Q1) Circular motion A carnival ride has people stand inside a vertical cylinder with their backs to the wall. The cylinder starts spinning counterclockwise and the riders find that they are “stuck” to the wall and don’t slide down, even when the floor is removed. The ride has a radius of r. The person has a mass of m and is moving with a constant speed of v. The coefficient of static friction between the person and the wall is μs , and kinetic friction μk. The person is only touching the wall, not touching the floor. a) Draw a free body diagram for the person when they are on the left-hand side, as shown. Clearly label all forces. Use the notation used in class. b) What is the magnitude and direction of the acceleration of the person? Give your answer in terms of variables only (r, v, m, μs, μk, and g) c) What is the magnitude of the normal force of the wall on the person? Solve this problem using Newton’s 2nd Law. Show all your work. Give your answer in terms of variables only (r, v, m, μs, μk, and g) d) What is the smallest speed v for which the person will not slide down the wall? Solve this problem using Newton’s 2nd Law. Show all your work. Give your answer in terms of variables only (r, m, μs, μk, and g) e) Suppose that the ride spun clockwise instead of counterclockwise, but the speed was the same. Would the magnitude and direction of the normal force you found in part c) change? If so, how would it change? If not, why not? Briefly (one or two sentences) explain your answer

An Introduction to Physical Science

14th Edition

ISBN:9781305079137

Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Publisher:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Chapter15: Place And Time

Section15.3: Time

Problem 1PQ

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Q1) Circular motion
A carnival ride has people stand inside a vertical cylinder with their
backs to the wall. The cylinder starts spinning counterclockwise and the
riders find that they are “stuck” to the wall and don’t slide down, even
when the floor is removed.
The ride has a radius of r. The person has a mass of m and is moving
with a constant speed of v. The coefficient of static friction between the
person and the wall is μs , and kinetic friction μk. The person is only
touching the wall, not touching the floor.
a) Draw a free body diagram for the person when they are on the left-hand side, as shown.
Clearly label all forces. Use the notation used in class.
b) What is the magnitude and direction of the acceleration of the person?
Give your answer in terms of variables only (r, v, m, μs, μk, and g)
c) What is the magnitude of the normal force of the wall on the person?
Solve this problem using Newton’s 2nd Law. Show all your work.
Give your answer in terms of variables only (r, v, m, μs, μk, and g)
d) What is the smallest speed v for which the person will not slide down the wall?
Solve this problem using Newton’s 2nd Law. Show all your work.
Give your answer in terms of variables only (r, m, μs, μk, and g)
e) Suppose that the ride spun clockwise instead of counterclockwise, but the speed was the
same. Would the magnitude and direction of the normal force you found in part c) change? If
so, how would it change? If not, why not?
Briefly (one or two sentences) explain your answer.

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