**30. The drawing shows a baggage carousel at an airport. Your suitcase has not slid all the way down the slope and is going around at a constant speed on a circle (r = 11.0 m) as the carousel turns. The coefficient of static friction between the suitcase and the carousel is 0.760, and the angle q in the drawing is 36.0°. How much time is required for your suitcase to go around once?

First Free Body Diagram

Now sum forces

 

 

 

 

 

 

We will assume max static friction since we are trying to find the time it takes for the luggage to move around the carousel.

 

From diagram we can see

 

However, things are a bit different for normal force components.  Again look at diagram.

 

 

Now we plug these components into the two sum of the force equations

The y equation then gives us

 

 

 

So we have the normal force.

Now we consider the x component

 

 

Now plug in for N

 

 

Rearrange and cancel the masses

Factor out a cos (q)

 

 

Now solve for T

 

 

 

 

 

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This page last updated on January 11, 2020