Centripetal Forces Practice Problems

A 1.0 kg stone is attached to one end of a rope, which has negligible mass. The stone moves in a uniform circular motion in a vertical circle of radius 2.0 m. Calculate the tension at the bottom point, if the tension in the rope is zero at the topmost point.

A 5.0 kg object is attached to one end of a rope, which has negligible mass. The object moves in a uniform circular motion in a vertical circle of radius 2.0 m. Calculate the period of revolution, if the tension in the rope is zero at the topmost point.

You are riding a roller coaster that has a 60 m-diameter circular loop with a top speed of 25 m/s. What is your apparent weight at the bottom of the loop if your mass is 50 kg? What is your apparent weight at the top of the loop if the roller coaster's speed has decreased to 20 m/s?

A 5.0 kg object is attached to one end of a rod which has negligible mass. The object moves in a uniform circular motion in a vertical circle of radius 2.0 m. If the period of revolution is 1.2 s, calculate the speed of the object while it is revolving.

A 55 kg skateboarder is moving down a ramp with a 5.0 m radius of curvature. If at the bottom of the ramp he reaches a speed of 8.0 m/s, what is the upward force acting on him when he is at the bottom of the ramp?

A 50 kg child is riding a Ferris wheel with a 15 m radius and a period of 20 s What is the normal force that the seat exerts on the child at the top of the ride?

A 70 kg person is riding a Ferris wheel with a radius of 40.0 m and a tangential speed of 6.0 m/s. Calculate the normal force exerted on the passenger at the bottom.

In an amusement park, a design of the carousel has two wires, one of which is horizontal, and the seat is attached to them. A horizontal circle of radius 7.50 m is formed by the seat as it swings at a speed of 20.0 rpm (rev/min). Determine the tension in each cable if the seat weighs 200 N and a person weighing 850 N is seated in it.

The merry-go-round at an amusement park is made up of a vertical center shaft with a number of horizontal arms attached to it at the top. The top end of a 7.00 m long cable is attached to an arm, 4.00 m from the central shaft and suspends a seat from the lower end. If the cable holding a seat makes a 60.0° angle with the vertical, find the duration of one swing revolution.

On a smooth floor, a ballet dancer weighing 50 kg is spinning at 3.0 rotations per second while holding outstretched arms. 1.80 meters is the distance from one hand to the other. The average hand weighs about 1.50 percent of the body, per biometric studies. How much force must be applied horizontally by her wrist on her hand?