Concept explainers
(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 piece of luggage having mass 30.0 kg is placed on the carousel at a position 7.46 m measured horizontally from the axis of rotation. The travel bag goes around once in 38.0 s. Calculate the force of staticfriction exerted by the carousel on the bag. (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 another position, 7.94 m from the axis of rotation. Now going around once in every 34.0 s, the bag is on the verge of slipping down the sloped surface. Calculate the coefficient of static friction between the bag and the carousel.
(a)
The force of static friction exerted by the carousel on the bag.
Answer to Problem 6.47AP
The force of static friction exerted by the carousel on the bag is
Explanation of Solution
Given info: The metallic surface of a luggage carousel slopes downward toward outside at an angle
Formula to calculate the centripetal force is,
The horizontal force acting on the bag in horizontal direction is,
Substitute
Here,
Substitute
Draw the free body diagram for the luggage.
From the Figure (1), the component of force in
From the Figure (1), the component of force in
Substitute
Simplify the above equation.
Substitute
Conclusion:
Therefore, the force of static friction exerted by the carousel on the bag is
(b)
The coefficient of friction between the bag and the carousel.
Answer to Problem 6.47AP
The coefficient of friction between the bag and the carousel is
Explanation of Solution
Given info: The metallic surface of a luggage carousel slopes downward toward outside at an angle
Substitute
Calculate the centripetal force for the bag.
Substitute
Calculate the normal force for the bag when it is on the carousel.
Substitute
Formula to calculate the coefficient of friction between the bag and the carousel is,
Substitute
Conclusion:
Therefore, the coefficient of friction between the bag and the carousel is
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