What is the power consumption of the electric motor in horsepower when it is running a belt-driven machine with a tension difference of 20 lb between the upper and lower part of the belt?
The power consumed by the electric motor, given its efficiency and the tension difference in the belt, is calculated to be approximately 3.539 Horsepower.
Understanding Power Consumption Calculation
Power Consumption Equation:
The power consumption of the belt-driven machine operated by the motor can be computed by analyzing the power provided by the motor and its efficiency. The power provided by the motor, which directly drives the machine, is given by the force difference in the upper and lower part of the belt times the angular speed, i.e. P = Tω where T is the tension difference and ω is the angular speed.
Calculating Power Consumption:
In this scenario, the difference in tension is 20 lb, and the angular speed is 25 rad/s. By converting the tension into equivalent SI unit (Newton), we have 1 lb equals approximately 4.44822 N, hence 20 lb would be around 89.7644 N. So, the power delivered by the motor to the machine can be calculated as P = 89.7644 N * 25 rad/s = 2244.11 Watts.
Considering Motor Efficiency:
However, we consider the efficiency of the motor. The power consumed by the motor would be the power provided by the motor divided by the motor's efficiency, which in this scenario is 85%. Therefore, the power consumption of the motor, Pmotor = P / efficiency = 2244.11 / 0.85 = 2639.54 Watts.
Converting to Horsepower:
Finally, we convert this power consumption from Watts to Horsepower, as the problem specifically asks for the answer in horsepower. Knowing that 1 Horsepower equals about 746 Watts, the power consumption of the motor in horsepower is Pmotor_hp = Pmotor / 746 = 2639.54 / 746 = 3.539 Horsepower.