As a gasoline engine operates, a flywheel turning with the crankshaft stores energy after each fuel explosion, providing the energy required to compress the next charge of fuel and air. For the engine of a certain lawn tractor, suppose a flywheel must be no more than 18.0 cm in diameter. Its thickness, measured along its axis of rotation, must be no larger than 8.00 cm. The flywheel must release energy 60.0 J when its angular speed drops from 800 rev/min to 600 rev/min. Design a sturdy steel (density 7.85 × 103 kg/m3) flywheel to meet these requirements with the smallest mass you can reasonably attain. Specify the shape and mass of the flywheel.
The design of sturdy steel flywheel with the small mass and specify it shape.
Answer to Problem 10.88CP
The shape of the flywheel is hollow cylinder of inner radius
Explanation of Solution
The diameter of the flywheel must be no more than
From the law of energy conservation,
Here,
Write the expression for the initial rotational energy of the flywheel is,
Here,
Write the expression for the final rotational energy of the flywheel is,
Here,
Substitute
Substitute
Formula to calculate the outer radius of the hollow cylinder is,
Here,
Substitute
For large energy storage by the moment of inertia of flywheel must be large but the mass should be small as much as possible for design to fulfill this requirement the mass should place as far away from the axis as possible to increase the moment of inertia.
Let choose a hollow cylinder to make the flywheel of
Formula to calculate the moment of inertia of the flywheel is,
Here,
Write the expression for the moment of inertia of the disk is,
Here,
Assume the radius of the disk is equal to the outer radius of the hollow cylinder.
Write the expression for the moment of inertia of the hollow cylinder is,
Here,
Substitute
Write the expression for the mass of the hollow cylinder wall is,
Here,
Write the expression for the mass of the disk is,
Here,
Substitute
Substitute
Solve the equation further,
Formula to calculate the mass of the flywheel is,
Substitute
Conclusion:
Substitute
Therefore, shape of the flywheel is hollow cylinder of inner radius
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Chapter 10 Solutions
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
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