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Example 9-15

Example 9-15 - moment of inertia The...

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Example 9-15 Stopping the Wheel The specifications for the London Eye include that it be able to brake to a stop so that the  passenger compartments move no more than 10 m during braking. The operating speed of the  135-m-diameter 1600-tonne wheel is 2.0 rev/h. (One tonne equals 1000 kg.) A picture of the  wheel can be found at the beginning of this chapter. ( a ) Estimate the torque that is required to  stop the wheel so the rim travels 10 m during the braking. ( b ) Assuming that the braking force is  applied at the rim, what is the magnitude of the breaking force? PICTURE  The work done on the wheel is equal to its change in kinetic energy. Use  ( Equation       9-     24 ) to calculate the work in terms of the torque. Almost all of the mass is near the perimeter of the  wheel (see the picture on the first page of this chapter). This suggests a way to estimate the 
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Unformatted text preview: moment of inertia. The braking force can be found from the torque. SOLVE ( a ) 1. Set the work done equal to the change in kinetic energy: Answer: 2. Using ( Equation 9-24 ), relate the work to the torque and the angular displacement: Answer: 3. Using ds = r d θ ( Equation 9-2 ), relate the angular displacement to the stopping distance s : Answer: 4. The mass is concentrated near the rim of the wheel, so I ≈ mr 2 : Answer: 5. Substitute into the step-1 result and solve for the torque. The initial angular velocity is 2.0 rev/h = 3.49 × 10−3 rad/s: Answer: ( b ) 1. The line of action of the braking force is tangent to the rim, so the moment arm is equal to the radius of the wheel. Answer:...
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Example 9-15 - moment of inertia The...

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