Concept explainers
(a)
The force of static friction exerted by the carousel on the bag.
(a)
Answer to Problem 47AP
The static
Explanation of Solution
Write the expression for the angular speed of the luggage as.
Here,
Write the expression for the angular speed of the luggage in terms on linear speed as.
Here,
Substitute
Simplify the above expression for
Write the expression for centripetal acceleration for luggage as.
Here,
If the luggage carousel is steadily rotating about its vertical axis then three forces act on the luggage. The static friction force acts along the inclined metallic surface in an outward direction, normal reaction force exerts by the metallic surface on the luggage in normal to the metallic plane and force due to weight acts downward.
As the luggage is rotating in a horizontal plane so centripetal acceleration will acts in
The forces act on the luggage on luggage carousel as shown below.
Write the expression corresponding to Newton’s second law of motion in
Substitute
Multiply
Simplify the equation (VII).
Here,
Write the expression corresponding to the condition of equilibrium in
Re-arrange the terms.
Multiply
Substitute
Simplify the above expression for
Conclusion:
Substitute
Substitute
Thus, the static friction force exerted by the carousel on the bag is
(b)
The coefficient of static friction between the bag and the carousel.
(b)
Answer to Problem 47AP
The coefficient of static friction between the bag and the carousel is
Explanation of Solution
Multiply equation (VI) by
Simplify the above expression for
Multiply
Substitute
Simplify the above expression for
Write the expression for the coefficient of static friction as.
Here,
Conclusion:
Substitute
Substitute
Substitute
Thus, the coefficient of static friction between the bag and the carousel is
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Chapter 6 Solutions
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