Walking and friction

If walking is a result of the reaction to a kick backwards to the ground (reaction being friction), it appears that it should be true that the kick will have to be less than the kinetic friction (which is less than the static friction threshold = $\mu$mg) or the acceleration will never be more than $\mu$g. What happens if the kick exceeds this force, there still has to be a reaction? Is that reaction distinguished from the kinetic friction?

• FYI: When you're walking, your foot may not be exactly sticking to ground. Thus, normal force may increase faster than friction (static friction threshold), then your feet may become a self-locking machine. (maybe applicable for running) Commented Feb 6, 2016 at 10:51

Depending on if you kick into the ground or place your foot firmly on the ground and then "kick" to move forward, you either have to kick with less force than the threshold values for kinetic or static friction respectively to maintain "normal" walking.

Overcoming this threshold value will result in your foot having a relative velocity to the ground, or in laymans terms, you will slip and slide. This does not mean you can not maintain walking, you will just not be able get a firm foothold. When sliding like this, the friction you experience is the kinetic friction threshold value, meaning you will not be able to use more force to accelerate your body than this value. This for example happens when you thrust too hard while walking on ice.

• Thanks for the answer. Your second paragraph makes sense and matches what I would expect. I am not sure I understand your first paragraph. I think you are missing a matching "or" for your "either" that is making it hard to comprehend.
– pran
Commented Nov 1, 2013 at 4:21
• I have fixed the wording now. =) The first paragraph deals with what friction coefficient you have to use in different situations. Basically it says that if your foot is still when the kick starts, then you have to use the static friction coefficient, but if your foot have some relative motion to the ground when the kick starts you have to use the kinetic friction coefficient. Commented Nov 1, 2013 at 19:18
• Sorry, I thought I had found a different explanation but I realized the mistake I was making. I am going back to your explanation. I am still not sure though. You talk about slipping and sliding. If I am experiencing kinetic friction, I have already overcome the threshold value of static friction. I have never heard of the threshold value of kinetic friction. Kinetic friction is supposed to be less than the static fraction. Can you explain the slip and slide phenomenon more in detail?
– pran
Commented Nov 11, 2013 at 18:22

the kick will have to be less than the kinetic friction (which is less than the static friction threshold...)

Not quite. The kick will have to apply less force than the static friction. There is no need to consider kinetic friction at all. Only when the kick applies a larger force than the static friction limit, will the foot start to slide and kinetic friction will be relevant.

Those two kinds of friction are for two different cases:

• Static friction when there is no slip: $f_s\leq \mu_s n$
• Kinetic friction when there is slip (sliding): $f_k=\mu_k n$

$n$ is the normal force. Kinetic friction will only happen when there is (relative) motion; static friction will only happen when there is not.

• So, you put your foot on the ground. It doesn't slip, so we are talking static friction. As you see from the formula, static friction $f_s$ can take any value up to a certain limit! Static friction will always have the magnitude that is needed to keep your foot still, but if it is not able to, because the required amount exceeds the limit, then static friction cannot hold your foot still anymore and then it will slip and start to slide.

• Then you are in the kinetic friction region. As you see from the formula, there is no "limit" for kinetic friction $f_k$ simply because it doesn't vary like static friction can. It always has a specific value - just only during relative motion (sliding). This means that while you walk, your foot skids and slides backwards, but you still get some forward drift. Like walking in sand. Or like accelerating too much in a car, so the tires start burning because they skid and roll uncontrollably on the asphalt without grip but the car still begins to move slowly forwards.

The extreme case is a perfectly smooth icy surface, where $\mu_k=0$, so there will never be any friction nomatter what and thus never any forward drift. But this is only a thought-experiment as an ideal model. Ice in the real world does have friction - otherwise ice-hockey would be impossible.