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
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Please help me with this question : one questions with 3 parts in the image below
Transcribed Image Text: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 µs (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.
d) Plug in some realistic numbers: r = 2.0m and us = 0.5. Convert the speed v you find into an "rpm"
rating, revolutions minute. Hint: one revolution is once around the circle. Treat it like a unit
per
conversion from m/s to rev/min.
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