Calculating Time to Complete One Revolution of Airport Carousel

[gmunoz18]

Homework Statement

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 = 12.8 m) as the carousel turns. The coefficient of static friction between the suitcase and the carousel is 0.760, and the angle in the drawing is 32.6°. How much time is required for your suitcase to go around once?

Homework Equations

v=sqrt(R*g*tan(theta))

2*pi*r

v=sqrt(r*friction*9.8)

The Attempt at a Solution

2*pi*12.8=80.424 meters

v=sqrt(125.44*tan(32.6)

v=sqrt(80.222)= 8.95 m/s


v=sqrt(8.95*.760*9.8)


this is incorrect, i know it has something to do with the frictional force but I am not sure where it goes into play

 

[Doc Al]

Rather than plugging into a formula that neglects friction, analyze the problem using first principles. Identify the forces acting on the suitcase, draw a free body diagram, and apply Newton's laws.