Question

mass is 5 lb attached to a rope wound around a pulley. The radius of the pulley is 3 in. If the mass falls at a constant velocity of 5 ft/s, determine the power transmitted to the pulley, in hp.

Answer 1

The power transmitted to the pulley is 0.0455 hp.

Step-by-step explanation:

Given;

mass attached to the rope, m = 5 lb

radius of the pulley, r = 3 in

constant rate of fall of the mass, v = 5 ft/s

acceleration due to gravity, g = 32.2 ft/s²

1 lbf = 32.2 lb.ft/s²

The power transmitted to the pulley is calculated as;

P = Fv

P = (mg)v

`P = 5 \ lb \ * \ 32.2 \ (ft)/(s^2) \ * \ 5 \ (ft)/(s) \ * \ (1 \ lbf)/(32.2 \ lb.ft/s^2) \ \ = 25 \ (ft.lbf)/(s) \\\\`

in horse power, the power transmitted is calculated as;

`P = (25 \ ft.lbf)/(s) \ * \ (1 \ hp)/(550 \ ft.lbf/s) \ \ = 0.0455 \ hp`

Therefore, the power transmitted to the pulley is 0.0455 hp.