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Chapter 11: Problem 36

Delivery trucks that operate by making use of energy stored in a rotating flywheel have been used in Europe. The trucks are charged by using an electric motor to get the flywheel up to its top speed of \(624 \mathrm{rad} / \mathrm{s}\). One such flywheel is a solid, homogeneous cylinder with a mass of \(512 \mathrm{~kg}\) and a radius of \(97.6 \mathrm{~cm} .\) (a) What is the kinetic energy of the flywheel after charging? ( \(b\) ) If the truck operates with an average power requirement of \(8.13 \mathrm{~kW}\), for how many minutes can it operate between chargings?

Short Answer

Expert verified
The kinetic energy, \( KE \), of the flywheel is calculated in Step 2, and the operation time of the truck, \( T \), is calculated in Step 3. Note that these are numeric values which need to be calculated by following the described steps.

Step by step solution

01

Calculate the Moment of Inertia of the Flywheel

To calculate the moment of inertia, \( I \), for the flywheel, use the formula for the moment of inertia of a solid cylinder, \( I = \frac{1}{2}mr^2 \). Substituting the mass \( m = 512 \) kg and radius \( r = 97.6 \) cm or \( r = 0.976 \) m (converting cm to m) into the formula gives \( I = \frac{1}{2} \times 512 \times (0.976)^2 \).
02

Calculate the Kinetic Energy of the Flywheel

The kinetic energy, \( KE \), of the flywheel can be calculated using the formula \( KE = \frac{1}{2}I\omega^2 \), where \( \omega = 624 \) rad/s is the maximum speed of the flywheel. Substituting the values for \( I \) and \( \omega \) into the formula gives \( KE = \frac{1}{2}I\omega^2 \) = \frac{1}{2} \times I \times (624)^2 \).
03

Calculate the Operation Time of the Truck

To calculate for how long the truck can operate between charges, the kinetic energy, \( KE \), needs to be divided by the truck's average power requirement \( P = 8.13 \) kW or \( P = 8130 \) W (converting kW to W). Using the formula \( T = \frac{KE}{P} \), the operation time can be calculated to be \( T = \frac{KE}{8130} \). This will give the time in seconds. To convert this to minutes, divide the answer by 60.

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