1. Friction
Chapter Opener. Caption: Newton’s laws are fundamental in physics. These photos show two situations of using Newton’s laws which involve some new elements in addition to those discussed in the previous Chapter. The downhill skier illustrates friction on an incline, although at this moment she is not touching the snow, and so is retarded only by air resistance which is a velocity-dependent force (an optional topic in this Chapter). The people on the rotating amusement park ride below illustrate the dynamics of circular motion.

2. Consider An Object Coming to Rest
Aristotle’s Idea: At rest is the “natural state” of terrestrial objects

3. Consider An Object Coming to Rest
Aristotle’s Idea: At rest is the “natural state” of terrestrial objects
Newton’s View: (Galileo’s too!)
A moving object comes to rest because a force acts on it.

4. Consider An Object Coming to Rest
Aristotle’s Idea: At rest is the “natural state” of terrestrial objects
Newton’s View: (Galileo’s too!)
A moving object comes to rest because a force acts on it.
Most often, this stopping force is
Due to a phenomenon
called friction.

5. There are 2 types friction: Static (no motion) friction
Friction is always present when 2 solid surfaces slide along each other. See 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

6. 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.

7. Ffr  kFN (magnitudes)
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 = FN 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

8. The Kinetic Coefficient of Friction k
Properties of 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 soon). Further,
k is dimensionless
Usually, k < 1

9. 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:

10. 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)

11. 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

12. 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

13. Static Friction Static Friction
In many situations, the 2 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.

14. (In the horizontal (x) direction):
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

15. (In the horizontal (x) direction):
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

16. (In the horizontal (x) direction):
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.

17. s  Coefficient of Static Friction
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

18. 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 (next slide). Further,
s is dimensionless
Usually, s < 1
Always, k < s

19. Coefficients of Friction
μs > μk Ffr (max, static) > Ffr (kinetic)

20. Conceptual Example A hockey puck is moving at a constant
speed v, with NO friction. Which free
body diagram is correct?

21. Static & Kinetic Friction

22. 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
Ffriction = μk N
The force of Static Friction varies:
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

23. Friction & Walking The person “pushes” off during each step.
The bottoms of his shoes exert a force on the ground. This is Fon ground .
If the shoes do not slip, the force is due to static friction
The shoes do not move relative to the ground

24. This force propels the person as he moves
Newton’s Third Law
This tells us that there is a reaction force Fon shoe
This force propels the person as he moves
If the surface was so slippery that there was no frictional force, the person would slip

25. This is the force that propels
Friction & Rolling
The car’s tire does not slip. So, there is a friction force Fon ground between the tire & road.
There is also a Newton’s 3rd Law reaction force Fon tire on the tire.
This is the force that propels
the car forward

26. 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.

27. 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?
Figure 5-4.
Answer: Friction, of course! The normal force points out from the wall, and the frictional force points up.