Centripetal Motion

Question

While flipping through channels on your TV, you see a circus show in which a woman drives a motorcycle around the inside of a vertical ring. You observe that she ensures that she goes around at a constant speed and that it takes her 4.0 seconds to make a full loop when she is going at her slowest. If she is going at the minimum speed for this stunt to work, the motorcycle is just barely touching the ring when she is upside down at the top. Calculate the height of the ring.

Answer 1

The key here is that if she is going at minimum speed, she is almost about to lose contact with the ring and fall off it at the top of the circle. The ring is providing zero normal force, so the force of gravity alone provides the centripetal force.

mg = mv²/r, so g = v²/r.

You also know that she travels one circumference in 4 seconds, so v = dist / time = 2πr/4

Substitute that for v, and solve for r.

Remember that the height of the ring is the diameter, not the radius.

Answer 2

If we use energy equation 22

The minimum KE at the bottom of the ring has to be

1/2MV₁²

= Mg(2R) + 1/2 MV₂²

Where V1 is Speed at bottom of the ring of Radius R and V2 is speed of object at top of the ring

Also

(MV₂²) /R = Mg(2R)

From these two equations calculate 2R , Which is height ( Plug in values in these equations0 to get H = 2R