An electric motor exerts a constant torque of =10Nm on a grindstone mounted on i

Question

An electric motor exerts a constant torque of =10Nm on a grindstone mounted on its shaft; the moment of inertia of the grindstone is I=2.0kgm2. If the system starts from rest, find the work done by the motor in 8.0 s and the kinetic energy at the end of this time. What was the average power delivered by the motor? Part A:Suppose we now turn off the motor and apply a brake to bring the grindstone from its greatest angular speed of 36 rad/s to a stop. If the brake generates a constant torque of 13 Nm , find the total work done (including signs) needed to stop the grindstone. Part A:Suppose we now turn off the motor and apply a brake to bring the grindstone from its greatest angular speed of 36 rad/s to a stop. If the brake generates a constant torque of 13 Nm , find the total work done (including signs) needed to stop the grindstone. Part B:Find the average power (including signs) needed to stop the grindstone in Part A.

Explanation / Answer

average power

P = torque * angle rotated

angle = 1/2*alpha *t^2

alpha = torque/ I

alpha = 10/2 = 5 rad/s^2

angle = 1/2*5*8*8

angle = 160 radian

P = torque * abngle

P = 10*160 = 1600watt

P =1600W

Part A

work done required to stop

W = 1/2Iw^2

W = 1/2*2*36*36

W = 1296W

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