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Q.49

Expert-verified
Found in: Page 201

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

In an old-fashioned amusement park ride, passengers stand inside a-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 suddenlydrops 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 to and a kinetic coefficient in the range to A sign next to the entrance says “No children under allowed.” What is the minimum angular speed, in rpm, for which the ride is safe?

The minimum angular speed is

See the step by step solution

Step 1: Given information

diameter of cylinder

mass

static coefficient of friction

kinetic coefficient of friction

Step 2: calculation of minimum angular speed

The force of static friction must be no lower than the weight of the person.

The normal force that cylinder wall applies to person is equal to the centripetal force and it is given by,

The friction force that keeps the person from sliding down is given by,

The weight of the person is given by

When the net force is zero, we got,

Use the lowest coefficient of static friction in the above equation , to get the minimum speed.

The minimum angular speed is given by,