Q4.4 Power (S)
The force (but not the power) required to tow a boat at constant velocity is proportional to the speed. If a speed of 2.5 mph requires 10 hp, how much horsepower does a speed of 7.5 mph require?Solution
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Solution
The work done in a given time will give the average power. To calculate
the work done, we need to know:
(i) what is the applied force
(ii) over what distance is it applied.
(i) The force applied to do the work to move the boat increases by a factor 3 if the speed increases by a factor 3.
(ii) In a given time, the boat travels 3 times faster, and therefore 3 times further.
Therefore the work done in the same time interval will be 3×3=9 times larger than at 2.5 mph, so 90 hp.