Friction
Consider An Object Coming to Rest
• Aristotle’s idea: Rest is the
“natural state” of terrestrial objects
• Newton’s view: A moving object
comes to rest because a force acts on it.
• Most often, this stopping force is
Due to a phenomenon
called friction.
Friction
• Friction is always present when 2 solid
surfaces slide along each other. See the figure.
• It must be accounted for when
doing realistic calculations!
• It exists between any 2
sliding surfaces.
• There are 2 types friction:
Static (no motion) friction
Kinetic (motion) friction
• Two types of friction:
Static (no motion) friction
Kinetic (motion) friction
• The size of the friction force depends on the
microscopic details of the 2 sliding surfaces.
• These details aren’t fully understood &
depend on the materials they are made of
Are the surfaces smooth or rough?
Are they wet or dry?
Etc., etc., etc.
• Kinetic Friction is the same as
Sliding Friction.
• The kinetic friction force Ffr
opposes the motion of a mass.
Experiments find the relation used to
calculate Ffr.
• Ffr is proportional to the
magnitude of the normal force N
between 2 sliding surfaces. The
DIRECTIONS of Ffr & N are 
each other!! Ffr  N
• We write their relation as
Ffr  kFN (magnitudes)
k  Coefficient of Kinetic
Friction
The Kinetic Coefficient
of Friction k
• Depends on the surfaces &
their conditions.
• Is different for each pair of
sliding surfaces.
• Values for μkfor various
materials can be looked up in
a table (shown later). Further,
k is dimensionless
Usually, k < 1
Problems Involving Friction
• Set up the problem as usual, including the force of
friction. For example, the hockey puck in the figure:
Newton’s 2nd Law for the Puck:
(In the horizontal (x) direction):
ΣF = Ffr = -μkN = ma
(1)
(In the vertical (y) direction):
ΣF = N – mg = 0
(2)
• Combining (1) & (2) gives
-μkmg = ma so a = -μkg
• Once a is known, we can do kinematics, etc.
• Values for coefficients of friction μkfor
various materials can be looked up in a
table (shown later). These values depend
on the smoothness of the surfaces
Static Friction
• In many situations, the two
surfaces are not slipping (moving)
with respect to each other. This
situation involves
Static Friction
• The amount of the pushing force Fpush
can vary without the object moving.
• The static friction force Ffr is as
big as it needs to be to prevent
slipping, up to a maximum value.
Usually it is easier to keep an object
sliding than it is to get it started.
Static Friction
• The static friction force Ffr is as big as it
needs to be to prevent slipping, up to a
maximum value. Usually it is easier to keep
an object sliding than it is to get it started.
• Consider Fpush in the figure.
Newton’s 2nd Law:
(In the horizontal (x) direction):
∑F = Fpush - Ffr = ma = 0
so Ffr = Fpush
• This remains true until a large enough
pushing force is applied that the
object starts moving. That is, there is
a maximum static friction force Ffr.
• Experiments find that the maximum static
friction force Ffr (max) is proportional to
the magnitude (size) of the normal force N
between the 2 surfaces.
• The DIRECTIONS of Ffr & N are  each other!!
Ffr  N
• Write the relation as Ffr (max) = sN (magnitudes)
s  Coefficient of Static Friction
• Always find s > k
 Static friction force: Ffr  sN
The Static Coefficient of
Friction s
• Depends on the surfaces &
their conditions.
• Is different for each pair of
sliding surfaces.
• Values for μs for various
materials can be looked up in
a table (shown later). Further,
s is dimensionless
Usually, s < 1
Always, k < s
Coefficients of Friction
μs > μk Ffr (max, static) > Ffr (kinetic)
Conceptual Example
Moving at constant v, with NO friction,
which free body diagram is correct?
Static & Kinetic Friction
Kinetic Friction Compared
to Static Friction
• Consider both the kinetic and static friction cases
– Use the different coefficients of friction
• The force of Kinetic Friction is just
Ffriction = μk N
• The force of Static Friction varies by
Ffriction ≤ μs N
• For a given combination of surfaces, generally
μs > μk
• It is more difficult to start something moving than
it is to keep it moving once started
Friction & Walking
• The person “pushes” off
during each step.
• The bottoms of his shoes
exert a force on the ground
This is
• If the shoes do not slip, the
force is due to static friction
– The shoes do not move
relative to the ground
• Newton’s Third Law
tells us there is a
reaction force
• This force propels the
person as he moves
• If the surface was so
slippery that there was
no frictional force, the
person would slip
Friction & Rolling
• The car’s tire does not
slip. So, there is a
frictional force
between the tire & road.
• There is also a Newton’s 3rd Law
reaction force
on the tire.
This is the force that propels
the car forward
Example: Friction; Static & Kinetic
A box, mass m =10.0-kg rests on a horizontal floor. The
coefficient of static friction is s = 0.4; the coefficient of
kinetic friction is k = 0.3. Calculate the friction force on the
box for a horizontal external applied force of magnitude:
(a) 0, (b) 10 N, (c) 20 N, (d) 38 N, (e) 40 N.
Conceptual Example
You can hold a box against a
rough wall & prevent it from
slipping down by pressing
hard horizontally. How does
the application of a horizontal
force keep an object from
moving vertically?
a
FN2
FN1
F21
FA =
F12
Ffr1
m1 g
m1: ∑F = m1a;
Ffr2
m2 g
x: FA – F21 – Ffr1 = m1a
y: FN1 – m1g = 0
m2: ∑F = m1a;
x: F12 – Ffr2 = m2a
y: FN2 – m2g = 0
Friction:
Ffr1 = μkFN1; Ffr2 = μkFN2
3rd Law:
F21 = - F12
m1 = 75 kg
m2 = 110 kg
a = 1.88 m/s2
F12 = 368.5 N