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 how fast work is done. To raise a weight, the required work equals weight times height: 3500 lb × 175 ft = 612,500 ft-lb of useful work. Because the system is 60% efficient, you must supply more energy than that: input work = 612,500 / 0.60 = 1,020,833 ft-lb. Horsepower is a rate of doing work. If the lift is completed in one minute (60 seconds), the input power is 1,020,833 / 60 ≈ 17,015 ft-lb per second. Since one horsepower equals 550 ft-lb per second, the required horsepower is 17,015 / 550 ≈ 30.93, or about 31 hp. If the lift time were different, the required horsepower would scale accordingly.

Power is how fast work is done. To raise a weight, the required work equals weight times height: 3500 lb × 175 ft = 612,500 ft-lb of useful work.

Because the system is 60% efficient, you must supply more energy than that: input work = 612,500 / 0.60 = 1,020,833 ft-lb.

Horsepower is a rate of doing work. If the lift is completed in one minute (60 seconds), the input power is 1,020,833 / 60 ≈ 17,015 ft-lb per second. Since one horsepower equals 550 ft-lb per second, the required horsepower is 17,015 / 550 ≈ 30.93, or about 31 hp.

If the lift time were different, the required horsepower would scale accordingly.