How to Calculate Power, Work, and Efficiency of a Motor

a) What is the power of the motor in watts?

a) The power of the motor can be expressed in watts by converting the horsepower to watts. Given that 1 horsepower is approximately equal to 735.5 watts, calculate the power of a motor with 10 horsepower.

b) What work does the motor perform?

b) The work done by the motor can be determined using the formula for work, which involves calculating the force exerted and the distance moved. Find out the work done by a motor that lifts 1000 kg of iron to a height of 50 m in 2 minutes.

c) Calculate the efficiency of the motor.

c) Efficiency of a motor can be calculated by comparing the useful work done by the motor to the total work input. Calculate the efficiency of the motor lifting 1000 kg of iron to a height of 50 m in 2 minutes.

Answer:

The power of the motor is 7355 W, the work done by the motor is 490,000 J, and the efficiency of the motor is 55%.

Explanation:

a) To express the power of the motor in watts, remember that 1 horsepower is equal to approximately 735.5 watts. Therefore, a motor with 10 horsepower has a power of 10 * 735.5 = 7355 watts.

b) The work done by the motor can be calculated using the work formula, which is force multiplied by distance. In this case, the force is the weight of the iron, which is the mass (1000 kg) times gravity (9.8 m/s^2), and the distance is the height (50 m). So, the work done is (1000 kg * 9.8 m/s^2) * 50 m = 490,000 J (joules).

c) The efficiency of the motor can be calculated using the efficiency formula, which is the useful work done divided by the total work input. The useful work done is the work done to lift the iron, and the total work input is the power of the motor multiplied by the time. However, you need to convert the time to seconds because the power of the motor is in watts, which is joules per second. Therefore, the efficiency is 490,000 J / (7355 W * 2 min * 60 s/min) = 0.55, or 55%.