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Chapter 10: Problem 77

You're skeptical about a new hybrid car that stores energy in a flywheel. The manufacturer claims the flywheel stores 12 MJ of energy and can supply \(40 \mathrm{kW}\) of power for 5 minutes. You dig deeper and find that the flywheel is a \(39-\) cm-diameter ring with mass \(48 \mathrm{kg}\) that rotates at 30,000 rpm. Are the specs correct?

Short Answer

Expert verified
No, the specs are not correct. The calculated kinetic energy was found to be 8.6072 MJ, which is less than the manufacturer's claim of 12 MJ.

Step by step solution

01

Convert rpm to rad/s

First, convert 30000 rpm to rad/s by multiplying by \( \frac{2\pi}{60} \). Calculating it gives \( \omega = 3141.59 \) rad/s.
02

Calculate moment of inertia

Now, calculate the moment of inertia for the ring using \( I = m r^2 \). Note that the diameter is 39 cm which makes the radius \( 19.5 \) cm or \( 0.195 \) m. Substituting \( m = 48 \) kg and \( r = 0.195 \) m into the moment inertia equation gives \( I = 1.8342 \) kg m\(^2\).
03

Compute kinetic energy

Next, use the kinetic energy formula \( KE = \frac{1}{2} I \omega^2 \) Using the calculated \( \omega \) and \( I \) values, obtain \( KE = 8.6072 * 10^6 \) J or \( 8.6072 \) MJ.
04

Compare with Manufacturer's Claim

Compare the calculated kinetic energy value with the manufacturer's claim of 12 MJ. Since the calculated kinetic energy is less than the manufacturer’s claim, the specs may not be correct.

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