Kinetic Friction
The specific manifestation of friction that is directly opposed to an object's sliding motion along a surface. The force of kinetic friction has a size independent of the speed of the object, and proportional to the normal force exerted on the object by the surface.
Kinetic Friction as a Force
Magnitude
For an object that is already sliding along a surface or is accelerating from rest on a surface, the size of the friction force will be given by:
\begin
[ F_
= \mu_
N]\end
Note that the size of the kinetic friction is fixed by the normal force and the coefficient. In contrast to the case of
static friction, there is no upper limit in the expression. Thus, it is not necessary to consider the complete net force to find the friction force for the kinetic case.
where μk is the coefficient of kinetic friction. The coefficient of kinetic friction is a dimensionless number, usually less than 1.0 (but not required to be less than 1.0). Rough or sticky surfaces will yield larger coefficients of friction than smooth surfaces. N is the normal force exerted on the object by the surface which is creating the friction, which is a measure of the strength of the contact between the object and the surface.
The coefficient of kinetic friction for a given object on a given surface will usually be different than the corresponding coefficient of static friction. It is usually the case that μk < μs.
Direction
There are two possibilities to consider when determining the direction of kinetic friction:
- For a sliding object, the direction of the kinetic friction must be opposite to the direction of the velocity.
- For an object just beginning to slide (the object still has zero velocity) then the friction must oppose the acceleration.
Kinetic Friction as Non-Conservative Work
When an object is sliding on a surface that can be considered to be at rest in an inertial frame of reference, kinetic friction is the prototypical non-conservative force. When the motion of an object sliding on a surface is viewed from a frame at rest with respect to the surface, the force of friction always opposes the object's motion, and so always does negative work. For the case of a constant friction force, the definition of work can be integrated to give:
\begin
[W_
= -F_
d]\end
where d is the distance traveled by the object along the surface.
Contrast this with a conservative force like gravity (near-earth), which does negative work on an object that is rising, and then returns energy by doing positive work on the object as it falls.
The work done by friction becomes very confusing when a reference frame is chosen in which the surface is moving. See the discussion of static friction for more details.