A lumberjack is sharpening his axe by pressing it against a grindstone. The grin

Question

A lumberjack is sharpening his axe by pressing it against a grindstone. The grindstone is a solid disk which has a weight   1300 N    and radius   0.5 m   . The lumberjack pushes the head of his axe against the grindstone with a normal force of   124 N   ; the coefficient of friction between the axe head and the grindstone is   0.91  .

Part A

What is the magnitude of the torque on the grandstone?

706.42N•m

Incorrect

Part B

We choose the direction of the initial angular velocity of the grindstone to be positive. With this convention, what is the angular acceleration of the grindstone when the lumberjack is sharpening his axe?

4.34rads2

Incorrect

Part C

If the grindstone is initially rotating with angular velocity   4.4 rad/s   , how long does it take for the grindstone to stop?

1.425s

Incorrect

Part D

What angle has the grindstone rotated through during this time?

706.42N•m

Explanation / Answer

torque = r*f = r*u*N = 0.5*0.91*124 = -56.42 Nm

part(B)

torque = I*alpha

I = (1/2)*m*r^2

56.42 = -(1/2)*(1300/9.81)*0.5^2*alpha

apha = -3.41 rad/s^2

+++++++

C)

alpha = (wf - wi)/t

-3.41 = (0-4.4)/t

t = 1.29 s

+++++

D

theta = wi*t + 0.5*alpha*t^2

theta = (4.4*1.29)-(3.297*1.29^2) = 0.0199 rad = 10.8 degrees

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