Two horses (Mr. Ed and one of his pals, for those who remember the great Mr. Ed)

Question

Two horses (Mr. Ed and one of his pals, for those who remember the great Mr. Ed) are pulling a barge as shown.Mr. Ed and his friend can each work at a maximum rate of 2 horse power = 1500 W (Hey, this IS Mr. Ed, remember --he's one strong horse -- of course)

(i) When Mr. Ed and his pal are walking at a steady speed of 1.73 m/s. Calculate the tension in the cables.

(ii) If the water exerts a resistive force on the barge that varies with the barges speed as 120v (Newtons) where v is the speed of the barge in the water, calculate the maximum speed steady speed of the barge when each horse is exerting his maximum horsepower.

Explanation / Answer

The maximum power of the each horse P = 2hp = 1500W The steady speed of the horse is v = 1.73m/s Now the power            P = Fv             1500W = F (1.73) then F = 867 N therefore the tension in the string is      Tcos = 867 N       T = 867/cos30 = 1001N therefore the tension in the cables is 1001 N (ii) When the resistive force f = 120v then from Newton's laws        F = 2Tcos Then the power      P = Fv      2(1500) = (2*1001*cos30 -120v)(v)     3000 = 1733.78v - 120v^2      120v^2 - 1733.78v + 3000 = 0 therefore the maximum steady speed        v = 12.4 m/s

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