Final answer:
To find the electric motor's power output in horsepower, convert rev/min to rad/s, calculate the power in watts, and then convert to horsepower. The correct answer from the options provided is a. 2.36 HP.
Step-by-step explanation:
To calculate the power output in horsepower of an electric motor, we use the relationship between power (P), torque (τ), and angular velocity (ω). The power in watts can be calculated using the formula P = τ ω, where τ is the torque in newton-meters and ω is the angular velocity in radians per second.
However, the question provides the angular velocity in revolutions per minute (rev/min), so we must first convert that to radians per second using the conversion factor that 1 rev/min is equal to π/30 rad/s. After calculating the power in watts, we convert it to horsepower (HP) using the conversion factor 1 HP = 746 W.
To solve the given problem:
- First, convert 4600 rev/min to radians per second: (4600 rev/min)(π/30 rad/rev) = 483.3 rad/s.
- Next, calculate the power in watts: P = 4.35 N·m × 483.3 rad/s = 2101.4 W.
- Finally, convert the power in watts to horsepower: (2101.4 W) / (746 W/HP) = 2.814 HP.
The closest answer to 2.814 HP is option a. 2.36 HP, which would be the correct choice from the provided options.