-3

1.Why kinetic friction doesn't depend on speed of object? Also explain why static friction > kinetic friction > rolling friction?

2.when we keep a book on a table , the table is said to exert a force on the book called "normal reaction" . In a book it was given that this force is due to electromagnetic forces between the two surfaces of contact. Is this true ?

Jay
  • 1
  • Related: https://physics.stackexchange.com/q/154443/2451 , https://physics.stackexchange.com/q/16213/2451 and links therein. – Qmechanic Sep 16 '18 at 11:22
  • https://physics.stackexchange.com/questions/48534/does-kinetic-friction-increase-as-speed-increases This link might help you. – Mohan Sep 16 '18 at 12:25
  • Kinetic friction does depend on speed in many situations. What you learn in a first course in mechanics is the Coulomb model of friction, which is a simple approximation that can be used for solving problems by hand (rather than by computer simulation.) It is only "accurate" in the conditions that you find in simple experiments to measure it - hard, relatively inert materials, room temperatures, and low loads and velocities. The Coulomb friction model is of no practical use at all for the friction behaviour of high performance vehicle tires, for example. – alephzero Sep 16 '18 at 12:58
  • The reason why static friction > kinetic friction is because it is logically impossible for it to by anything else, by the definition of "static" and "kinetic". As Steeven's answer says, "kinetic friction > rolling friction" is false in general, though in practice it is often true. – alephzero Sep 16 '18 at 13:02
  • This is an empirical observation. – John Alexiou Sep 16 '18 at 13:55

1 Answers1

0

There are two usually odd things about, kinetic friction $$f_k=\mu n$$ One is that it doesn't depend on sliding speed as you mention, and the other that it doesn't depend on contact area (it might seem obvious that friction should be larger when the sliding surface is larger - but that isn't so).

  • Why no dependence on contact area? Because area is already taken into account due to the normal force $n$. The relationship is empirically formulated as: $$f_k=A \mu q$$

with $A$ being contact area and $q$ the normal pressure pushing the surface together. Pressure is a force-per-area measure, $q=n/A$, and thus $A$ cancels out of the formula. Intuitively, a larger contact area, which would increase friction, at the same time spreads the force out more, which would decrease friction. Those two effects cancel out.

  • Why no dependence on speed? The contacting surfaces have roughnesses, causing microscopic peaks and valleys that make the surfaces "fall into" and "grab onto each other", with the peaks of one "falling into" the valleys of the other. The peaks must "get lifted out" of those valleys again before we can have sliding, and this takes force - this is kinetic friction.

When speeding up the sliding, there is less time for them to "fall into" the valleys, so they don't go as deep. It would therefore take less force to lift them out, meaning lower friction. But at the same time, the higher speed requires them to be lifted out faster, in shorter time. This requires a larger force, meaning higher friction. Those two effects cancel out and speed has no effect.

With that said, the model $f_k=\mu n$ only holds true for low normal forces $n$. The force onto a surface will spread into the material as an internal stress or tension. When the peaks of one material hold up the other material, each peak is flattened a bit, and the spread internal stresses will slightly deform the peak in depth, propagating into the material. As long as the deformation zones do not overlap, this above kinetic friction model has shown close to reality. It is called Amonton's law or Coulomb's law in some circles.

But when the deformation zones do start to overlap, then the deformation at one peak will prevent the further deformation of another peak. Suddenly, the linear relationship is disturbed - and for high enough normal forces, there is no more deformation to do, at which point friction is constant regardless of normal force.

This scenario is not experienced in every-day situations such as the foot sliding off a slippery stairway or the slipping of a car tire on asphalt; here Amonton's law works just fine. But in the production industry with cutting tools applying enormous pressures onto a steel surface in order to cut or deform, for example in a milling or turning operation, the constant-friction model is the one to use. The in-between scenarios are unpredictable and may require an empirical relationship, experimentally proved beforehand.

why static friction > kinetic friction > rolling friction?

Note: It would be more correct to say maximum static friction > kinetic friction. Anyways.

If you consider the above description of why the slower speed allows the peaks to sink deeper into the valleys, then just extend this model to the case of no speed. Then valleys are sinking fully in, having plenty of time to fall into a fixed position. It takes some extra force to lift them out of this position for sliding to start, and the subsequent kinetic friction will never allow for full sinking again.

Every time you see a stick-slip phenomenon, such as when angling a rubber on paper, you can explain it with this max-static-friction-being-larger-than-kinetic-friction model.

Rolling friction is a completely different thing. It is wrong to say that it always is lower than static and kinetic friction, it could just as well be larger. Rolling friction is not a friction, but rather a word that covers all losses when stuff is rolling, such as axle frictions, soft surfaces, soft rubber contractions and expansions, non ideal wheel geometry causing non-radial normal forces etc. All such factors suck out energy from the motion, and thus reduce the speed - it may seem like a friction, but it is just an umbrella term for all such other negative effects.

Steeven
  • 50,707