Work done by varying friction against a constantly moving surface

[jamesadrian]

Suppose a metal disk is spinning at constant rate of one cycle per second and at a radius of about four inches a small metal block is pressed against the disk. The circumference of the path of the contact is exactly one foot.

The coefficient of kinetic friction between the disk and the small metal block is .1 and the small metal block is attached to an arm (the block arm). The other end of the block arm is attached with a bearing to the center of rotation of the disk.

A time-varying force is applied to the block arm so as to manipulate the force between the disk and the small metal block. This force follows the arm wherever it goes and we need not be concerned about where the force comes from. The direction of this force is into the face of the disk (at a right angle to the surface of the disk, or the normal).

The coefficient of kinetic friction is kept extremely constant, possibly because of the polish of the metal or possibly because of a special lubricant.

If anything opposes the rotation of the block arm, the work (force times distance) that can be done by the block arm against this resistance would seem to be proportional to the normal force applied by the block arm.

Do I have this right?

Thank you for your help.

Jim Adrian

 

[A.T.]

https://en.wikipedia.org/wiki/Work_(physics)#Work_done_by_a_variable_force