Find out the magnitude of:

a) The centripetal force and
b) The normal force which acts on the cycle.

problem 4: A roller coaster consists of a dip that bottoms out in a vertical circle of radius r. Passengers feel the seat of the car pushing on them with a force equivalent to three times their weight as they go through the dip. If r = 20.0 m, how fast is the roller coaster car traveling at the bottom of the dip?

problem 5: A 2100 kg demolition ball swings at the end of a 15 m cable on the arc of a vertical circle. At lowest point of the swing, the ball is moving at a speed of 7.6 m/s. Find out the tension in the cable.

problem 6: An unbanked curve in the road has a radius of 75.0 m. The greatest speed a motorcycle can encompass without skidding around that curve is 25.0 m/s. The other curve has an identical surface however consists of a radius of 125 m. What is the maximum speed that the motorcycle can have around the second curve devoid of skidding?

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