How Fast Does Your Suitcase Travel on a Baggage Carousel?

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SUMMARY

The discussion focuses on calculating the velocity of a suitcase on a baggage carousel inclined at 36 degrees, with static friction characterized by a coefficient of 0.760. The user presents equations for normal force (Fn), maximum static friction (Fsmax), and centripetal force (Fc), but struggles to progress in solving for Fc. Key equations include ΣFx and ΣFy, which involve resolving forces and summing components to find the maximum speed where friction equals the parallel forces acting on the suitcase.

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  • Understanding of static friction and its coefficient
  • Knowledge of centripetal force and its calculation
  • Familiarity with resolving forces into components
  • Basic principles of Newton's laws of motion
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A suitcase on a baggage carousel is spinning around at an unknown velocity. The carousel has an angle of 36 degrees above horizontal. The suitcase is held in place by static friction with a coefficient of 0.760. Find the velocity.

Eqn's
Fn = mg | Fsmax = µsmg | Fc = mV²/r

I get as far as this, and I am stuck as to what to do next.
I need to find Fc

ΣFx = -Fn cos54 + Fs cos36 = mV²/r

ΣFy = Fn sin 54 + Fs sin36 - mg = 0

Where do I go next? My prof tried to explain it to me but it didn't click, I am a step-by-step learner! Thanks all.
 
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I presume you were given the radius of this carousel as well? There is a lot of resolving components summing forces. There should be a normal component from the weight and the centrifugal force and a component parallel to the carousel from bot those forces. To find the max speed the friction must be equal to the parallel forces. The weight and the centrifugal force will act in the opposite direction however.