An electrical motor has a power rating of 500 W when it is lifting a mass of 80 kg through a height of 6 m in a time of 15 s. Calculate the efficiency of the motor?
F = ma = 80kg * 9.8 m/s^2
W = Fd = F * 6m
P = W/s = W / 15s
P = 80*9.8*6/15 = 313.6 W
Now you can figure the % eff.
To calculate the efficiency of the motor, we need to find the input power and the output power.
The input power is the power provided to the motor, which is equal to the electrical power rating of the motor. In this case, it is given as 500 W.
The output power is the power delivered by the motor to lift the mass through the height in the given time. We can calculate the output power using the work-energy principle.
The work done by the motor is given by the formula:
Work = Force * Distance
In this case, the force is the weight of the mass, which can be calculated using the formula:
Force = mass * acceleration due to gravity
The acceleration due to gravity is approximately 9.8 m/s^2.
So, the force is:
Force = 80 kg * 9.8 m/s^2 = 784 N
The work done by the motor is:
Work = Force * Distance = 784 N * 6 m = 4704 J (joules)
Now, we can calculate the output power using the formula:
Output power = Work / Time
Output power = 4704 J / 15 s = 313.6 W
Now, we can calculate the efficiency of the motor using the formula:
Efficiency = (Output power / Input power) * 100
Efficiency = (313.6 W / 500 W) * 100 = 62.72 %
So, the efficiency of the motor is approximately 62.72%.