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...

 

[tomcue]

I would first clarify the problem statement and make sure all the necessary information is provided. It is unclear if the suitcase is stationary on the carousel or already in motion. I would also ask for clarification on the "constant speed" mentioned in the problem.

Assuming the suitcase is initially stationary and starts moving due to the rotation of the carousel, the angle and coefficient of static friction would not affect the time required for one revolution. The velocity of the suitcase would depend on the radius of the carousel and the period of motion, which can be calculated using the given equation.

However, if the suitcase is already in motion and the constant speed mentioned in the problem refers to the speed of the suitcase, then the angle and coefficient of friction would play a role in determining the period of motion. In this case, I would use the equations for centripetal force and friction force to calculate the period of motion.

In either case, more information is needed to accurately calculate the time required for one revolution of the suitcase. It would be helpful to know the initial conditions of the suitcase (stationary or in motion) and the speed of the carousel.