PH 212

Uniform circular motion applications

A person rides on a Ferris wheel of radius r at constant speed v. (Image is exaggerated. Assume the person is on the outer rim of the wheel.)

 

How does the normal force exerted on the rider at the top compare to the normal force on the rider at the bottom?

Consider a car of mass m, going around a curve of radius r at a constant speed v. What is its acceleration?

What assumptions can you make about the system above?

 

X. There is no air resistance.
Y. There is no friction.

 

A. Only X is true.

B. Only Y is true.

C. Both X and Y are true.

D. Neither X nor Y is true.

Now consider a car of mass m, going around a banked curve with a banking angle of q and radius r. What is the speed at which the car can safely negotiate the turn? Assume there is no friction.

Side view

Now consider that there is friction between the tires and road, characterized by a coefficient of friction ms. What are the maximum and minimum speeds possible for the car to negotiate the curve without sliding? Consider a conical pendulum consisting of a ball of mass m on a string of length R at an angle q with the vertical, as pictured. How long does it take for the ball to go around the circle?

A ball of mass m is tied to the end of a string of length L and swung in a vertical clockwise circle. The center of the circle is a distance h above the floor. The ball is swung at the minimum speed necessary to make it over the top without the string going slack. If the string is released at the moment the ball is at the top of the circle, how far to the right does the ball hit the floor?

A ball of mass m is tied to the end of a string of length L and swung in a vertical clockwise circle. At the instant the ball is at angle t as shown, there is a tension T in the string. What is the magnitude and direction of the acceleration of the ball?

A block of mass m slides around an L-shaped track as shown, where the track is an arc of a circle of radius r. There is no friction between the block and the track underneath it, but there is friction characterized by the kinetic coefficient of friction mk between the block and the side of the track. The initial speed of the block is v0. What is the speed of the block at a later time t?