Friction of RIGID bodies can be approximated
by 3 rules:
1. The force of friction is directly proportional to the applied load. (Amontons 1st Law)
2. The force of friction is independent of the apparent area of contact. (Amontons 2nd Law)
3. Kinetic friction is independent of the sliding velocity. (Coulomb's Law)
Coulomb FrictionCoulomb friction, (named after Charles-Augustin de Coulomb), is a model used to calculate the force of dry friction. It is an approximation to what happens in real life, according to the 3 rules in the summary box above. It is meant to be used on rigid bodies, since soft and flexible materials (like rubber tyres for example) are more sensitive to the area of contact (See point 2 above).
The definition is below;
is the friction force.
is the coefficient of friction. (depends on materials)
is the normal force exerted between the surfaces, (which is equal to W in this diagram).
This formula is a rule of thumb giving an approximation of an extremely complicated physical interaction. In many cases, the relationship between normal force and frictional force is not exactly linear (the frictional force is not entirely independent of the contact area of the surfaces - especially so for soft materials like rubber). The Coulomb approximation works best for relatively hard, rigid materials.
Static FrictionWhen the two surfaces are not moving, the friction is slightly higher. = coefficient of static friction. Motion cannot begin until the applied force is higher than the maximum friction force
Kinetic FrictionWhen the two surfaces are moving, the friction usually goes down a little. = coefficient of kinetic friction. Friction force always opposes the direction of motion and is considered to be constant.
The force of friction is always exerted in a direction that opposes movement (for kinetic friction) or potential movement (for static friction) between the two surfaces.
Coefficients of FrictionThe coefficient of friction , is a dimensionless (scalar) value so it has no units. (This is because it is a ratio between two forces). The coefficient of friction depends on the materials used; for example, ice on steel has a low coefficient of friction, while rubber on pavement has a high coefficient of friction. Coefficients of friction range from near zero to greater than 1 – such as a soft rubber tyre on rough concrete.
The coefficient of friction is measured experimentally, and cannot be found through calculations. Rougher surfaces tend to have higher effective values. Most dry materials in combination have friction coefficient values between 0.3 and 0.6. Values outside this range are rarer, but teflon, for example, can have a coefficient as low as 0.04. A value of zero would mean no friction at all, which is impossible in any practical sense – even magnetic levitation vehicles have drag. Rubber in contact with other surfaces can yield friction coefficients from 1 to 2.
The normal force
The normal force is the net force compressing two parallel surfaces together, and is always perpendicular to the surfaces.
In the simple case of a mass resting on a horizontal surface, the only component of the normal force is the force due to gravity, so the normal force = weight. = W = mg.
If the object is on an inclined plane, the normal force is less, because less of the force of gravity is perpendicular to the face of the plane. Therefore, the normal force, and ultimately the frictional force, is determined using force components.
Note: There may be forces other than gravity - like springs.
In a typical friction problem, we must first determine and then multiply by to give us the friction force
Block on a ramp (top) and corresponding free body diagram of just the block (bottom).
Approximate coefficients of frictionThe most slippery solid known, discovered in 1999, dubbed BAM (for the elements boron, aluminum, and magnesium), has an approximate coefficient of friction of 0.02, about half that of Teflon.
Angle of frictionAnother way to define the friction is by the angle of the opposing force.
The friction angle is defined as;
tan = /
So tan =
Angle of reposeWhen a body is on an incline, there is a maximum angle that can be reached before it will begin to slide. That maximum angle is called the angle of repose, (Sometimes the angle of repose refers to the maximum slope of granular material instead. Never mind).
It is defined as:
where is the angle from horizontal and is the static coefficient of friction between the objects.
The angle of repose occurs when = .
The block will not slide as long as (friction force) is greater than (parallel force).
At the point where motion begins, we can use that angle to calculate the coefficient of friction.