Question

A luggage carousel at an airport has the form of a section of a large cone, steadily rotating about its vertical axis. Its metallic surface slopes downward toward the outside, making an angle of 21.0° with the horizontal. A 37.0 kg piece of luggage is placed on the carousel, 7.10 m from the axis of rotation. The travel bag goes around once in 44.0 s. (a) Calculate the force of static friction between the bag and the carousel. b) (b) The drive motor is shifted to turn the carousel at a higher constant rate of rotation, and the piece of luggage is bumped to a position 7.88 m from the axis of rotation. The bag is on the verge of slipping as it goes around once every 28.20 s. Calculate the coefficient of static friction between the bag and the carousel.

Answer 1

a. gravity down the slope=mgSinTheta
centripetal force : m*v^2/r
friction=gravity down+centripetal

v=2PI r/period

b. same logic, change r, and period.
for coefficent, friction then equals mu*mgCosTheta, solve for mu.

Answer 2

For a I am getting 43 and I don't think that is right and for b I am getting 12 and I don't think that is right either. Are your values any where close to mine?

Answer 3

I erred. centripetal force is directed outward, not down the slope, so
a. gravity down the slope=mgSinTheta
centripetal force : m*v^2/r * cosTheta
friction=gravity down+centripetal

v=2PI r/period

b. same logic, change r, and period.
for coefficent, friction then equals mu*mgCosTheta, solve for mu.