PhysicsLAB Resource Lesson
Properties of Friction

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Friction is a force and is measured in newtons. Friction comes in various types, for example: static, kinetic, and rolling. We will begin our study by listing some general properties. Friction
  • is essentially an electrostatic force between two surfaces
  • never initiates motion; it only responds to motion
  • depends on the types of materials that are in contact (µ - the coefficient of friction)
  • depends on the net force normal pressing the two surfaces in contact (N)
  • acts parallel to the surfaces that are (or might have the potential to be) moving with respect to each other
  • opposes the direction of motion
  • is independent of the area of the surfaces in contact
Some additional facts about frictional forces include:
  • static friction > kinetic friction > rolling friction for the same combinations of surfaces
  • when two surfaces are slipping across each other in the presence of kinetic friction, heat is generated and mechanical energy is not conserved
  • when a ball rolls (static friction) without slipping across a surface, mechanical energy is conserved and no heat is generated
Kinetic friction
When two surfaces are sliding across each other, the amount of kinetic friction present can be calculated using the equation
fk= µkN
where µk is the coefficient of kinetic friction and N is the net force normal.
The magnitude of kinetic friction does not vary as the object moves. The coefficient of friction, µ, depends on the materials that are in contact with each other - it is a value usually looked up in a table. This dimensionless ratio of the force required to overcome friction to the net force normal does not have a unit of measurement. The magnitude of the coefficient of friction is usually less than 1, although some combinations can be greater than one.
approximate values of some frictional coefficients
Static friction
The maximum amount of static friction can be calculated using the equation
fs max = µsN

where µs is the coefficient of static friction and N is the net force normal. 
However, according to Newton's Third Law, the amount of static friction required to maintain static equilibrium, when an object is resisting a push or pull, depends directly on the amount of external force applied to it. For example, consider the 10 kg box initially just resting on a table.
Suppose that the coefficient of static friction between the box and the table's surface is 0.4. This would mean that the maximum amount of static friction present between the two surfaces would be

fs max =  µsN
fs max =  (0.4)(10)(9.8)
fs max =  (0.4)(98)
fs max = 39.2 N
Now, suppose that you only push on the box with a horizontal force of 15 N.
Since the applied force, F = 15 N, is smaller than the maximum allowed static friction, fs max = 39.2 N, it would initially appear as if the box should begin to accelerate towards the left. That is, static friction would not only initiate motion, but would cause the box to have a non-zero acceleration!
That scenario would obviously be physically impossible! Thus, according to Newton's 3rd Law, the only amount of static friction required would be 15 N to keep the box in equilibrium. Notice that the friction vector is now equal in length to that of the applied force.
Once the applied force equals the maximum value for static friction, the object will slip and begin to slide. At that time, the friction between the two surfaces will be kinetic friction, no longer static friction.
Sometimes it is convenient to think of the static friction between two surfaces as being like a "saving account." You only use (withdraw) what you need at any given time to keep the system in equilibrium until you reach your maximum, or critical, amount available.
To read a discussion of static friction and rolling spheres see the lesson on rotational dynamics.

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