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PHY131H1F - Class 4

Today:

• Vector Math

• Velocity and

Acceleration in 2-

dimensions

• Relative Velocity

• Constant Acceleration in

x and y

• Projectile Motion

• Motion on a Circular

Path

Clicker Question

• A large, light beach ball is falling

towards the beach on a windless day.

The force of gravity on the ball, 𝐹𝑔, is

greater than the upward drag force from

the air, 𝐹𝐷. Which of the following

directions is closest to the direction of

the net force 𝐹net = 𝐹𝑔 + 𝐹𝐷 on the ball?

A.North

B.East

C.South

D.West

E.The net force makes an angle of 90°

with respect to all four of these

directions.

𝐹𝐷

𝐹𝑔East

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The Pointing Game

• There are three pairs of orthogonal directions in

this room.

• Within a pair, each direction is anti-parallel to the

other.

• Each pair is perpendicular to the other two pairs.

• Point with me:

North - South

West - East

Up - Down

Class 4 Preclass Quiz on MasteringPhysics

This was due this morning at 8:00am

92% answered correctly: In the study of physics, a scalar

is specified with a single number, but a vector is specified

using both a magnitude and direction.

Harlow note (based on student comments): A scalar can

have dimensions, or be dimensionless. ie: m = 5 kg. is a

scalar with dimensions of mass [M]. But π = 3.14 is a

dimensionless scalar (it is a ratio). Most vectors have

dimensions, but unit-vectors do not.

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Class 4 Preclass Quiz on MasteringPhysics

88% answered correctly: The speed of the mouse

relative to the floor is the vector sum of the

mouse speed relative to the belt and the belt

speed relative to the floor (5 m/s)

88% answered correctly: Both bullets hit the

ground simultaneously!

84% answered correctly: When an object moves

in a circular path at a constant speed, the velocity

and acceleration vectors are perpendicular.

Student comments from Class 4 Preclass Quiz

“Was the mouse on the conveyor belt or was it on the edge

of the belt before it saw the cheese?”

Harlow answer: It was on the belt. The belt was the

mouse’s universe at that time – it didn’t care that the factory

floor was moving at a different velocity.

“I understand that in theory, both bullets should reach the

earth at the same time. However, doesn't the curvature of

the earth become a factor when firing a bullet over longer

distances? If so, would that not alter the height at which the

bullet being fired actually hits the ground?”

Harlow answer: YES! That’s a really good point! In fact,

due to the curvature of the earth, the fired bullet would take

slightly longer to hit the ground, because it would fall a

further distance.

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Student comments from Class 4 Preclass Quiz

“I did this quiz without doing the assigned readings. I don't

even know what the assigned readings are, but I will find out

now and read it all posthaste.”

Harlow comment: Okay. Thank you for your honesty. Keep

in mind that you have defeated the entire purpose of the pre-

class quiz by doing this, though.

“Relative velocity seems like witchcraft. Please explain this

sorcery.”

“I just wonder what the rules are for this feedback section in

order to get the mark. Surely profanity is off the table, but

what about emoticons? Well, here goes nothing :P”

Student comments from Class 4 Preclass Quiz

“Confused why the section name includes 3-d motion, when

there isn't 3-d motion”

Harlow answer: 3-d motion exists. Most motion for this

course does happen in 2-D, which is a lot easier to draw.

But you should be aware that we live in a 3-D universe so, in

general, everything happens in 3-d.

“I like many people find frames of reference to be very

confusing. I watched the youtube video Frames of Reference

(1960) which helped me a lot with my understanding.

Surprisingly, this film was created in UofT many years ago.”

Harlow note: little known fact: Patterson Hume, one of the

two guys in that famous “Frames of Reference” video

https://youtu.be/aRDOqiqBUQY , was my grandmother’s first

cousin. (The taller one with straight hair.) I have hung out

with him on many family gatherings and he was a super-cool

guy.

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Student comments from Class 4 Preclass Quiz

“Q: What do you get when you cross a mosquito with a

mountain climber? A: You can’t cross a vector and a

scalar!”

“what is the prime of velocity, v'? (isn't that acceleration?)”

Harlow answer: No, no! This “prime” has nothing to do with

derivatives! It’s just a label to distinguish it from v.

“circular motion makes me dizzy”

Last day I asked at the end of class:

• Can you add a scalar to a vector?

• ANSWER: No. A 2-D vector is represented by a

pair of numbers (ie x- and y- components, or

magnitude and direction), and you can’t add a scalar

number to this.

• Can you multiply a vector by a scalar?

• ANSWER: YES! When you multiply a vector by a

scalar, you can either:

–Multiply both the x and y components by this

scalar, or

–Multiply the magnitude by the scalar, and keep the

direction unchanged (but you flip direction 180° for

a negative scalar)

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Vectors

• There are two kinds of Physical quantities we will deal with:

–Scalar (Only has a size)

•Quantity that can be described with only one number.

•Examples: time, speed (just a magnitude say “5 m/s”)

–Vector: (Has size and a direction)

•Quantity that is described with two numbers:

–Magnitude

–Direction

•Examples: Position, velocity (magnitude say “5 m/s” and direction say “north”)

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Distance vs Displacement Example

• From High Park, you ride

your bike 6 km East on

Bloor St, then 5 km North on

Yonge St to the corner of

Yonge and Eglinton.

a. What is the distance

traveled?

b. What is your displacement?

Which figure shows ? A A A1 2 3

Clicker Question:

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Components

add and

subtract like

scalars!

Vector Components

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Announcements

• The first term test will be on Tuesday Oct. 6, from 6:00pm

to 7:30pm.

• Test 1 will cover chapters 1-4 of Wolfson, plus what was

done in lectures and Practicals.

• You must bring a calculator and one 8.5x11’ aid sheet

which you prepare, double-sided

• If you have a conflict at that time with an academic activity

(test, lecture, tutorial, lab), you must register to write at the

Alternate Sitting of this test by going to portal and filling

out the online form no later than Sep. 29 by 4:00pm.

• (The Alternative Sitting is on Tuesday Oct. 6, from 4:30pm

to 6:00pm.)

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Where to get good help for free

• Your classmates: form a study group

• Your two graduate student TAs. Learn their email

address, office hours, and office location.

• Me. After class, office hours are T10, R2, F11, and my

office is MP121-B.

• The Physics Drop-In Centre in MP125, back corner

MTWR 12-3, F11-2

• Academic Success Centre in Koffler 1st floor, inside the

Career Centre

Student Comments from Class 4 Preclass Quiz

“For the "cheat sheet" can we write some info too or is it

strictly equations?”

Harlow answer: You can write whatever you would like. I

will be providing helpful numbers such as conversion factors

on the front page, so you shouldn’t need those. You will

need to write whatever equations might be useful for

chapters 1-4 questions.

“Is there going to be anything about the labs asked on the

test/exam?”

Harlow answer: Yes! The material in Practicals is also

testable.

“Are we allowed to use graphing/programming calculators on

the tests and exams?”

Harlow answer: Yes!

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Student comments from Class 4 Preclass Quiz

“Will these type of questions be asked on the exam? if not,

what is the purpose? "How much would it cost to cover the

entire land area of Canada with five dollar bills?“”

Harlow answer: Yes, there will be an estimation question on

test 1, and possibly on the final exam. It will be multiple

choice, where the five choices all differ by at least a factor of

10. You will be able to figure it all out using numbers and

simple equations which will be in the “possibly useful

information” on the front page of the test.

Are there assigned or recommended questions that we

should try out?

Harlow answer: Yes, suggested end-of-chapter items from

Wolfson chapters 1-4 have been posted on the portal page

for this course under “Extra Study Materials”

Projectile Motion

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Projectile Motion

Projectile motion is made up of two independent motions:

• uniform motion at constant velocity in the horizontal direction and

• free-fall motion in the vertical direction.

The kinematic equations that describe these two motions are:

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Clicker Question

A C

B

• A tennis ball is launched at an angle, and flies through the

air in a parabolic path, as shown, A B C.

• At point B

A. the velocity is horizontal, and the speed is maximum.

B. the velocity is horizontal, and the speed is minimum.

C. the velocity is horizontal, but the speed is neither a

maximum nor a minimum.

D. the velocity is not horizontal, but the speed is minimum.

E. the velocity is not horizontal, and the speed is neither a

maximum or minimum.

Monkey and Hunter Demonstration (and clicker question)

The classic problem: “A monkey hanging from the branch of a

tree is spotted by a hunter. The monkey sees that the barrel

of the gun is pointed directly at him. At the exact instant the

gun is fired, the monkey lets go of the branch. Will the bullet

(A) go above the monkey, (B) go below the monkey, or (C) hit

the monkey?

Our demonstration uses a

pressurized tennis ball

launcher. The laser is aimed

directly at the monkey, which

is supported by an

electromagnet. As the tennis

ball leaves the launcher, it

breaks a connection that

releases the magnet.

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Joke: Why Did the Chicken Cross

the Road?

Aristotle (330 BC):

“Because it is the nature of chickens to cross roads.”

Newton (1687):

“Because there is no external net force causing the chicken’s velocity across the road to change.”

Einstein (1905):

“Is the chicken crossing the road, or is the road moving under the chicken?”

[image downloaded 9/30/2013 from http://afgg.tumblr.com/post/3126636261/when-the-chicken-crossed-the-road ]

Relative Motion

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Relative Motion

If we know an object’s velocity measured in one reference

frame, S, we can transform it into the velocity that

would be measured by an experimenter in a different

reference frame, S´, using the Galilean transformation of

velocity.

Or, in terms of components,

Example: You are running on flat

ground at 7 m/s when you throw a

ball to a friend in front of you. In

your own reference frame, you

launch the ball at an angle of 45°

above the horizontal at a speed of

12 m/s. What is the ball’s initial

velocity relative to the ground?

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A. 40 m/s, West

B. 20 m/s, West

C. zero

D. 20 m/s, East

E. 40 m/s, East

• You are on an Eastbound subway train going at 20 m/s.

• You notice the Westbound train on the other track.

• Relative to the ground, that Westbound train has a speed

of 20 m/s.

• What is the velocity of the Westbound train as measured

by you?

Clicker Question

[image from http://www.cbc.ca/news/canada/toronto/ttc-closes-downtown-subway-loop-for-the-weekend-1.1347919 ]

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Analyzing the acceleration vector An object’s acceleration

can be decomposed into

components parallel and

perpendicular to the velocity.

𝑎|| is the piece of the

acceleration that causes the

object to change speed

𝑎⊥ is the piece of the

acceleration that causes the

object to change direction

An object changing

direction always has a

component of acceleration

perpendicular to the

direction of motion.

Acceleration

Uniform Circular

Motion

Speed is constant.

where T = Period [s]

𝑣 =2𝜋𝑟

𝑇

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Centripetal Acceleration

Centripetal Acceleration

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Before Class 5 on Monday

• Please read Chapter 4, sections 4.1

through 4.4 of Wolfson.

• Problem Set 1 is based on Wolfson

Chapters 1 and 2: it is due this Friday by

11:59pm.

• Something to think about: A paperback novel

has a mass of 0.3 kg and slides at a

constant velocity. A chemistry textbook has

a mass of 3.0 kg, and slides at the same

constant velocity. How does the net force on

the textbook compare to the net force on the

novel?