# Friction

Karen Tennenhouse

The actual reasons for friction are complicated, at the level of the atoms and molecules. However, the behaviour of large-scale (visible) objects is fairly simple and consistent, and we include some of it in our course, as follows.

There are three kinds of friction:

• Kinetic friction ( better called “sliding friction” )

• Static friction

• Fluid friction

#### Kinetic (Sliding) Friction

1. It acts only when an object IS sliding/slipping against a surface or other object. (Notice, I said “sliding”, not “moving”.)

2. Direction of the kinetic friction force, on each object, is whatever will tend to make it stop sliding. (Not necessarily to stop moving.)

3. Magnitude of kinetic friction has an exact formula:
• It depends only on the normal force of the surface pressing against the object, and on a coefficient called μ${\displaystyle _{k}}$, the “coefficient of kinetic friction” . Specifically,
${\displaystyle F_{fk}}$ = μ${\displaystyle _{k}}$ N
The value of the μ${\displaystyle _{k}}$ depends on the materials and roughness. (for example there is a μ${\displaystyle _{k}}$ for rubber tires sliding on cement, a different one for copper on steel, and so on.)
• Notice that the magnitude of kinetic friction does not physically depend on the object’s speed, acceleration, net force, nor on any other forces that may be acting at this instant (unless they affect the N.)
• Of course it may happen that we calculate ${\displaystyle F_{fk}}$ from knowing 'a' or 'Net F' etc; but these things are not causing the friction to have this value. Also, in many problems we calculate ${\displaystyle F_{fk}}$ from its formula μ${\displaystyle _{k}}$ N .

#### Static Friction

1. It acts only when an object is in contact with a surface or other object; is not sliding/slipping; but something is “trying” to make it slide. [The object may be stationary or moving, but it is not sliding.]

2. Direction of the static friction force, on each object, is whatever will prevent it from starting to slide. [Not necessarily to prevent it from moving. For example, static friction being used to walk, to make a car drive forward, etc. Also, object riding on a truck: the static friction makes the box accelerate forward, so it stays in contact with the same spot on the truckbed; if there was no friction the truck would slide out from under the box.]

3. Magnitude of static friction does NOT have a formula (In particular, it does not have the formula μ${\displaystyle _{s}}$ N . Really!)
• Magnitude of ${\displaystyle F_{fs}}$ will physically adjust itself, (if it can) to whatever value is needed to prevent slipping.
Therefore the actual value (magnitude) of ${\displaystyle F_{fs}}$ really, physically depends on all the other forces which have components parallel to the surface.
• In a problem, either ${\displaystyle F_{fs}}$ must be given, or else we figure it out from the second law, known acceleration value, and the other forces.

4. What did we mean by saying “${\displaystyle F_{fs}}$ will adjust itself (if it can)”, in point 3?
5. It turns out that there is a maximum (limit) to how large static friction can become in each situation. There actually is a formula for that limit, as follows:
• Any pair of surfaces also has another characteristic coefficient, which helps to determine the largest possible static friction. It is called μ${\displaystyle _{s}}$, the “coefficient of static friction”, and there is a true formula that
${\displaystyle F_{fs}}$ <= μ${\displaystyle _{s}}$ N
(<= means “less than or equal to”.)

• This allows us to solve various problems of the kind “will it start to slide?” or “what is the max/min value of (some physicsl quantity) for the object not to slide?” etc. (The Rotor ride is a cute example.)

• Just notice that in most problems, and in most real-life situations, the magnitude of static friction (really acting) is not equal to μ${\displaystyle _{s}}$ N.

• For most surfaces, μ${\displaystyle _{k}}$ is smaller than μ${\displaystyle _{s}}$ . That is, it is harder to make something start sliding than it is to keep it sliding.

#### Fluid Friction

1. This refers to the “drag” which tries to retard a body moving through a liquid or gas (eg water or air.) It may also be called “air friction” or “air resistance”.

2. Its direction is such as to slow down the object, or to drag along the fluid.

3. It has great practical importance, but because it is mathematically complicated, it is normally left until a university-level physics course. We do almost nothing with it in physics NYA. [ except that, of course, it can be one of the forces acting in a problem. Its value could be given, or could be figured out from knowing the accel and all the other forces.]

4. When a question says a body is falling “at terminal velocity”, it means that the upwards force of air friction is equal in magnitude to the weight, so Net ${\displaystyle {\bar {F}}}$ = 0, which means that the body is falling at constant velocity.

5. Because fluid friction gets larger with larger speeds, a real body in free fall does not continue to accelerate at 9.8 m/s2. Rather, as it falls, the upward air friction gets larger; the downward net force ( = W – F${\displaystyle _{air}}$ ) gets smaller, until F${\displaystyle _{air}}$ = W and the body falls at constant speed. The speed at which this happens is called the “terminal velocity”; it depends on the shape and density of the object, and the viscosity of the fluid. We are familiar with the fact that a penny falls much faster than a sheet of cardboard or aluminum foil, even if they have the same weight. Issues of shape affecting fluid friction are crucial to the design of cars, airplanes, etc,... and of birds, whales and fish! ]