In activity 1 of this chapter what is likely happen if you change the angle which the tray makes with the table top Does the angle made by the inclined plane with respect to horizontal affect the sliding? Discuss the finding with your teacher does the angle depend on the nature of the two surface in contact?
Answers
Explanation:
The angle which an inclined surface makes with the horizontal when a body placed on it is on the point of moving down is called Angle of Repose.
It does. But not dramatically.
Insofar as the concept of a “coefficient of [sliding] friction” μ is valid, the frictional force is proportional to the normal force, Ff=μN . The area A over which the normal force is distributed means a pressure p=N/A is pressing the two surfaces together.
Similarly, the perpendicular Shear stress due to friction is τ=μN/A . As explained in the Wikipedia page, the shear strain is presumed to be proportional to the shear stress with a constant of proportionality G, the shear modulus. This is valid up to the point where the material under shear stress breaks. Then one might expect the stress to be released until the next chunk of material bumps up against the shearing surface.
That’s what happens in friction between two solid surfaces: each surface is microscopically rough, so it has little peaks and valleys that get stuck against the valleys and peaks of the other surface. When one is pulled sideways, some of the peaks get sheared off… and then others.
You can imagine that, with more normal pressure, the peaks and valleys get squished together further so that a larger cross sectional area gets sheared off each time. Thus the shear stress required to break it off increases proportionally. QED.
It should be clear at this point that I’m making this up as I go. Any reasonable person would be suspicious by now and anticipate deviations from the simple law defining the coefficient of sliding friction. I think they would be correct; but since Leonardo we have been aware that it works surprisingly well. (Well, I’m surprised.) The Wikipedia page on Friction recounts much of this history, but (IMO) tries to make it seem simpler than it is. The science of Tribology seems to be attempting a deeper understanding. In the end it is just (so far) an empirical fact that this approximation is “pretty good”.