Physics 204A Class Notes
12-1
Section 12 – The Frictional Force
Outline
1. The Coefficient of Kinetic Friction
2. The Coefficient of Static Friction
Why do objects do what they do? Because of the forces acting on them is one answer. In the last
section we introduced four common forces in our everyday world, the gravitational force, tension, the
normal force and friction. For simplicity, we kept the forces acting along one coordinate axis. Now we
will focus on the frictional force and expand to forces that act along more than one axis.
Remember the big picture, once we know the forces that act on an object, we can use Newton’s Laws to
find the acceleration of the object and from there find the complete description of the motion of the
object. The general method is,
1. Find the forces acting on the object.
2. Use Newton’s Laws to find the acceleration.
3. Use the definitions of velocity and acceleration as well as the initial position and initial velocity
to completely describe the motion.
1. The Coefficient of Kinetic Friction
If you push on a crate to get it moving, it will quickly come to rest once you stop pushing. Newton’s
Laws explain that the crate comes to rest not because rest is the natural state of motion, but because
frictional forces cause the crate to slow down. The detailed behavior of the frictional force is quite
complex. It is due to the molecular forces between two surfaces. Let’s simplify matters as much as
possible by looking at the frictional force empirically. Let’s look at two cases: one where the crate is
moving and the frictional force is said to be “kinetic friction” and one where the crate is at rest and the
frictional force is said to be “static friction.”
Looking at the kinetic case, suppose the crate is moving to the right at
some speed v0, but skidding along so it will soon be at rest. The forces
on the crate are shown at the left. The crate will accelerate to the left
due to the frictional force and soon come to rest. Suppose, the crate is
moving to the right at the same speed, but someone had put a second
crate on top of it. What would be different? The weight of the one
crate we are looking at would still be the same, but the normal force,
and the frictional force would both be larger. The point is that you
probably have the sense that things that weigh more “sort of have more friction.” However, from the
point of view of Newton’s Laws, objects that feel more normal force feel more frictional force. We can
say that the frictional force is proportional to the normal force or
Fkf =
µ
Fn
where µ is mathematically, the constant of proportionality. Physically, µ represents all the complex
interactions between the molecules of the two surfaces. If the surfaces are rough, µ would be larger. If
the surfaces are smooth, µ is smaller. Instead of defining µ in terms of the intermolecular forces, it is
easier to define the coefficient of kinetic friction as the ration of the frictional force to the normal force.
Definition of Coefficient of Kinetic Friction
µk≡Fkf
Fn
Ffr
Fg
Fn
v0
