Dynamics of Uniform Circular Motion

[Cheddar]

Homework Statement

A suitcase is on a sloped carousel (slope = 36degrees) with a radius of 11m and a constant speed. The suitcase has not slid all the way down the carousel.The coefficient of static friction between the suitcase and the carousel is 0.76. How much time is required for the suitcase to go around once?

Homework Equations

velocity = 2 * (pi) * r / period of motion

The Attempt at a Solution

Not sure what to do here. 2 unknowns in the equation above. Does the angle even matter?

 

[cepheid]

The Attempt at a Solution

Not sure what to do here. 2 unknowns in the equation above.

Indeed. The period is what you are trying to solve for. Knowing the radius of the circular path taken by the suitcase requires knowing exactly where on the carousel (how far down) the suitcase is sitting. This can be figured out by evaluating the conditions required to keep the suitcase in static equilibrium on the surface of the carousel. So, yes, the angle of slope does matter.

EDIT: On second thought, that makes no sense. Static equilibrium just tells you that the suitcase will remain wherever it is. It doesn't tell you where it is in the first place.

You can verify that the suitcase won't slide at all by comparing the coefficient of static friction to the coefficient of static friction that would be required in order to keep the suitcase in place at that slope. That's all the insight I have right now...