A sleigh and driver with a total mass of 120kg are pulled up a hill with a 15deg

Question

A sleigh and driver with a total mass of 120kg are pulled up a hill with a 15degrees incline by a horse, as illustrated in the figure .

A.)If the overall retarding frictional force is 700N and the sled moves up the hill with a constant velocity of 5.0km/h , what is the power output of the horse? (Express in horsepower, of course.)

B.) Suppose that in a spurt of energy, the horse accelerates the sled uniformly from 5.0 to 17 in 6.0 . What is the horse’s maximum instantaneous power output? Assume the same force of friction.

Explanation / Answer

Part A)

Power = Force times velocity

velocity = 5 km/hr which is 1.39 m/s

P = (700)(1.39) = 972 W

Then 1 hp = 746 W, so the horsepower is 1.3 hp

Part B)

First, the work done is the change in KE

KE = .5mvf2 - .5mvi2

17 km/hr = 4.72 m/s

KE = (.5)(120)(4.72)2 - (.5)(120)(1.39)2

KE = 1452.63 J

P = KE/t

P = (1452.63)/6 = 242 W

Total Power = 242 + 972 = 1214 W which is 1.63 hp

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