Final answer:
The power of the electric hoist is approximately 3.6 kilowatts or 4.8 horsepower. The answer provided by the student contains incorrect numbers, as the calculation based on the given parameters does not match any of the provided options.
Step-by-step explanation:
The student has asked how to calculate the power of a hoist in kilowatts (kW) and in horsepower (hp) when lifting a 235.0 kg load to a height of 59.0 m in 37.8 s.
To find the power in kilowatts, we first calculate the work done by the hoist, which is equal to the change in gravitational potential energy of the load:
Work = m * g * h
Where:
- m = mass of the load (235.0 kg)
- g = acceleration due to gravity (9.8 m/s2)
- h = height (59.0 m)
Work = 235.0 kg * 9.8 m/s2 * 59.0 m = 136,049 J
The power in watts (W) is the work done divided by time (t):
Power = Work / t
Power = 136,049 J / 37.8 s = 3,600 W or 3.6 kW
To convert the power to horsepower:
Power (hp) = Power (kW) / 0.746
Power (hp) = 3.6 kW / 0.746 ≈ 4.8 hp
Therefore, the correct answer is not listed among the options provided. The hoist's power is approximately 3.6 kW or 4.8 hp.