g) The Force of Friction
A. Definition and Types
The force of friction is the force that ___________ motion caused by the
interaction of atoms and molecules between ____________. It is always
______________ to the surface plane. We often think of friction in a negative
sense, ie engine wear or aircraft drag but it is also can be positive. You would not
be able to play sports or warm your hands up by rubbing them together without
___________.
If you look at the surfaces of all objects, there are tiny __________ and ridges.
Those microscopic peaks and valleys catch on one another when two objects are
moving past each other.
Frictional force is classified with two major types. ____________ friction
opposes the initial motion of an object from rest. ____________ friction opposes
the motion of an object that is already moving. Static friction is always
_____________than kinetic friction given the same surface. ‘Coin on a book demo’
B. Quantifying Friction
The force of friction depends on ______ criteria. If a desk is pushed along
the floor some amount of force will oppose this motion which is the force of
friction. If some one stands on the desk and the desk is pushed again,
__________ force will have to be applied to move it. The frictional force varies
with the _____________ force. Secondly, the force of friction will vary
according to the type of surface interaction present. If Teflon was put on the
bottom of the legs of the desk, friction would be ____________. Each type of
surface will have its own _______________ of friction, a ratio of the frictional
force divided by the normal force.
s  static friction
m=
F
F
f
or
Ff  FN
N
K  kinetic friction
FN  normal force
Ff  frictional force
C. Assumptions About Friction
1. The frictional force is independent of area of contact.
Exception:
2. The frictional force is independent of the velocity of motion.
Exception:
3. The frictional force is proportional to the normal force.
Exception:
“While this general description of friction has practical utility, it is by no means a
precise description of friction. Friction is in fact a very complex phenomenon which
cannot be represented by a simple model. Almost every simple statement you make
about friction can be countered with specific examples to the contrary. Saying that
rougher surfaces experience more friction sounds safe enough - two pieces of
coarse sandpaper will obviously be harder to move relative to each other than two
pieces of fine sandpaper. But if two pieces of flat metal are made progressively
smoother, you will reach a point where the resistance to relative movement
increases. If you make them very flat and smooth, and remove all surface
contaminants in a vacuum, the smooth flat surfaces will actually adhere to each
other, making what is called a "cold weld".
Taken from http://hyperphysics.phy-astr.gsu.edu/hbase/frict.html
When studying friction there are definitely some hidden surprises!
In the columns below, list some examples where friction can be helpful and where
friction is a hindrance.
Friction Good
Friction Bad
Specific Friction Problems:
1. A 10.0 kg mass rests on a table. If μs = 0.450 and μK = 0.250, find the
amount of force required to move the mass from rest and the amount of
force required to keep it moving at a constant velocity.
2. A 25.0 N force is necessary to keep a 15.0 kg mass moving at a constant
velocity. What is the coefficient of kinetic friction?
3. A 0.54 kg puck is sliding across the ice (μK = 0.150) with a velocity of 12.0
m/s. How far will it travel before it comes to a complete stop?
h) General Dynamic Scenarios (Dynamic Notes cont’d)
*All dynamic problems can be attempted using this general algorithm:
a) Draw a diagram with all forces present
b) Construct at least three Fnet statements
c) Isolate variable asked for and make the implicit explicit
d) Plug and Chug
1. Horizontal Plane – No Friction
FN
FA
Fg
Fnet = FA + FN + Fg
FnetH = FA
FnetV = FN + Fg = 0
FA  ma
add to O
Notice that in this situation we are interested in acceleration in the horizontal
direction so the normal and gravitational are excluded. They add to zero anyways.
Example: Find acceleration if m = 20.0 kg, FA = 50.0 N
2. Horizontal Plane - with Friction
FN
Ff
add to 0
FA
Fg
Fnet = FA + Ff + FN + Fg
FnetH = FA + Ff = ma
FnetV = FN + Fg = 0
\FA + Ff = ma
Notice that in this situation the sign of the Ff (usually negative) will be opposite to
FA and therefore be subtracted from FA. Once again, we are interested in
acceleration in the horizontal direction and exclude FN and Fg. Here we assume that
FA is larger than Ff. *It is possible to drag an object at a c.v. in which case FA = Ff.
Example: Find acceleration if m = 20.0 kg, FA = 50.0 N and Ff = 20.0 N
3. Horizontal Plane – Force at an Angle (Sled)
FN
FA
FAV
θ
Ff
Fnet = FAH + Ff + FN + Fg + FAV
FnetH = Ff + FAH = ma
FnetV = FN + Fg + FAV = 0
FAH
Fg
Notice that it is not FA but its component FAH combined with Ff that creates the
net force accelerating the object. Assuming no torque, FN will decrease by the
amount of FAV thereby decreasing friction. *It is possible to balance the forces so
the object travels at c.v. *Unless stated an FA might not be enough to overcome
static friction.
Example: Find acceleration if m = 20.0 kg, FA = 50.0 N and Ff = 10.0 N and θ = 30.0°
4. Horizontal Plane – Force at an Angle (Lawnmower)
FA
FAV
FAH
FN
θ
Ff
Fnet = FAH + Ff + FN + Fg + FAV
FnetH = Ff + FAH = ma
FnetV = FN + Fg + FAV = 0
Fg
Notice that it is not FA but its component FAH combined with Ff that creates the
net force affecting the acceleration the object. Assuming no torque, FN will
increase by the amount of FAV thereby increasing friction. *It is possible to
balance the forces so the object travels at c.v. *Unless stated an FA might not be
enough to overcome static friction.
Example: Find acceleration if m = 20.0 kg, FA = 50.0 N and Ff = 20.0 N and θ = 30.0°
5. Inclined Plane (no friction)
Fnet = FN + 𝐹𝑔⊥ + Fg//
Fnet// = Fg// = ma
Fnet⊥ = Fg⊥ + 𝐹𝑁 = 0
FN
Fg// = mgsinθ
Fg⊥ = mgcosθ
Fg//
Fg
∴ 𝑎 = 𝑔𝑠𝑖𝑛θ
θ
𝐹𝑔⊥
θ
*Notice that you have to decide which sign down the plane will be so that your
calculation are consistent with your FBD. Whether or not you use negative or
positive does not matter, just make sure that the sign of your variables (ie ‘g’)
agree with that decision.
Example: mass = 12.0 kg, θ = 35.0°
6. Inclined Plane (with friction)
Ff
Fnet = FN + 𝐹𝑔⊥ + Fg// + Ff
Fnet// = Fg// + Ff
Fnet⊥ = Fg⊥ + 𝐹𝑁 = 0
FN
Fg//
Fg// = mgsinθ
Fg⊥ = mgcosθ
𝐹𝑔⊥
∴𝑎=
Fg
θ
𝐹𝑔∕∕ + 𝐹𝑓
𝑚
θ
*Note that there is a point at which the mass does not accelerate due to static
friction.
Example: mass = 12.0 kg, θ = 55.0°, μs = 0.250, μk = 0.150
7. Elevator Type Questions (Acceleration in the Vertical Dimension)
Fnet= FN + Fg Most of the time you will be dealing with the normal and
gravitational forces. When no surface is involved the
applied force often replaces the normal force.
*Note: When Fnet= 0 there is no acceleration and the object’s velocity is constant
and vica versa.
*When Fnet≠ 0 acceleration is taking place and Fnet= ma.
Three possible scenarios: a = 0, a < 0 and a > 0.
1. (a = 0) Normal Weight – If there is no acceleration, Fnet = 0 so your weight is
what it would be at rest.