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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.

Respuesta :

Answer:

Part a)

[tex]F = 182.3 Lb[/tex]

Part b)

[tex]P = 0.55 HP[/tex]

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

[tex]t = \frac{3600}{144} s[/tex]

[tex]t = 25 s[/tex]

now the speed of the horse is given as

[tex]v = \frac{2\pi r}{t}[/tex]

[tex]v = \frac{\pi(7.3152)}{25}[/tex]

[tex]v = 0.92 m/s[/tex]

Part a)

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

it is given as

[tex]P = F v[/tex]

[tex]746 = F(0.92)[/tex]

[tex]F = 810.9 N[/tex]

[tex]F = 182.3 Lb[/tex]

Part b)

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

[tex]W = mgh[/tex]

now we have

[tex]Power = \frac{Work}{time}[/tex]

[tex]P = \frac{mgh}{t}[/tex]

[tex]P = \frac{(70kg)(9.81)(3)}{5.0s}[/tex]

[tex]P = 412.02 Watt[/tex]

now we know that 1 HP = 746 Watt

so we have

[tex]P = \frac{412}{746} = 0.55 HP[/tex]