PCS 211Physics: Mechanics

Catherine Beauchemin

Department of Physics, Ryerson University

Email: cbeau@ryerson.caURL: http://phymbie.physics.ryerson.ca/cbeau

Welcome to University!University is not like high school

Teaching is only half of what I do... but it doesnt mean I dont care. If you do no work at all and never come to class I wont know so you

wont get in trouble... but youre more likely to fail!

You are the only person responsible for your success: give yourself thebest chance!

So if you dont understand something...

Dont wait and dont be lazy: seek help IMMEDIATELY! COME SEE ME during office hours: Im really super helpful! Contact Learning Success for additional help and advice. Do all assigned problems. Physics is like practicing a sport: you cant

cram, youve got to work steadily all semester long.

Do unassigned problems. If youve done them all, do more! Your successin exams have a lot to do with your level of confidence.

Your first class!Welcome to your first physics class. Here are a few thing you really need toremember:

REMEMBER: Your instructors name is Catherine Beauchemin Know when to be where, e.g. PCS211 341

PCS211 is the code name for your course 34 is your section number 1 is the course component (1=class, 2=lab, 3=tutorial)

Take responsibility: you are not in high school anymore. Your successis entirely dependent on YOU! Seek help as soon as you see your marksdropping. You should be spending about 10 h/wk on this class:

3 h/wk on lectures 1.5 h/wk on labs (2h lab + 1h report per 2 wk) 1 h/wk on tutorials 5 h/wk reading textbook and doing the problems

Your resources Closely examine your Course Outline and keep it safe. It is a binding

agreement that both you and your instructor have entered.

Your Course Outline also details all the subjects you are expected toknow.

Your class schedule and course announcements are available onBlackboard at http://my.ryerson.ca.

You absolutely MUST activate and regularly check your Ryerson Matrixemail account. I will be sending you important information by email andyou are responsible for checking it. If you miss something because youdid not check your email, it will be your responsibility.

I will be holding fixed office hours. During office hours, you can comein at any time, unannounced and get help. My office hours are...

If you absolutely must see me outside office hours, you must set up an ap-pointment by email (cbeau@ryerson.ca). If you come unannouncedoutside of office hours, I will not help you.

Blackboard: my.ryerson.ca

O.K., lets start!

Chapter 1: Physics and measurementThe Basic Quantities

Length: meter (m) the distance traveled by light in vacuum during a time of1/299, 792, 458 s.

Mass: kilogram (kg) the mass of a specific platinum-iridium alloy cylinder kept at the In-

ternational Bureau of Weights and Measures at Se`vres, France.

Time: second (s) atomic clock: 9,192,631,770 times the period of vibration of radiation

from the cesium-133 atom.

Force or weight: newton (N) This is a derived unit: 1 N 1 kg m s2

NOTE: your weight should not be given in units of mass but in units of force.

Chapter 1: Physics and measurementUS UnitsAll scientists hate these, but many engineersstill use these so... here they are

feet (ft) A unit of length: 1 ft = 0.3048 m

inches (in) A unit of length: 1 in = 0.0254 m

slug (slug) A unit of mass:1 slug = 14.593 kg

pounds (lb) A unit of force: 1 lb = 4.448 N

kip (kip) A unit of force:1 kip = 1, 000 lb = 4448 N

foot-pound (ft lb) A unit of work/energy:1 ft lb = 1.3558 J

pound-foot (lb ft) A unit of torque:1 lb ft = 1.3558 N m

Chapter 1: Physics and measurementSI Units

The concept of units is probably more central to physics than to any otherscience. Units give physical meaning to a number and allow you to verifythat your equation makes physical sense.

Le Syste`me International dUnites (SI) is the international committeewhich establishes the standards for the fundamental quantities of sciencesuch as length, mass, time, etc. These standard units are refered to as SIunits.

One example of the importance of agreed units is the failure of the NASAMars Climate Orbiter, which was accidentally destroyed on a mission tothe planet Mars in September 1999 instead of entering orbit, due to mis-communications about the value of forces: different computer programsused different units of measurement (newton (NASA) versus pound force(Lockhead Martin)). Enormous amounts of effort, time, and money(327.6 M$) were wasted.

A measurement without units has no value and use of units needs tofollow standards!

Chapter 1: Physics and measurementThe importance of units

Units are critical to expressing quantities with a physical meaning.

If you think units are only useful/important/critical in Physics and Engineer-ing, think again!! This is the true and horrifying story of what happens whenmembers of the general public dont understand units.

Lets listen to the customers call. Youll find the full audio online here.

Chapter 1: Physics and measurementUnit prefixes

Although I do not encourage you to use them (it is better to use the scientificnotation except for kg), these are the standard unit prefixes you will encounterin the literature and in your everyday life. You MUST know these.

Prefix Symbol Spoken Numeric Scientificpeta P quadrillionth 1 000 000 000 000 000 1015

tera T trillion 1 000 000 000 000 1012

giga G billion 1 000 000 000 109

mega M million 1 000 000 106

kilo k thousand 1 000 103

deci d tenth 0.1 101

centi c hundredth 0.01 102

milli m thousandth 0.001 103

micro millionth 0.000 001 106

nano n billionth 0.000 000 001 109

pico p trillionth 0.000 000 000 001 1012

femto f quadrillionth 0.000 000 000 000 001 1015

Chapter 1: Physics and measurementSome SI Units rules

No Plurals (e.g., m = 5 kg not 5 kgs) No componded prefixes (e.g., m = 5 Gg not 5 Mkg) Clearly separate units using the correct symbols

Note that N/m s 6= N/(m s). Preferably it should be N m1 s1 For more info about SI Units and usage rules, check out the National In-

stitute of Standards and Technology (NIST) reference page on the subject.

Scientific notation:

Physics is probably the field which studies phenomenon over the vastestrange of sizes because we deal with the extremely small (electrons) andextremely large (solar systems).

The age of the universe is about 500, 000, 000, 000, 000, 000 s. Usingscientific notation, this is 5 1017 s. The exponent gives you the numberof digits after the .. Here, we have 17 zeros after the radix point.

Chapter 1: Physics and measurementSignificant figures

Scientific notation is used to clearly identify the number of figures (digits)we actually know. These digits are called significant figures or digits.E.g., an altitude of 5, 100 m should be expressed as 5.1 103 m. In the lab, the number of significant figures you should use when reporting

your results will depend on your measurements uncertainties. You willhear more about that in your labs.

In class/assignments/tests, we ask that you always use 3 sig. fig. for finalresults and as many sig. fig. as possible (at least 5) for intermediate results.

Rounding off numbers

Digits < 4 (04) round down, digits 5 (59) round up. E.g., 3.44 3.4, 3.45 3.5, 3.95 4.0, 16, 254 1.63 104.

Chapter 1: Physics and measurementExample Express the following quantity using proper SI units notation, withthe correct round-off, and removing any prefix

(118.72 km/h)2 (3129.12 Gs)Solution

1. Convert all units to SI units (should have no prefixes)(118.72

km

h 1000 m

1 km 1 h

3, 600 s

)2(3129.12 Gs 10

9 s

1 Gs

)2. Carry out the calculation(

32.977778m

s

)2 (3129.12 109 s) = 3.40302384 1015 m2

s

3. Round-off your answer to 3 significant figures

3.40 1015 m2 s1

Chapter 1: Physics and measurementDimensional analysis

The word dimension has a special meaning in physics: it denotes thephysical nature of the quantity. E.g., a distance can have various units(meter, feet, etc.), but it will always have dimensions of length.

Equations are all dimensionally homogeneous, i.e., the dimensions onboth side of an equation have to match. A few rules:

Addition and subtraction require that all terms have the same dimen-sions. E.g., It took me 3 minutes and 2 meters to get to the grocerystore.?! That is NOT going to work out.

Multiplication and division can be done with terms of different dimen-sions and the dimensions are compounded. E.g., I worked for 3 hoursand earned 10 dollars per hour so I made 30 dollars today.

Argument of some functions such as cos, sin, exp, log must be dimen-sionless.

Chapter 1: Physics and measurementUsing dimensional analysis

The dimensions of an arbitrary physical quantityA is a way of expressingthe quantity A in terms of the basic quantities L (length), M (mass) andT (time).

In general, [A] = LaM bT c where a, b and c are dimensionless exponentswhich can be either positive, negative or zero.

Formally, we indicate that we are talking about the dimensions of a phys-ical quantity by enclosing it in square brackets. E.g., [A].

Doing a dimensional analysis is a great way to verify if youve made anymistakes in your equation.

Now lets work on an example together...

Chapter 1: Physics and measurementExample: Find the value of exponents m and n in

a = krnvm

which gives the acceleration a of a particle moving with uniform speed v ina circle of radius r, where k is a dimensionless proportionality constant.

Solution1. Identify the dimensions of each quantity

[a](L1 M0 T2)

= [k](L0 M0 T 0)

[r]n(L1 M0 T 0)n

[v]m(L1 M0 T1)m

L1 T2 = (1)(Ln)(Lm Tm)L1 T2 = Lm+n Tm

2. Match the dimensions on each side

from T 2 = m m = 2from L 1 = m + n n = 1

3. Solve

a = kr1v2 = kv2

r

Chapter 1: Physics and measurementDimensional analysis

Exercise: Determine which of the following equation(s) is(are) NOT correctbased only on dimensional analysis.

A) v = dt

B) p = vm + Ft

C) v = v0 + at2

D) v2 = v20 + 2ad

E) d = v0t + 12at2

where a is acceleration, v is speed, d is displacement, t is time, p is momen-tum, F is force, and m is mass.

This is the end of Chapter 1

Get back to your notes forChapter 3