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In an old-fashioned amusement park ride, passengers stand
Chapter 8, Problem 38P(choose chapter or problem)
Problem 38P
In an old-fashioned amusement park ride, passengers stand inside a 5.0-m-diameter hollow steel cylinder with their backs against the wall. The cylinder begins to rotate about a vertical axis. Then the floor on which the passengers are standing suddenly drops away! If all goes well, the passengers will “stick” to the wall and not slide. Clothing has a static coefficient of friction against steel in the range 0.60 to 1.0 and a kinetic coefficient in the range 0.40 to 0.70. A sign next to the entrance says “No children under 30 kg allowed.” What is the minimum angular speed, in rpm, for which the ride is safe?
Questions & Answers
QUESTION:
Problem 38P
In an old-fashioned amusement park ride, passengers stand inside a 5.0-m-diameter hollow steel cylinder with their backs against the wall. The cylinder begins to rotate about a vertical axis. Then the floor on which the passengers are standing suddenly drops away! If all goes well, the passengers will “stick” to the wall and not slide. Clothing has a static coefficient of friction against steel in the range 0.60 to 1.0 and a kinetic coefficient in the range 0.40 to 0.70. A sign next to the entrance says “No children under 30 kg allowed.” What is the minimum angular speed, in rpm, for which the ride is safe?
ANSWER:
Step 1 of 2
Here we have to find the minimum angular speed in rpm, for which the ride is safe.
Here,
The radius of the cylinder is,
.
The coefficient of static friction is,
.
In order to keep the thing moving, the frictional force must be equal to the gravitational force.
So,
.
The maximum frictional force is,
The centripetal force will be,
Where N is the normal reaction.