# What’s does “co efficient of friction” mean and how is it different from Friction Force?

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What’s does “co efficient of friction” mean and how is it different from Friction Force?

In: 1 Oh man this is going back years so hopefully someone can chime in to keep me honest.

Coefficient of friction is an amount of force that is needed to overcome for the objects to start moving and friction force is what’s needed to keep the object moving. If I remember correction COF is usually a higher value. When you drag an object along a flat floor, the friction you have to overcome depends on how hard the object is pushing itself into the floor. In other words, it depends on the object’s weight: the heavier the object, the more friction there is, assuming that we’re keeping the materials the same. It turns out that, for practical purposes, the friction is almost exactly proportional to the weight: double the weight, you double the friction; divide the weight by 3 and you divide the friction by 3.

General math fact: when two things are proportional, you can write an equation: one of them equals some constant value times the other. In this case, we have weight and friction proportional, so we can write Friction Force = k * Weight. But of course the value of *k* (which is just some number that depends on the materials involved) here matters: if *k* is very small, then the friction is small even if the weight is very large. If *k* is very big, the friction is big even if the weight is pretty small.

The number *k* in this equation is the *coefficient of friction*. It describes how high the friction force is *relative to the weight of the object*. A material that has lots of friction relative to its weight has a high coefficient of friction; a material that has less friction relative to its weight has a low coefficient of friction. A coefficient is a number you multiply an input value by to get the output. In this case, you’ve got the equation:

f = μN

f is the friction force
μ is the coefficient of friction
And N is the *normal force*

The normal force is just the force pushing the two surfaces together. So for a box sitting on the floor, it’s just gravity.

Since friction force is the product of the coefficient of friction, you can make friction go up by either increasing the normal force (i.e. pushing them together harder) or increasing the coefficient of friction (e.g. by making one or both surfaces rougher).

Coefficient of friction is a property of *both materials together*. Some materials have pretty low friction with most materials (Teflon is a great example) and some materials have a much higher friction with most materials (like sandpaper). But it’s the *interaction* between the two that gives the coefficient of friction.

If that seems confusing, imagine a board with a bunch of nails poking out of it. If you put a big block of rubber on it, the nails would stab in and it’d be really hard to push the block around. On the other hand, if you put a sheet of metal, the nails wouldn’t poke in at all, and the sheet would move much more easily. Friction works partially like this on a microscopic level Ok so the coefficient of friction is the constant that relates the pressure force often weight with the friction force. So Ff ~ Fp this Fp is often just the weight of the object Fg=m×g, m is mass g = 9.8 m/s². This coefficient has information about how much friction is between the two surfaces. If the table is frictionless this coefficient is 0. Any greater than 0 and you got friction but this friction is proportional to this Fp. So its simply Ff = mu×Fp. If Fp=1N, measure the force of friction and that is going to equal mu. This coefficient has no dimension its just a number. If this coefficient is small you got a little amount of friction like ice, if its large Ff will be big like with sandpaper. The coefficient of friction is the material-specific number you multiply by to find the friction force.

For example, train wheels on steel rails have a coefficient of around 0.002, meaning that a 50 ton train has a friction force of ~980 Newton on horizontal rail, while a 500kg car (with its wheels replaced) would only have a friction force ~9.8N.