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AxioWolf
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Homework Statement
Okay, so I have a homework-like question that I need help with. It seems so simple, but I'm stumped and can't find anything online. A similar real world example if my description below isn't clear would be a clutch mechanism where one disk is pressed up against another and the friction prevents the disks from slipping.
I have two disks that have a radius, r.
The disks are assumed to be perfectly rigid.
One disk is fixed and the other can rotate about an axis centered in the fixed disk.
The non-fixed disk has a torque, T, applied of say 200 in-lbs
There is static friction, [tex] μ_s [/tex] between the two disks
These disks are sandwiched together with a force, N, that is applied along the axis of rotation (nut and bolt basically).
Goal: Plot N vs [tex] μ_s [/tex] with varying r values, which will result in multiple curves. This will be at the equilibrium point when the floating disk is just about to rotate.
Homework Equations
[tex] f_s = μ_s*N [/tex]
[tex] T = F*x [/tex]
...?
The Attempt at a Solution
The set-up seems nearly complete except for the missing piece of the distance, x, away from the center of the disk that the friction force acts. The distance is needed to calculate the resulting moment that resists the applied moment.
[tex] f_s = μ_s*N [/tex]
[tex] T = f_s*x [/tex]
[tex] T = μ_s*N*x [/tex]
Thus, what is x?:
x = r/2
x = r
or maybe the circle that divides the disk's contact area equally in half... (see image)
x = r*√(2)/2
My suspicion is that I need to integrate to solve this, but I'm not sure how to set up the integration.
Thanks for your help!
AxioWolf
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