PHY131H1F – Introduction to Physics I
Class 2
Today: Chapter 1
• Scaling
• Dimensions
• Significant Figures and
Scientific Notation
• Units, Unit Conversions
Garden-Variety Clicker Instructions
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clicker questions:
• Status light will
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your response is
registered on my
computer.
• Status will flash red
On/Off Switch
if your response is
Please turn on your clicker now
not registered.
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
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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
Photo courtesy of Delwin Allred https://www.google.com/maps/views/profile/110731735211348037360
Clicker Question
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/hr
B. 25 km/hr
C. 50 km/hr
D. 100 km/hr
E. 200 km/hr
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.
• The wave equation
(Eq.14.5):
𝜕2𝑦
1 𝜕2𝑦
= 2 2
2
𝜕𝑥
𝑣 𝜕𝑡
• Where v is the
speed of the wave.
• Let’s measure v for
a big crowd of
people.
Convocation Hall (11am)
Speed of “The Wave”
• d:
• t:
• v:
One of the most important equations in this course: constant
speed:
𝑑
𝑣=
𝑡
MS3153 (5pm)
Speed of “The Wave”
• d:
• t:
• v:
One of the most important equations in this course: constant
speed:
𝑑
𝑣=
𝑡
Clicker question: Estimation
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
Density
• Amount of mass per unit volume of a
material.
mass
Density =
volume
• Unit of density is kg/m3 or g/cm3.
• Example:
Density of water is 1000 kg/m3, or 1 g/cm3.
[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.)
Image of bronze duck from http://ancientpoint.com/category/220-antiques_decorative_arts_metalware_/page_34.html ]
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?
Clicker Question
When you “scale up” an object to 3 times its linear
size, the surface area increases by
A.
B.
C.
D.
E.
3 and the volume by 3.
3 and the volume by 9.
3 and the volume by 27.
9 and the volume by 27.
4 and the volume by 8.
So the surface area to volume ratio is
Surface area size 2
1
~
~
3
Volume
size
size
[Image credit: http://eshgheman.livejournal.com/2025.html ]
[Image credit http://bwog.com/2011/01/30/hidden-talents-the-skydiver/ ]
Scaling
• 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.
[Image credit http://bwog.com/2011/01/30/hidden-talents-the-skydiver/ ]
[Image credit: http://eshgheman.livejournal.com/2025.html ]
Check your neighbour
If the volume of an object were to double, with no
change in mass, what would happen to its
density?
A.
B.
C.
D.
It would remain unchanged.
It would double.
It would decrease by a factor of two.
None of these.
Dimensions and Dimensional
Analysis
Dimensions 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.
Clicker Question: basic math
• Which of the following is the same as 1/x?
A. x0.1
B. −x
C. x/1
D. x−1
E. 0.1x
Survey Question: just for fun
• 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!).
• 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 System
Quantity Unit
Standard
Length
Meter
Length of the path traveled by
light in 1/299,792,458 second
Time
Second
Mass
Kilogram
Time required for
9,192,631,770 periods of
radiation emitted by cesium
atoms
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?
I don’t like the sig figs
on that conversion,
Daddy!
Zainab Harlow
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.
Convert 9 m to feet
Facts you are given:
1 in
2.54 cm
1=
=
2.54 cm
1 in
100 cm
1m
1=
=
1m
100 cm
12 in
1 foot
1=
=
1 foot
12 in
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?