Today: Chapter 1

• Scaling

• Dimensions

• Significant Figures and

Scientific Notation

• Units, Unit Conversions

PHY131H1F – Introduction to Physics I

Class 2

Garden-Variety Clicker Instructions

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When I start asking

clicker questions:

• Status light will

flash green when

your response is

registered on my

computer.

• Status will flash red

if your response is

not registered.

On/Off Switch

Please turn on your clicker now

2

i-Clicker+ Instructions

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When I start asking

clicker questions:

• Status light will flash

green when your

response is registered

on my computer.

• Status will flash red

if your response is not

registered.On/Off Switch

Please turn on your clicker now. It will

blink “A” twice to indicate you’re on

frequency code AA, which is good.

i-Clicker2 Instructions

Status Window

Tells you when your

response has been

registered on my

computer.

• Note that the

frequency-code for

this course is the

default: “AA”On/Off Switch

Please turn on your clicker

now

If you drive to Buffalo to shop at Trader Joes (which is awesome), when you cross the Niagara River, the speed limit will suddenly change to 65 mph. How fast is this approximately?A. 10 km/hrB. 25 km/hrC. 50 km/hrD. 100 km/hrE. 200 km/hr

Clicker Question

Photo courtesy of Delwin Allred https://www.google.com/maps/views/profile/110731735211348037360

Introducing: Charles

Charles is a graduate student working on a Ph.D.

in atmospheric physics.

He will be coming to each lecture this semester to

help you give me questions.

If you have a question, please write it on a scrap

piece of paper, and hold it up so Charles can see it.

Charles will pile questions on the table on the

stage, and, when I get a chance, I will look at the

questions and answer them, if they are

appropriate.

No questions from second or third balconies, sorry!

Class 2 Preclass Quiz on MasteringPhysics

This was due this morning at 8:00am

1035 students submitted the quiz on time (out of

1247 students in the course, so 83% of you)

The first 4 questions, worth 1 point each for

answering correctly, had certain correct answers

which you can now review. The average on these

4 questions was 80.4%.

The last question was “Did you complete quiz?” for

which 99.5% of you got 21 points for answering

“Yes”.

The total is out of 25 for this quiz, worth (1/20th) of

2% of the course

Class 2 Preclass Quiz on MasteringPhysics

95% got correct: The basic SI units are second,

meter, kilogram

74% got correct: In the calculation of the area of a

rectangle with dimensions of 4.282 m by 0.050 m,

which of the following answers has the correct

number of significant figures? Use two sig figs

because 0.050 has two: 0.21 m2.

74% got correct: In the equation z = ct + d, z is

measured in meters and t is measured in

seconds. What are the dimensions (units) of d?

Each term must be meters. (You can only add

apples to apples)

Student comments on preclass quiz

• “the question ‘z=ct+d, what are the dimensions of d?’ was, at least

for me, a bit odd, just as the question never stated what the variable

c is measured in?”

• Harlow answer: Good point: It has to be [m/s]! (since t is in [s],

and we know that ct must be in [m].)

• “Is it necessary to memorize all the SI Prefixes mentioned in the

textbook?”

• Harlow answer:

– #1 anything you don’t feel like memorizing can always be

written on your aid-sheet for the tests and exam.

– #2 I will put these prefixes on page 1 of the tests and exam as

“possibly helpful information”, along with numerical values for

gravity, speed of sound, etc.

Student comments on preclass quiz

• “Just wondering can we use the textbook from last year?”

• Harlow answer: No, sorry.

• “And why there are only answers to odd questions? How could I

check the even questions.”

• Harlow answer: You need to develop your confidence and don’t

rely on the back of the book so much. But if you are every curious,

I have full solutions on my office computer so feel free to stop by

my office hours and I can look up specific even questions.

Student comments on preclass quiz• “Why isn't ‘grams’ the SI unit of mass?”

• Harlow answer: I don’t know. Blame the French.

• “I found in interesting how many brain cells we had!!”

• “Basic question such as, ‘why do we represent an election as a

sphere if we've never seen one?’, came to mind.”

• “My first mistake was skimming through instructions, since I only

wrote down the first name of a classmate instead of his full name -

easy marks lost. However, I don't think it would be necessary to

mention this common tragedy in lecture.”

• “In truth i haven't done the assigned reading which is a rough start

but in my defense i haven't actually had time to breathe in these

last two days so as soon as i figure out how to fit in the whole

inhale exhale thing readings are next on my list of to do's.”

• “I wonder how can a person like me read this kind of textbooks

faster. (It takes nearly 2 hours for me to read chapter 1.)”

Overview of PHY131

• Over the next 3 months, we will cover:

• Kinematics (velocity, acceleration, along a line and in

2-dimensions)

• Forces and Newton’s Laws

• Uncertainties in Physical Measurements

• Energy, Work and Power

• Momentum and Collisions

• Rotational Motion, Torque and Angular Momentum

• Oscillations and Simple Harmonic Motion

• Waves and Sound

From the LAST Chapter we will cover this

semester in PHY131, in December

• Chapter 14: Wave Motion

• A wave is a traveling disturbance that transports

energy but not matter.

𝜕2𝑦

𝜕𝑥2=

1

𝑣2

𝜕2𝑦

𝜕𝑡2

• The wave equation

(Eq.14.5):

• Where v is the

speed of the wave.

• Let’s measure v for

a big crowd of

people.

Speed of “The Wave”

• d:

• t:

• v:

One of the most important equations in this course: constant

speed:

𝑣 =𝑑

𝑡

Convocation Hall (11am)

Speed of “The Wave”

• d:

• t:

• v:

One of the most important equations in this course: constant

speed:

𝑣 =𝑑

𝑡

MS3153 (5pm)

What is the approximate density of water?

A. 10−5 kg/m3

B. 0.01 kg/m3

C. 0.1 kg/m3

D. 1 kg/m3

E. 1000 kg/m3

Clicker question: Estimation

Density

• Amount of mass per unit volume of a

material.

• Unit of density is kg/m3 or g/cm3.

• Example:

Density of water is 1000 kg/m3, or 1 g/cm3.

volume

massDensity =

[Image retrieved Jan. 11, 2013 from http://www.amazon.com/Evian-Water-Liter-Pack/dp/B0041HVMU0 ]

Scaling

Scaling Example• A sculptor is making a statue of a duck.

• She first creates a model.

• To make the model requires exactly 2 kg of bronze.

• The final statue will be 5 times the size of the model in all

three dimensions.

• How much bronze will she require to cast the final statue?

• (You may find it helpful to

think about the model

being constructed of Lego

blocks, with the final

statue made of Lego

blocks that are 5 times

the size in each

dimension as the ones

used to make the model.)

Scaling Example• A sculptor is making a statue of a duck.

• She first creates a model.

• To make the model requires exactly 2 kg of

bronze.

• The final statue will be 5 times the size of

the model in all three dimensions.

• How much bronze will she require to cast

the final statue?

Image of bronze duck from http://ancientpoint.com/category/220-antiques_decorative_arts_metalware_/page_34.html ]

When you “scale up” an object to 3 times its linear

size, the surface area increases by

A. 3 and the volume by 3.

B. 3 and the volume by 9.

C. 3 and the volume by 27.

D. 9 and the volume by 27.

E. 4 and the volume by 8.

Clicker Question

So the surface area to volume ratio is

size

1

size

size

Volume

areaSurface3

2

~~

[Image credit: http://eshgheman.livejournal.com/2025.html ]

[Image credit http://bwog.com/2011/01/30/hidden-talents-the-skydiver/ ]

Scaling

[Image credit: http://eshgheman.livejournal.com/2025.html ]

[Image credit http://bwog.com/2011/01/30/hidden-talents-the-skydiver/ ]

• Air resistance (drag) is proportional to surface area.

• Force of gravity is proportional to mass, which is proportional to volume.

• So the ratio of air resistance to weight decreases as size increases.

If the volume of an object were to double, with no

change in mass, what would happen to its

density?

A. It would remain unchanged.

B. It would double.

C. It would decrease by a factor of two.

D. None of these.

Check your neighbour

Dimensions and Dimensional

AnalysisDimensions of a quantity are the base units that

make it up; they are generally written using square

brackets.

Example: Speed = distance/time

Dimensions of speed: [L/T]

Quantities that are being added or subtracted must

have the same dimensions. In addition, a quantity

calculated as the solution to a problem should

have the correct dimensions.

• Which of the following is the same as 1/x?

A. x0.1

B. −x

C. x/1

D. x−1

E. 0.1x

Clicker Question: basic math

• Do you speak or understand Mandarin?

A. Yes

B. No, not at all but I do speak at least one

language other than English.

C. No, I am monolingual (English only!).

Survey Question: just for fun

• Results from Sep. 16, 2015:

A. Yes 38% (383 out of 991)

B. No, not at all but I do speak at least one

language other than English. 48% (478 out

of 991)

C. No, I am monolingual (English only!). 13%

(130 out of 991)

The SI Unit SystemQuantity Unit Standard

Length Meter Length of the path traveled by

light in 1/299,792,458 second

Time Second Time required for

9,192,631,770 periods of

radiation emitted by cesium

atoms

Mass Kilogram Platinum cylinder in

International Bureau of

Weights and Measures, Paris

These are the only prefixes used in PHY131/132.

Radians and Degrees

• The SI Unit of angular measure is radians.

Significant Figures

The number of significant figures is the number of

reliably known digits in a number.

It is usually possible to tell the number of significant

figures by the way the number is written:

• 23.21 cm has four significant figures.

• 0.062 cm has two significant figures (the initial

zeroes don’t count).

• 80 km is ambiguous—it could have one or two

significant figures. If it has three, it should be written

80.0 km.

Rules for Significant Figures

When multiplying or dividing numbers, the result

has as many significant figures as the number used

in the calculation with the fewest significant figures.

Example: 11.3 cm x 6.8 cm = 76.84 cm ≈ 77 cm.

When adding or subtracting, the answer is no more

accurate than the least accurate number used.

The number of significant figures may be off by

one; use the percentage uncertainty as a check.

Scientific Notation and Significant Figures

Scientific notation is commonly used in physics; it

allows the number of significant figures to be

clearly shown.

For example, we cannot tell how many significant

figures the number 36,900 has.

However, if we write 3.69 x 104, we know it has

three; if we write 3.690 x 104, it has four.

Student comments on preclass quiz

• “Significant digits. Significant digits. Significant digits.”

• Harlow response: Yeah, yeah, yeah…

• “For instance, weight = mg m= 1 kg; g = 9.8 m/s^2 on earth, So

would the answer be 9.8 N or 10N?”

• Harlow answer: technically it should be 10 N, since m was given

to 1 sig fig. But 9.8 N is fine with me. You will not lose any

marks for this.

Student comment on preclass quiz

• “The importance of significant figures when it comes

to tests, exams, practicals, and homework

questions (i.e. will we lose a mark if we have the

incorrect number of significant figures?) would be

useful to know.”

• Harlow promise: You will not lose marks on tests or

final exams for rounding to the wrong number of

significant figures.

Student comments on preclass quiz

• “Calculation part, where we had to change SI unit into American

mps unit. The conversion written on the appendix of the book was

in m/s, where the question was given as km/h. This two different

unit question was confusing, and it is still confusing for me.”

• +[Lots of requests for unit conversion examples!]

Unit Conversion: What’s wrong with this picture?

Zainab Harlow

I don’t like the sig figs

on that conversion,

Daddy!

Here is the actual bylaw from

http://www.toronto.ca/legdocs/municode/1184_608.pdf :

Clearly Toronto City Council intended only one significant

figure in this rule.

1 =1 in

2.54 cm=

2.54 cm

1 in

1 =100 cm

1 m=

1 m

100 cm

Convert 9 m to feet

1 =12 in

1 foot=

1 foot

12 in

Facts you are given:

Gas prices• Today the price of gas at Costco on the

Queensway is $0.959 Canadian per litre.

• In Buffalo today the price of gas at Doogie’s

on Soutwestern Blvd is $2.12 US per

gallon.

• $1.00 Canadian = $0.75 US.

• 1 gallon = 3.785 litres.

• Is gas cheaper in Buffalo today?

Gas prices• Today the price of gas at Costco on the Queensway is $0.959

Canadian per litre.

• In Buffalo today the price of gas at Doogie’s on Soutwestern

Blvd is $2.12 US per gallon.

• $1.00 Canadian = $0.75 US.

• 1 gallon = 3.785 litres.

• Let’s convert the price of gas in Buffalo to $CDN per litre:

Suggested Problem Solving Strategy

• INTERPRET

• DEVELOP

• EVALUATE

• ASSESS

Think about and simplify the situation,

guess at what the right answer might be.

Draw a diagram. It doesn’t have to be

artistic: stick figures and blobs are okay!

Set up the equations, solve for what

you want to find. (This takes time..)

Check your units, significant figures, do a

“sanity check”: does my answer make sense?

This is just a suggested strategy. Whatever method works for you is fine, as long as you don’t make a mistake, and you show how you got to the correct answer, it’s 100%!

Before Class 3 on Monday

• Please read Chapter 2 of Wolfson, or at least

watch the Preclass Video on YouTube.

• Please do the short pre-class quiz

• Problem Set 1 on MasteringPhysics is due

Sep.25: take a look at it. There’s no time limit, just

a deadline

• Something to think about: Does constant velocity

imply constant acceleration? Does constant

acceleration imply constant velocity?