# Is the deceleration of a body coming to rest due to friction completely smooth right up to the end?

Referring to the (empirical) laws of (dry) friction from Wikipedia it would appear that the deceleration is constant until the speed is zero.

"Coulomb's Law of Friction: Kinetic friction is independent of the sliding velocity."

I'm wondering though whether there is a threshold (speed) below which the body will suddenly stick (i.e. stop), similar to the static friction (force) threshold before which motion doesn't start.

• This question could be rephrased this way: A bonding occurs between objects that are at rest and in contact with each other (adhesion). This is the reason that the coefficient of static friction is higher than the coefficient of kinetic friction (due to "peaks and valleys" of the surfaces of the materials). Do the two objects have to be totally at rest with respect to each other for this bonding to occur?? – Jack R. Woods May 23 '17 at 14:00
• Intuition tells me that it would depend on the materials and the speed would be extremely slow. Otherwise, the bonding would never take place at all. – Jack R. Woods May 23 '17 at 14:13
• So the question boils down to: What is the maximum relative speed at which adhesion bonds can form? This is quite an interesting question. – Steeven Jul 5 '17 at 8:29
• I would assume that dependent on the surface and the object, you could conclude that there would be a sticking action at the point when the object is moving slow enough to form bonds with the surface. Essentially, it would make sense that when the kinetic friction becomes static, there would be a sticking action, but static friction only exists in still systems, so there is an argument either way. – BooleanDesigns Feb 7 '18 at 15:22
• Re: the relative speed at which bonds can form — the formation of bonds, i.e. rearrangement of electrons, once the atoms are more or less in place, is fast. Significant fraction of c sort of fast, I think. – colinh Feb 19 '18 at 14:53

I think this is a complex situation than cannot be resolved only considering rigid bodies. IRL everything is "deformable" and as a result not all parts of a sliding body may move with the exact same speed.

As a body is sliding under friction it is reasonable to assume that the force of friction deforms the body in a shear fashion like this:

Now, at the moment where the object stops (or rather starts to stop), the friction force might instantaneously jump up in order to remove enough momentum from the bottom part of the object to stop (at an instant).

But the rest of the body will still be in motion, and a damped oscillation would occur during which the contact friction force will vary. In the end the motion and friction will die down.

Qualitatively I would describe the situation as follows:

You can imagine the molecules binding up as some very small speed at the bottom, and the top part swinging back and forth for a short amount of time.

Both static and dynamic friction are limited, but to go from speed $v$ to 0 in $t$ seconds requires an acceleration of ${v\over t} \frac{m}{s^2}$. But there is a limit to how small $t$ can be because the acceleration is limited due to the limit in the friction. So there are no jumps in the speed, as it will always take some time to change the speed.

• I think by smooth, the OP meant zero jerk, as opposed the mathematical definition of there term: continuous. – JEB Feb 28 '18 at 17:48