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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?”