Essential University Physics: Volume 1 (3rd Edition)

Published by Pearson
ISBN 10: 0321993721
ISBN 13: 978-0-32199-372-4

Chapter 10 - Exercises and Problems - Page 187: 71


It reaches specifications for the time to start up, starting up in 53 seconds, but it does not have 96 percent efficiency.

Work Step by Step

We see how long it takes to get to 17 rpm: $\alpha=\frac{\tau}{I}=\frac{896,000\ Nm}{2.65\times10^7 \ kgm^2}=.034\ rads/s^2$ 17 rpm equals 1.78 radians per second, so it follows: $\Delta t =\frac{1.78\ rads/s}{.034\ rads/s^2}=53 \ seconds $ We now see about efficiency specifications: We find the power: $P=\frac{I\omega^2}{2t}=\frac{2(2.65\times10^7)(1.78)}{2(53)}=8.96\times10^5$ 96 percent of 1.5 is 1.41, not .896, so the turbine is not meeting efficiency specifications.
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