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PHY131H1F - Class 9
Today, finishing Chapter 5:
• Kinetic Friction
• Static Friction
• Rolling without slipping (intro)
• Drag
Microscopic bumps
and holes crash into
each other, causing a
frictional force.
Kinetic Friction
creates internal
energy (thermal).
A box is being pulled to the
right at steady speed by a
rope that angles upward. In
this situation:
A. n > mg.
B. n = mg.
C. n < mg.
D. n = 0.
E. Not enough information to judge the size
of the normal force.
Clicker Question
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Test 1 Marks Posted
You should now see your mark
out of 32 under “My Grades” on
portal.
The raw average was 19/32 =
59%.
The instructors in this course
have decided to adjust the marks
by adding 2 points to every
student’s mark, but holding the
maximum mark to 32/32 = 100%.
The mark posted on portal is your adjusted mark.
The adjusted average and median were 21/32 = 66%.
After the adjustment, 263 students (23% of the class) got less than
16/32 (fail).
After the adjustment, 72 students (6% of the class) got 32/32 =
100%.
Test 1 Marks Posted
You will receive the long-answer part of your test in
Practicals between today and Oct.20.
The multiple choice bubble sheet is stored in MP129 – if you
would like to review it, please stop by and ask April.
Check over the marking and compare it to the Test 1 Marking
Scheme posted on the portal.
If there has been a mistake in the marking or computation of
your mark, please bring the test to me or April Seeley in
MP129 and we will fix the mistake.
The deadline to report mistakes in the marking of Test 1 is
Oct. 30.
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Class 9 Preclass Quiz on MasteringPhysics
This was due this morning at 8:00am
84% of students answered correctly: A packing crate is
sitting at rest on an inclined loading ramp. The magnitude of
the force of static friction is equal to the magnitude of the
component of the weight of the crate parallel to the inclined
ramp.
74% of students answered correctly: The coefficient of static
friction is greater than the coefficient of kinetic friction.
55% of students answered correctly: You are driving your car
along a horizontal road and you see the light turn yellow, and
then red. You apply the brakes and the car slows to a stop.
While the car is slowing down, the main external force on the
car which causes it to slow down is static friction.
95% of students answered correctly: “Terminal speed” is the
speed a falling object reaches at which the drag force and
gravity have equal magnitudes.
Last day I asked at the end of class:
Does friction always slow things down?
ANSWER: No!
Kinetic friction does oppose the relative motion of
two surfaces. If the one of these surfaces is
stationary, then it will tend to slow down the
moving object.
Can friction ever speed things up?
ANSWER: Yes!
Static friction between your feet and the floor is
what allows you to walk! Walking certainly
involves speeding up, and this would not be
possible if the floor were frictionless or covered
in marbles!
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Class 9 Preclass Quiz Student Comments
“Friction can be a real drag sometimes”
“How a rolling wheel could have static friction. (But I could
just read chapter 10 in advance too.)”
Harlow response: Right. In order to fully understand rolling
without slipping, you need to study rotation, which is not
until chapter 10. For now you should trust me that for cars
and bikes, it is static friction between the road and the
wheel, not kinetic.
“I am confused with static friction and kinetic friction being
related to the normal force. Why?”
Harlow answer: I’m not really sure!! The short answer is
that it’s an experimental result! (ie it is an empirical law, not
a theoretical law). But it makes sense: as the normal force
increases, the surfaces will have more microscopic contact
points, which allows the parallel forces to also increase.
Class 9 Preclass Quiz Student Comments
“it made me feel good about myself knowing that physicists
too, have bad hair days”
“my goal in this course is not to pass physics but to get one
of my comments posted on your lecture slides”
Harlow comment: why not both? Dream big!
“why don't we get a reading week, even two or three days
would help.”
Harlow response: You do get two days actually: November
9 and 10
Harlow comment: wait did
someone give me ASCII
roses on
MasteringPhysics? Thanks!
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Class 9 Preclass Quiz Student Comments
New rule: No swearing (ie f***, sh**, etc) or sexual
references in the comments section, please. It’s
unprofessional. You will get a zero on that particular
preclass quiz if I catch this. Thank you.
Why does
friction exist?
Because at the
microscopic level,
nothing is smooth!
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“Kinetic Friction”• Also called “sliding friction”
• When two flat surfaces are in contact and sliding relative to
one another, heat is created, so it slows down the motion
(kinetic energy is being converted to thermal energy).
• Many experiments have shown the following approximate
relation usually holds for the magnitude of fk:
kf
kf
fk kn
where n is the magnitude of the
normal force.
The direction of fk is opposite the
direction of motion.
A wooden block weighs 100 N, and is sliding to the right on a
smooth horizontal concrete surface at a speed of 5 m/s. The
coefficient of kinetic friction between wood and concrete is
0.1.
A 5 N horizontal force is applied to the block, pushing toward
the right. What is the force of kinetic friction of the concrete
on the block?
A. 100 N, to the left
B. 10 N, to the left
C. 5 N, to the left
D. 10 N, to the right
E. 5 N, to the right
v
Clicker Question
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A sled of mass 5.0 kg is pulled
at a constant velocity by a
rope which makes an angle of
20.0° above the horizontal.
The coefficient of kinetic
friction between the sled and
the surface snow is 0.030.
What is the tension in the
rope?
Example
20°
𝑇
“Static Friction”
• When two flat surfaces are in contact but are not moving
relative to one another, they tend to resist slipping. They
have “locked” together. This creates a force
perpendicular to the normal force, called static friction.
sf
There is no general
equation for fs.
The direction of fs is whatever
is required to prevent slipping.
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• A car is parked on flat, horizontal pavement.
• Which of the following forces are acting on
the car?
A.Gravity
B.Normal
C.Static friction
D. All of the above
E. A and B, but not C
Multiple Forces on a Single Object
Maximum Static Friction
where n is the magnitude of the normal force, and the
proportionality constant μs is called the “coefficient of
static friction”.
There’s a limit to how big fs can get. If you push hard
enough, the object slips and starts to move. In other words,
the static friction force has a maximum possible size fs max.
• The two surfaces don’t slip against each other as long as fs
≤ fs max.
•A static friction force fs > fs max is not physically possible.
Many experiments have shown the following approximate
relation usually holds:
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A wooden block weighs 100 N, and is sitting stationary on a
smooth horizontal concrete surface. The coefficient of
static friction between wood and concrete is 0.2.
A 5 N horizontal force is applied to the block, pushing toward
the right, but the block does not move. What is the force of
static friction of the concrete on the block?
A. 100 N, to the left
B. 20 N, to the left
C. 5 N, to the left
D. 20 N, to the right
E. 5 N, to the right
F
Clicker Question
A wooden block weighs 100 N, and is sitting stationary on a
smooth horizontal concrete surface. The coefficient of static
friction between wood and concrete is 0.2.
A horizontal force is applied to the block, pushing toward the
right. What is the magnitude of the maximum pushing force
you can apply and have the block remain stationary?
A. 200 N
B. 100 N
C. 20 N
D. 10 N
E. 5 N
F
Clicker Question
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𝜇
𝜇
Accelerating
Here the kinetic friction is constant as
the applied force continues to increase.
As the magnitude of the net force
increases, so does the magnitude of the
object’s acceleration.
What happens if
you steadily
increase the
applied force on
an object which is
resting on a
surface?
F
Typical Coefficients of Friction
Student comment
from this morning’s
preclass quiz:
“Right after I finished
the reading, I gave my
mom a lecture about
the static friction in
driving.”
Harlow comment:
Good! If her tires are
slipping, she is not
maximizing the friction!
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Rolling Without Slipping
Under normal driving conditions,
the portion of the rolling wheel
that contacts the surface is
stationary, not sliding
In this case the speed of the
centre of the wheel is:
If your car is accelerating or decelerating or turning,
it is static friction of the road on the wheels that
provides the net force which accelerates the car.
(More about this coming in Chapter 10!!)
where C = circumference [m] and T = Period [s]
𝑣 =𝐶
𝑇
When an object moves through the air, the
magnitude of the drag force due to air resistance
A. increases as the object’s speed increases.
B. decreases as the object’s speed increases.
C. does not depend on the object’s speed.
Clicker Question
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Class 9 Preclass Quiz Student Comments
“what will happen if an object travels faster than its terminal
speed?”
Harlow answer: Interesting question.. If an object is thrown
or propelled downward at faster than its terminal speed,
then the upward drag force will be greater than the
downward force of gravity, so the net force will be up. It will
slow down to terminal speed as it falls.
“I found the paragraph about terminal speed interesting
because it reminded me of the time I went skydiving with my
dad.”
Section 5.5: Drag
Objects moving through fluids like water or air
experience a drag force.
Faster objects experience a greater drag force than
slower objects.
The drag force on
a high-speed car is
significant.
The drag force
direction is opposite
the object’s velocity
relative to the fluid.
Image from http://www.bmw.com/com/en/insights/technology/efficientdynamics/phase_2/technology/aerodynamics_2013.html
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From http://www.tpub.com/gunners/228.htm on Exterior Ballistics.
Non-Free Fall
When an object falls downward through the air it
experiences:
• force of gravity pulling it
downward.
• air drag force acting
upward.
𝐹drag
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Drag force in a fluid, such as air
• Air resistance, or drag, is complex and involves fluid dynamics.
• For objects on Earth, with speeds between 1 and 100 m/s and size between 1 cm and 2 m, there is an approximate equation which predicts the magnitude of air resistance
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drag AvCF
where A is the cross-sectional area of the object, ρ is the
density of the air, C is the drag coefficient, and v is the
speed.
• The direction of air resistance, or Drag Force, is opposite
to the direction of motion.
• It depends on size and shape, but not mass.
Drag force in a fluid, such as air
• Air resistance, or drag, is complex and involves fluid dynamics.
• For objects on Earth, with speeds between 1 and 100 m/s and size between 1 cm and 2 m, there is an approximate equation which predicts the magnitude of air resistance
Which falls faster, a piece of paper that is uncrumpled, or
crumpled?
A. Uncrumpled (flat)
B. Crumpled
Why??? What is different?
2
21
drag AvCF
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Terminal Speed
• Fdrag increases with speed
• Net force goes to zero when the object is moving fast enough so that Fdrag = mg(air resistance = weight)
• Then no net force
No acceleration
Velocity does not change
Non-Free Fall—Example
• A skydiver jumps from plane.
• Weight is the only force until air
resistance acts.
• As falling speed increases, air
resistance on diver builds up, net force
is reduced, and acceleration becomes
less.
• When air resistance equals the diver’s
weight, net force is zero and
acceleration terminates.
• Diver reaches terminal velocity, then
continues the fall at constant speed.
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Consider a heavy and light person jumping
together with same-size parachutes from the same
altitude. Who will reach the ground first?
A. The light person.
B. The heavy person.
C. Both will reach at the same time.
D. Not enough information.
Clicker Question
Free Fall vs. Non-Free Fall
Coin and feather fall with air present• Feather reaches terminal velocity very
quickly and falls slowly at constant speed, reaching the bottom after the coin does.
• Coin falls very quickly and air resistancedoesn’t build up to its weight over short-falling distances, which is why the coin hits the bottom much sooner than the falling feather.
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Coin and feather fall in vacuum
• There is no air, because it is vacuum.
• So, no air resistance.
• Coin and feather fall together.
Free Fall vs. Non-Free Fall
Watch Brian Cox do this experiment at
https://youtu.be/E43-CfukEgs .
Before Class 10 on Monday
• Note that MasteringPhysics Problem Set 4 is
due Monday evening (not Fridays any more)!
• Please read Wolfson Chapter 6.
• Something to think about:
“A pendulum bob swings back and forth on the
end of a string, describing a circular arc.
Does the tension force in the string to any
work?”