Centripetal Force Question

[deleted92121]

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I cannot figure this question out for the life of me. I thought I solved it but forgot to use coefficient of static friction. Any help would be grand.

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 = 12.2 m) as the carousel turns. The coefficient of static friction between the suitcase and the carousel is 0.760, and the angle θ in the drawing is 35.6°. How much time is required for your suitcase to go around once?

So far I have the following:

x= mgsinø - µsmgcosø = ma

y = mgcosø - mg = ma

 

[noobtech]

set it up this way:
mg sin35.6 = mv^2/r + .76mg cos35.6
solve for v
d = 2*3.14*r
so t = d/v

 

[deleted92121]

set it up this way:
mg sin35.6 = mv^2/r + .76mg cos35.6
solve for v
d = 2*3.14*r
so t = d/v

I don't think this works because I don't have mass (m) so that would leave me with two unknowns.

 

[rjosh33]

I don't think this works because I don't have mass (m) so that would leave me with two unknowns.

I think noobtech has it right. You can factor out the m on the right side and cancel it, leaving you just the one unknown, v. So, your equation will look like:

mg sin35.6 = m[(v^2/r) + (.76g cos35.6)]

g sin35.6 = (v^2/r) + .76g cos35.6