Calculating Horsepower: A Formula for Power and Speed

How can we calculate the amount of horsepower delivered by a motor?

Given a motor runs at 20 rev/s and supplies a torque of 75 Nm, what is the horsepower it is delivering?

Answer:

The horsepower delivered by the motor running at 20 rev/s and supplying a torque of 75 Nm is approximately 12.62 hp.

Calculating horsepower in a rotational system, such as a motor, involves understanding the relationship between power, torque, and rotational speed. The formula for power in a rotational system is P = τω, where P is power, τ is the torque, and ω is the rotational speed.

In this specific case, the motor is running at 20 rev/s and supplying a torque of 75 Nm. First, we need to convert the rotational speed to rad/s. Since there are 2π radians in one revolution, we multiply 20 rev/s by 2π to get ω = 40π rad/s.

Next, we substitute the given values into the formula: P = 75 Nm * 40π rad/s = 9424.778 Watts. To convert this figure from watts to horsepower, we use the conversion factor of 1 horsepower = 746 watts.

Therefore, P = 9424.778/746 ≈ 12.62 hp. This is the amount of horsepower being delivered by the motor running at 20 rev/s and supplying a torque of 75 Nm. None of the provided options A, B, C, or D is correct based on this calculation.

Understanding how to calculate horsepower in different contexts can provide valuable insights into the performance and efficiency of various machines and systems. By grasping the underlying principles of power and speed, we can optimize the operation of motors and other devices to enhance their functionality and output.