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8/3/2019 Lecture 8 Friction&Drag
http://slidepdf.com/reader/full/lecture-8-frictiondrag 1/21
Example 5:
F
m1
m2
m1=12kg
m2=3kg
F=45N
Find the tension in the rope
connecting the two masses
Find the acceleration of the
two masses
8/3/2019 Lecture 8 Friction&Drag
http://slidepdf.com/reader/full/lecture-8-frictiondrag 2/21
Friction
Friction is a result of contact between dry solid surfaces.
Even though friction is considered as a restricting force
and a waist of energy, such as in car engine..
In many other cases it is very important.
For example:
1) Motion of a wheel
2) Walking
3) Tying knots4) Holding things
5) And much more
8/3/2019 Lecture 8 Friction&Drag
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What is the source of friction?
Friction is the sum of all the forces acting between thesurface atoms of one body and the surface atoms of
another body.
Therefore the better the contact is the larger the friction.
Remember: No surface is perfect.
8/3/2019 Lecture 8 Friction&Drag
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How do we “see” friction?
1) If we send an object sliding
horizontally across a table it
slows down.
v2) In order to move and object
on a smooth surface with
constant velocity we have toconstantly apply a force.
v
8/3/2019 Lecture 8 Friction&Drag
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Exploring friction
Friction, f = 0F N
mg F N
mg
F
If object is not moving, f = F
F N
mg
2F If object is still not moving, f = 2F
8/3/2019 Lecture 8 Friction&Drag
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Exploring fr iction (continue)
F N
mg
F f
The direction of f is to the left
F N
mg
F f
The direction of f is to the right
Friction is always opposing the applied force
8/3/2019 Lecture 8 Friction&Drag
http://slidepdf.com/reader/full/lecture-8-frictiondrag 7/21
What happens during motion?
Once the object starts moving we usually feel a relief.This is because the friction force opposing the motion
is reduced.
The friction between sliding surfaces is less than
between static surfaces.
f s > f k
Summary:
F (applied)
f
f s,max
f k
Start of motion
8/3/2019 Lecture 8 Friction&Drag
http://slidepdf.com/reader/full/lecture-8-frictiondrag 8/21
What determines f s and f k ?
F
F f
Will f increase when we add
the mass on top?
F f
Will f increase when we push
the object down without
increasing the mass?
The force that is changing in both cases is F N .
Conclusion f is proportional to F N .
8/3/2019 Lecture 8 Friction&Drag
http://slidepdf.com/reader/full/lecture-8-frictiondrag 9/21
The friction is also dependent on the interaction
between the two surfaces involved.
That determines the coefficient of proportionality
between f and F N .
N F f
N s s F f max,
Finally:
But since, the static friction is different than
the kinetic friction it implies that the coefficientis different.
N k k F f
8/3/2019 Lecture 8 Friction&Drag
http://slidepdf.com/reader/full/lecture-8-frictiondrag 10/21
Conceptual Question 1:
A block of mass 10 kg lies on the floor.What is the magnitude of the frictional force acting
on it from the floor?
A)98 N
B)0 N
C)50 N
D)49 N
8/3/2019 Lecture 8 Friction&Drag
http://slidepdf.com/reader/full/lecture-8-frictiondrag 11/21
Conceptual Question 2:
If a horizontal force of 50 N is now applied to the blockbut the block does not move.
What is the magnitude of the frictional force on it?
A)98 N
B)0 N
C)50 N
D)49 N
8/3/2019 Lecture 8 Friction&Drag
http://slidepdf.com/reader/full/lecture-8-frictiondrag 12/21
Conceptual Question 3:
If the maximal static frictional force f s,max is 100 N.Will the block move if we push it with a horizontal force
of 98 N?
A)Yes
B)No
8/3/2019 Lecture 8 Friction&Drag
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Conceptual Question 4:
If the maximal static frictional force fs,max is 100 N.What will be the magnitude of the frictional force on the
block if we push it with a horizontal force of 98 N?
A)100 N
B)49 N
C)98 N
D)2 N
8/3/2019 Lecture 8 Friction&Drag
http://slidepdf.com/reader/full/lecture-8-frictiondrag 14/21
Numerical Example:
A truck is trying to unload its
cargo by lifting its container in
an angle.
At what angle will the cargo
start sliding down assuming it’sa one mass m and that the
coefficient of static friction
between the cargo and the floor
of the container is µ s ?
8/3/2019 Lecture 8 Friction&Drag
http://slidepdf.com/reader/full/lecture-8-frictiondrag 15/21
Drag Force
The “Drag Force” is caused by a FLUID.
Fluid is anything that can flow (gas, liquid).
The Direction of the drag, as friction, always
against the direction of the motion.
v D
8/3/2019 Lecture 8 Friction&Drag
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What does Drag depend on?
Fluid density
Effective cross-sectional Area of the object A
The velocity of the object v
8/3/2019 Lecture 8 Friction&Drag
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Dimensional Analysis
t L
time Lengthv
L Area A
L
M
volume
mass
2
3
22
t
LM
time
Lengthmass Force D
2v A D
8/3/2019 Lecture 8 Friction&Drag
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2
2
1
AvC D
Finally:
C is called the “DRAG COEFFICIENT”
and it is determined experimentally.
Typical values range 0.4 – 1.0
8/3/2019 Lecture 8 Friction&Drag
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Question:
What happens to an object which is dropped from avery high building if we consider the drag force?
Remember: the drag force increases with the velocity
It reaches a maximum velocity called
“Terminal Velocity” given by:
AC
F vt
2
8/3/2019 Lecture 8 Friction&Drag
http://slidepdf.com/reader/full/lecture-8-frictiondrag 20/21
Example
Calculate the magnitude of the drag force on a missile53cm in diameter cruising at a 250m/s at low altitude,
where the air density is 1.2kg/m3, assuming C=0.75.
What will the propelling force of the missile have to be?
d v
DF p
8/3/2019 Lecture 8 Friction&Drag
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Conceptual Question 1:
If an object that is being dragged by a force F through air has a terminal velocity v.
What will be its terminal velocity if we drag it with the
same force through another gas of density ¼ that of
air?
A)¼ v
B)½ v
C)2 v
D)4 v
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