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 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 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
diameter of cylinder
static coefficient of friction
kinetic coefficient of friction
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,
A model rocket is on a cart that is rolling to the right at a speed of . The rocket engine, when it is fired, exerts an vertical thrust on the rocket. Your goal is to have the rocket pass through a small horizontal hoop that is above the ground. At what horizontal distance left of the hoop should you launch?
While at the county fair, you decide to ride the Ferris wheel. Having eaten too many candy apples and elephant ears, you find the motion somewhat unpleasant. To take your mind off your stomach, you wonder about the motion of the ride. You estimate the radius of the big wheel to be , and you use your watch to find that each loop around takes .
a. What are your speed and the magnitude of your acceleration?
b. What is the ratio of your weight at the top of the ride to your weight while standing on the ground?
c. What is the ratio of your weight at the bottom of the ride to your weight while standing on the ground?
A 500 g steel block rotates on a steel table while attached to a 1.2-m-long hollow tube as shown in FIGURE CP8.70. Compressed air fed through the tube and ejected from a nozzle on the back of the block exerts a thrust force of 4.0 N perpendicular to the tube.
The maximum tension the tube can withstand without breaking is 50 N. If the block starts from rest, how many revolutions does it make before the tube breaks?
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