Answer :
The power required to raise the concrete hopper is 20,625 ft-lb/s, 37.5 hp, and 27,214 W.
To find the power required to raise a concrete hopper, we need to apply the concept of work and power in physics.
- Weight of the hopper (F): 750 lb
- Height raised (h): 165 ft
- Time taken (t): 6.00 s
(a) Power in ft-lb/s
First, we calculate the work done (W):
W = F × h
W = 750 lb × 165 ft = 123,750 ft-lb
Next, we calculate the power (P):
P = W ÷ t
P = 123,750 ft-lb ÷ 6.00 s = 20,625 ft-lb/s
(b) Power in hp
We know that 1 hp = 550 ft-lb/s. So, converting the power to horsepower:
P (hp) = 20,625 ft-lb/s ÷ 550 ft-lb/s = 37.5 hp
(c) Power in W
We know that 1 hp = 745.7 W. So, converting the power from horsepower to watts:
P (W) = 37.5 hp × 745.7 W/hp = 27,214 W
