How many horsepower are required to raise 3500 pounds to a height of 175 feet at 60% efficiency?

How many horsepower are required to raise 3500 pounds to a height of 175 feet at 60% efficiency?

• A. 23
• B. 31
• C. 45
• D. 60

Answer: (B)

Power is the rate at which work is done. To lift a weight, the useful work equals weight times height, and efficiency tells us how much input power is needed to deliver that useful work.

First find the work done against gravity: 3500 lb raised 175 ft gives 3500 × 175 = 612,500 ft-lb of useful work.

If this work is done in one minute, the useful power output is 612,500 ft-lb per minute. Since 1 horsepower equals 33,000 ft-lb per minute, the useful horsepower is 612,500 / 33,000 ≈ 18.56 HP.

Accounting for 60% efficiency, the input horsepower required is higher: 18.56 / 0.60 ≈ 30.93 HP, which is about 31 HP.

So the required horsepower is approximately 31 HP.