Question

In creating his definition of horsepower, James Watt, the inventor of the steam engine, calculated the power output of a horse operating a mill to grind grain or cut wood. The horse walked in a 24-ft diameter circle, making, according to Watt, 144 trips around the circle in an hour.

(a) Using the currently accepted value of 746 watts for 1 horsepower, calculate the force (in pounds) with which Mr. Watt's horse must have been pulling. (See Appendix D for useful conversion factors.)
(b) Calculate the power output, in hp, of a 70-kg human being who climbs a 3.0-m-high set of stairs in 5.0 seconds.

Answer 1

Part a)

`F = 182.3 Lb`

Part b)

`P = 0.55 HP`

Step-by-step explanation:

Diameter of the circle = 24 ft

Diameter = 731.52 cm = 7.3152 m

now the horse complete 144 trips in one hour

so time to complete one trip is given as

`t = (3600)/(144) s`

`t = 25 s`

now the speed of the horse is given as

`v = (2\pi r)/(t)`

`v = (\pi(7.3152))/(25)`

`v = 0.92 m/s`

Part a)

Now we know that the power is defined as rate of work done

it is given as

`P = F v`

`746 = F(0.92)`

`F = 810.9 N`

`F = 182.3 Lb`

Part b)

Work done to climb up to 3 m height is given by

`W = mgh`

now we have

`Power = (Work)/(time)`

`P = (mgh)/(t)`

`P = ((70kg)(9.81)(3))/(5.0s)`

`P = 412.02 Watt`

now we know that 1 HP = 746 Watt

so we have

`P = (412)/(746) = 0.55 HP`