Question

An electric motor supplies 200 N·m of torque to a load. What is the mechanical power supplied to the load if the shaft speed is 1000 rpm? Express the result in watts and horsepower.

Answer 1

Part 1) Power required for motor = 20944 watts.

Part 2) Power required for motor in Horsepower equals = 28.075H.P

Step-by-step explanation:

Power is defined as the rate of consumption of energy. For rotational motion power is calculated as

`Power=Torque* \omega`

where,

`\omega` is the angular speed of the motor.

Since the rotational speed of the motor is given as 1000 rpm, the angular speed is calculated as

`\omega =(N)/(60)* 2\pi`

where,

'N' is the speed in rpm

Applying the given values we get

`\omega =(1000)/(60)* 2\pi=104.72rad/sec`

hence the power equals

`Power=200* 104.72=20944Watts`

Now since we know that 1 Horse power equals 746 Watts hence 20944 Watts equals

`Power_(H.P)=(20944)/(746)=28.075H.P`

Answer 2

power = 20943.95 watts

power = 28.086 horsepower

Step-by-step explanation:

given data

torque = 200 N

speed = 1000 rpm

to find out

What is the mechanical power in watts and horse power

solution

we know that mechanical power formula that is

power = torque × speed ...................1

here we have given both torque and speed

we know speed = 1000 rpm =
`(2* \pi *1000)/(60)` = 104.66 rad/s

so put here value in equation 1

power = 200 × 104.719

power = 20943.95 watts

and

power =
`(20943.95)/(745.7)`

power = 28.086 horsepower