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

Question

A sleigh and driver with a total mass of 120 are pulled up a hill with a 15 incline by a horse, as illustrated in the figure . If the overall retarding frictional force is 950 and the sled moves up the hill with a constant velocity of 5.0 , what is the power output of the horse? (Express in horsepower, of course.) Express your answer using two significant figures. = hp Suppose that in a spurt of energy, the horse accelerates the sled uniformly from 5.0 to 17 in 5.0 . What is the horse?s maximum instantaneous power output? Assume the same force of friction. hp

Explanation / Answer

a)

Fg = mg = 120 * 9.81 = 1177 N

Fg_slope = sin(15) * Fg = 1177 * 0.259 = 304.6 N

F_tot = Fg + F_friction = 304.6 + 950 = 1255 N

P = F v = 1255* (5.0 / 3.6) = 1.7 * 10^3 W equals 2.3 hp (assuming the speed is given in km/h)

b)

a = dv/t = (17-5)/(5*3.6) = 0.67 m/s^2

F_acc = m * a = 120 * 0.67 = 80N

v_max = 17/3.6 = 4.7 m/s

F_max = Fg + F_friction + F_acc = 1255 + 80 = 1335 N

P_max = v_max * F_max = 1335 * 4.7 = 6.2 * 10^3 W equals 8.4 hp

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