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Chapter 12: Problem 21

Referring to Figure 12.7, examine performance at \(5 \mathrm{~m} / \mathrm{s}\) and at \(10 \mathrm{~m} / \mathrm{s}\), picking a representative power for each in the middle of the cluster of black points, and assigning a power value from the left-hand axis. What is the ratio of power values you read off the plot, and how does this compare to theoretical expectations for the ratio going like the cube of velocity?

Short Answer

Expert verified
Question: The exercise asks us to examine the performance of an object at two different velocities, 5 m/s and 10 m/s, and compare the power values obtained from a figure. Calculate the ratio of the power values and compare it to the theoretical expectations for the ratio going like the cube of the velocity.

Step by step solution

01

Read power values from the plot for the given velocities

For the given velocities (5 m/s and 10 m/s), pick a representative power value from the middle of the cluster of black points. Assign a power value from the left-hand axis corresponding to these velocities.
02

Calculate the ratio of power values

Divide the power value obtained at 10 m/s by the power value obtained at 5 m/s to find the ratio of the power values: \[\text{Power Ratio} = \frac{\text{Power at 10 m/s}}{\text{Power at 5 m/s}}\]
03

Compare calculated ratio with theoretical ratio

The theoretical expectation for the ratio of power values should be the cube of the ratio of velocities. Calculate the theoretical power ratio as follows: \[\text{Theoretical Power Ratio} = \left(\frac{10 \, \text{m/s}}{5 \, \text{m/s}}\right)^3\] Compare the calculated power ratio from Step 2 with the theoretical power ratio obtained above. If both ratios are approximately equal, then the performance observed in the plot aligns with the theoretical expectations.

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