- #36
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Hi Amin2014.
The reason that kinetic friction work is so tricky to quantify is because of the idealized macroscopic model we are using to describe it. The macroscopic model features a velocity discontinuity at the boundary, but the rate of doing work is determined by the shear force times the velocity. But, with a velocity discontinuity, which velocity do you use? There's to rub.
You yourself envisioned a way to work around this by imagining an intermediate material layer (on the microscale) between the two surfaces in which the velocity varies continuously (velocity profile). Unfortunately we do not know all the microscopic details of dry kinetic friction, but, what we can do is conceive of a microscopic model that, on the macroscopic scale behaves exactly the same as the idealized kinetic friction model, but without the velocity discontinuity. This is what I was talking about also when I proposed introducing a microscopic fluid layer between the surfaces to mimic the kinetic friction. Such a fluid would have a viscosity that varies inversely with the velocity gradient (non-Newtonian fluid) so that the shear force is always constant irrespective of the magnitude of the velocity difference between the surfaces. So, on the macroscopic scale, it would behave exactly the same as our macroscopic model of dry kinetic friction, except that it would eliminate the velocity discontinuity by providing a linear velocity profile across the intermediate microscopic layer. Thinking of it in this way would totally eliminate the confusion that we have been experiencing, and would be consistent with what we were discussing in several of our last few posts. And, most importantly, it would enable us to correctly determine the work done by whom on what, and by what on whom.
Thoughts?
Chet
The reason that kinetic friction work is so tricky to quantify is because of the idealized macroscopic model we are using to describe it. The macroscopic model features a velocity discontinuity at the boundary, but the rate of doing work is determined by the shear force times the velocity. But, with a velocity discontinuity, which velocity do you use? There's to rub.
You yourself envisioned a way to work around this by imagining an intermediate material layer (on the microscale) between the two surfaces in which the velocity varies continuously (velocity profile). Unfortunately we do not know all the microscopic details of dry kinetic friction, but, what we can do is conceive of a microscopic model that, on the macroscopic scale behaves exactly the same as the idealized kinetic friction model, but without the velocity discontinuity. This is what I was talking about also when I proposed introducing a microscopic fluid layer between the surfaces to mimic the kinetic friction. Such a fluid would have a viscosity that varies inversely with the velocity gradient (non-Newtonian fluid) so that the shear force is always constant irrespective of the magnitude of the velocity difference between the surfaces. So, on the macroscopic scale, it would behave exactly the same as our macroscopic model of dry kinetic friction, except that it would eliminate the velocity discontinuity by providing a linear velocity profile across the intermediate microscopic layer. Thinking of it in this way would totally eliminate the confusion that we have been experiencing, and would be consistent with what we were discussing in several of our last few posts. And, most importantly, it would enable us to correctly determine the work done by whom on what, and by what on whom.
Thoughts?
Chet