Interpreting a banked circular motion question

[BOAS]

Hello,

I think I know how to do this question, but i'd really like to check that I'm interpreting what the question means correctly.

Homework Statement

The drawing shows a baggage carousel at the airport. Your suitcase has not slid all the way down the slope and is going around at a constant speed on a circle (r = 11.0m) as the carousel turns. The coefficient of static friction between the suitcase and the carousel is 0.760 and the angle θ of the slope is 36°. How much time is required for your suitcase to go around once?

Homework Equations

The Attempt at a Solution

I can't provide the picture, but it is simply a cone with a slope of 36° to the horizontal with a suitcase partway down the sloped surface.

The question provides a coefficient of static friction but since the suitcase isn't moving relative to the carousel, surely there's no friction, right?


I've drawn free body diagrams and summed my forces in the x and y direction which all boil down to tanθ = v² / rg Which is easily solvable for v and then simple enough to find time period T.

I'm just a bit worried that I haven't used the information about friction in the question, but I can't actually see a reason to...

Thanks!

 

[Tanya Sharma]

You have done it correctly .If the normal force is sufficient to provide the required centripetal acceleration as well as balance the weight,then friction doesn't come in picture .

 

[BOAS]

Awesome, I imagine the coefficient of friction is there to try and catch us out :)

Thank you.

 

[haruspex]

You have done it correctly .If the normal force is sufficient to provide the required centripetal acceleration as well as balance the weight,then friction doesn't come in picture .

If it's anything like the carousels I'm familiar with, it's a cone, not an inverted cone. The slope is the wrong way to provide centripetal acceleration. The static friction is necessary not only to provide the acceleration but also overcome the adverse camber.

 

[BOAS]

Yes, it's a standard carousel and it does make sense about the slope being the wrong way.

f^max = μ_s f_N

Does this act perpendicular to the normal force in the opposite direction of mgsinθ?

And then I need to resolve in the usual manner

 

[haruspex]

Yes, it's a standard carousel and it does make sense about the slope being the wrong way.

f^max = μ_s f_N

Does this act perpendicular to the normal force in the opposite direction of mgsinθ?

And then I need to resolve in the usual manner

Yes.