a)-The massive grinder for wood-pulp in a newsprint paper factory, which can ren

Question

a)-The massive grinder for wood-pulp in a newsprint paper factory, which can render about a half Tonne of wood into a thin soup in less than a minute, is essentially a stone cylinder of radius 0.650 m and mass about 6.00 Tonnes. An enormous motor spins this cylinder on its axis while hydraulic cylinders press the pocket of wood against its rim. A typical rotational speed for the motor is 66.0 rpm (rotations per minute). Suppose that while the paper plant is in full operation there is a power outage due to an ice-storm. How much energy (in J) is available to grind wood just from the rotational kinetic energy of the grinding wheel?

b)-If the grinding wheel comes to rest in 60.0 ms what is the tangential force (in N) that the wood presents to the grinding wheel if this force is constant during the slowing down?

Explanation / Answer

Answer:

moment of inertia = 1/2*mR^2
omega = 2pi*frequency

rotational energy = 1/2*I*?^2

E rot = 1/2*(1/2*6000*0.65^2)(2pi*66/60)^2
E rot = 30273.53 Nm <-- ans.
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The grinding wheel comes to rest in 60 ms (milliseconds)

First find the angular acceleration, using the standard constant acceleration equations but with s v and a.

wf= wi+ at

wf= 0, so

-wi= at

(where wi= 66 rpm/60 sec * 2pi rad = 6.91 rad/s)

so

- 6.91 = a(.06)

a= -115.19 rad/s2

so the tangential force is

thnq

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