14.3: Chapter 14 Homework Problems

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Exercise \(\PageIndex{1}\)

A flywheel with a diameter of 2 ft and a weight of 60 lbs is rotating at a rate of 600 rpm. A brake applies a friction force to the outer rim of the flywheel, bringing it to a stop in 1.5 seconds. Based on this information, what was the average friction force applied by the brake over this time?

A circular flywheel is rotating counterclockwise at 600 rpm. A brake at the rightmost edge of the circle, whose location does not change over time, applies a braking force whose direction points toward the bottom of the page. — Figure \(\PageIndex{1}\): problem diagram for Example \(\PageIndex{1}\). A brake that is fixed in place applies a tangent frictional force to the outer rim of a rotating flywheel wheel.

Solution: \(F_{brake} = 39.01 \ lbs\)

Exercise \(\PageIndex{2}\)

A ring-shaped space station can be approximated as a thin ring 60 meters in diameter with a mass of 500,000 kg. Centrifugal acceleration of the spinning station will be used to simulate gravity.

To simulate the acceleration of Earth (9.81 m/s²), how fast will the station need to be spinning?
If two thrusters each capable of exerting 10 kN of force will be used to get the station up to this speed, how long will we need to run the thrusters?

A ring-shaped space station is rotating counterclockwise due to the force provided by two thrusters, one located on the rightmost outer edge of the ring and the other on the leftmost outer edge of the ring. The thruster on the right exerts a force that points towards the top of the page, and the thruster on the left exerts a force of the same magnitude in the opposite direction. — Figure \(\PageIndex{2}\): problem diagram for Exercise \(\PageIndex{2}\). A ring-shaped space station is rotating counterclockwise, due to thrust forces in opposite directions provided by two thrusters on opposite sides of the ring.

Solution

\(\omega_f = 0.571 \ \frac{rad}{s}\)

\(t_{thrust} = 428.25 \ s\)