A grindstone used to sharpen tools is rotating at an angular speed fo 8 rad/s wh

Question

A grindstone used to sharpen tools is rotating at an angular speed fo 8 rad/s when an axe is pressed against it. Because of the torque produced on the grindstone by the force of friction between it and the axe, it comes to rest in four rotations.

a) find the frictional force produced, assuming the grindstone is a cylinder of mass 5kg and radius 0.4m.

b) if the coefficient of friction between the axe and grindstone is 0.4, find the normal force with which the axe was pressed aginst the grindstone.

Explanation / Answer

wf^2 -wi^2 =2*angular acceleration*theta => 8^2 -0 =2*angular acceleration*4*2*3.14 => angular acceleration = 1.274 rad/s2 a). torque =I* angular acceleration => f*0.4 =5*0.4^2/2 *1.274 => f= 1.274 N b). friction =coefficient of friction *N => N =1.274/0.4 =3.185 N

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