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Chapter 6: Problem 32

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 0.67 horsepower.

Step by step solution

01

Calculation of Work Done

The work done by the horse in plowing the field can be calculated using the formula \( \text{Work = Force x Distance} \). Here, the force exerted by the horse is 750 N and the distance over which the force is exerted is 200 m. Hence, the work done by the horse is \( 750 \, \mathrm{N} \times 200 \, \mathrm{m} = 150,000 \, \mathrm{J} \) (Joules).
02

Calculation of Power in Watts

The power output of the horse can be calculated using the formula \( \text{Power = Work / Time} \). Here, the work done by the horse is 150000 J and the time taken by it is 5.0 minutes, which is equal to \( 5.0 \times 60 = 300 \) seconds. Hence, the power output of the horse is \( 150000 \, \mathrm{J} / 300 \, \mathrm{s} = 500 \, \mathrm{W} \) (Watts).
03

Conversion of Power Output to Horsepower

The power output of the horse can be converted from Watts to horsepower using the conversion factor \( 1 \, \mathrm{horsepower} = 746 \, \mathrm{Watts} \). Hence, the power output of the horse is \( 500 \, \mathrm{W} / 746 \, \mathrm{W/horsepower} = 0.67 \, \mathrm{horsepower} \).

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