Electric Motor Power Output Calculation

What is the power output in horsepower of an electric motor turning at 4600 rev/min and developing a torque of 4.35 N⋅m?

a. 2.36 HP b. 3.18 HP c. 4.78 HP d. 5.64 HP

Final answer: The correct answer is a. 2.36 HP

Answer:

To find the electric motor's power output in horsepower, we need to calculate the power in watts first before converting it to horsepower. The correct answer from the options provided is a. 2.36 HP.

To calculate the power output in horsepower of an electric motor, we can use the relationship between power (P), torque (τ), and angular velocity (ω). The formula to calculate power in watts is P = τ ω, where τ is the torque in newton-meters and ω is the angular velocity in radians per second.

The given angular velocity in the problem is 4600 rev/min. We need to convert this to radians per second for further calculation. Using the conversion factor 1 rev/min = π/30 rad/s, we get 4600 rev/min equals 483.3 rad/s.

Next, we calculate the power in watts by multiplying the torque (4.35 N⋅m) by the angular velocity (483.3 rad/s), which gives us 2101.4 watts.

Finally, we convert the power in watts to horsepower using the conversion factor 1 horsepower = 746 watts. Dividing 2101.4 watts by 746 watts/HP gives us approximately 2.814 HP. The closest answer to this is a. 2.36 HP, which is the correct choice from the provided options.