An electric motor develops 70 kw of power as it lifts a loaded elevator 28.5 m in 42 seconds. How much force does the motor exert?
To calculate the force exerted by the motor, we can use the equation:
Power = Force × Velocity
Given that the power developed by the motor is 70 kW, we need to convert it to watts.
1 kW = 1000 W
Therefore, 70 kW = 70,000 W.
Now we can rearrange the equation to solve for force:
Force = Power / Velocity
To find the velocity, we can use the equation:
Velocity = Distance / Time
Given that the elevator has lifted a distance of 28.5 m in 42 seconds:
Velocity = 28.5 m / 42 seconds
Now we can substitute the values into the equation to find the force:
Force = 70,000 W / (28.5 m / 42 seconds)
Simplifying further:
Force = 70,000 W / (0.6786 m/s)
Now we can calculate:
Force = 103,000 N
Therefore, the motor exerts a force of 103,000 Newtons to lift the loaded elevator.