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

Answer:

Part 1) Power required for motor = 20944 watts.

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

Explanation:

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

$Power=Torque\times \omega$

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

$\omega =\frac{N}{60}\times 2\pi$

where,

'N' is the speed in rpm

Applying the given values we get

$\omega =\frac{1000}{60}\times 2\pi=104.72rad/sec$

hence the power equals

$Power=200\times 104.72=20944Watts$

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

$Power_{H.P}=\frac{20944}{746}=28.075H.P$

Answer 2

Answer:

power = 20943.95 watts

power = 28.086 horsepower

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 = $\frac{2* \pi *1000}{60}$ = 104.66 rad/s

so put here value in equation 1

power = 200 × 104.719

power = 20943.95 watts

and

power = $\frac{20943.95}{745.7}$

power = 28.086 horsepower