1. A "Gravitron" is an amusement park ride in which riders stand against the wall of a cylindrical room. When the room spins around at a sufficient rate, the floor drops down but the riders remain against the wall without sliding down. a) Thinking carefully about all the forces on a rider, draw a free body diagram for a sample rider. Draw it as a side view. Hint: there are only 3 forces. b) Write down Newton's Second Law for both the x and y directions. The speed the ride must spin is dependent on the coefficient of static friction us (static instead of kinetic, because if everything goes according to plan they won't be sliding down the wall!) and on the radius of the room r. But it can't depend on the mass m of a rider - the speed of the ride isn't changed based on the weights of the riders, after all. c) Solve the two equations you set up in part (b) for the speed v of the ride. Notice that the mass does actually cancel out, as promised. = Plug in some realistic numbers: r = 2.0m and us 0.5. Convert the speed v you find into an "rpm" ting, revolutions per minute. Hint: one revolution is once around the circle. Treat it like a unit onversion from m/s to rev/min.
1. A "Gravitron" is an amusement park ride in which riders stand against the wall of a cylindrical room. When the room spins around at a sufficient rate, the floor drops down but the riders remain against the wall without sliding down. a) Thinking carefully about all the forces on a rider, draw a free body diagram for a sample rider. Draw it as a side view. Hint: there are only 3 forces. b) Write down Newton's Second Law for both the x and y directions. The speed the ride must spin is dependent on the coefficient of static friction us (static instead of kinetic, because if everything goes according to plan they won't be sliding down the wall!) and on the radius of the room r. But it can't depend on the mass m of a rider - the speed of the ride isn't changed based on the weights of the riders, after all. c) Solve the two equations you set up in part (b) for the speed v of the ride. Notice that the mass does actually cancel out, as promised. = Plug in some realistic numbers: r = 2.0m and us 0.5. Convert the speed v you find into an "rpm" ting, revolutions per minute. Hint: one revolution is once around the circle. Treat it like a unit onversion from m/s to rev/min.
College Physics
10th Edition
ISBN:9781285737027
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter4: The Laws Of Motion
Section: Chapter Questions
Problem 32P: Two blocks of masses m1 and m2 (m1 m2) are placed on a frictionless table in contact with each...
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