   Chapter 7, Problem 71AP

Chapter
Section
Textbook Problem

(a) 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 20.0° with the horizontal. A 30.0-kg piece of luggage is placed on the carousel, 7.46 m from the axis of rotation. The travel bag goes around once in 38.0 s. Calculate the force of static friction between the bag and the carousel. (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 7.94 m from the axis of rotation. The bag is on the verge of slipping as it goes around once every 34.0 s. Calculate the coefficient of static friction between the bag and the carousel.

(a)

To determine
The force of static friction.

Explanation

Given info: Mass of the luggage (m) is 30.0 kg. Distance between the luggage and axis of rotation (r) is 7.46 m. The time taken for completing one circle (T) is 38.0 s.

Explanation:

The free body diagram is,

From the diagram,

fscosθNsinθ=4π2mrT2

fssinθ=mgNcosθ

• fs is the force of static friction.
• N is the normal force.
• g is the acceleration due to gravity.

From the above equations,

fs=m[gsinθ+4π2rcosθT2]

Substitute 30

(b)

To determine
The co-efficient of static friction.

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