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Chapter 6: Problem 34

A horse plows a 200 -m-long furrow in 5.0 min, exerting a \(750-\mathrm{N}\) force. Find its power output, measured in watts and in horsepower.

Short Answer

Expert verified
The power output of the horse is 500 Watts or approximately 0.67 horsepower.

Step by step solution

01

Convert time to seconds

The time that the horse takes to plow the furrow is given in minutes, but in our power formula, the time needs to be in seconds. Since 1 minute equals to 60 seconds, then \( 5.0 \) minutes will equal to \(5.0*60 =300\) seconds.
02

Calculate the work done

The work done, represented by W, is calculated by multiplying the force by the distance. The force, F, is \(750 \,N\) and the distance, d, is \( 200\,m\). So the work done is \(W = F * d = 750\,N * 200\,m = 150000\, N.m =150000\,J\). The unit changes to Joules (J) because work is measured in Joules.
03

Calculate the Power in Watts

The power is calculated by dividing the work done by the time. Substituting the values from the previous steps, we get \(P=\frac{W}{t}=\frac{150000\,J}{300\,s}= 500\,W\). Thus, the power output of the horse is 500 Watts.
04

Convert Power from Watts to Horsepower

To convert from Watts to horsepower, divide the number of Watts by 746, since 1 horsepower is equivalent to 746 Watts. So, \(500\,W = \frac{500}{746} \approx 0.67 \,hp\).

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