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 58 rad/s to a stop. If the brake generates a constant torque of 21 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

torque = I*alfa

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

alfa = (wf-wi)/t

wf = 5*8 = 40 rad/s

W = dKE = 0.5*I*(wf^2-wi^2) = 0.5*2*40^2 = 1600 J

+++++++++++++

KE = 0.5*I*(wf^2-wi^2) = 0.5*2*40^2 = 1600 J

+++++

Work done = dKE = -0.5*I*w^2 = -0.5*2*58^2 = -3364 J

power = W/t = 1600/8 = 200 W

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