BIT1002 Introduction: Theories, Models, Laws and all that

This is a general introduction to physics What is Physics What is a theory What do we mean by a model How we make measurements How to do a rough calculation What dimensional analysis means

What is Physics?

• Physics is about the way the universe works: i.e. what are the laws of nature.
• How do we deduce laws from Nature?
• Guess them, and see what the consequences are
• How do we guess?
• Look for patterns in Nature
• e.g. Everything Stops
• This one happens to be false!

Pattern All of these increase together

Heat ~ Energy

• Heat of fusion~energy needed to drag one atom off. i.e. breaking strength of spring
• Melting/Boiling point ~ strength of bond
• Hardness~ compressibility of Spring

Predict : Elasticities will show similar variation

Metal	Melting Point	Boiling Point	Heat of Fusion	Hardness	Elasticity
Lead	327	1744	4.77	1.5	.16
Magnesium	651	1107	8.95	2.0	.5
Copper	1083	2595	13.05	2.5	1.2
Nickel	1453	2732	17.61	-	1.9
Platinum	1769	3827	19.66	4.3	1.7
Iridium	2410	4527	26.36	6.5	5.3
Tungsten	3410	5927	35.23	-	4.0

A theory or Law must

1. Refer to the Physical World
2. be Testable which means that
3. it must make predictions

1. Could be good mathematics
2. NOTHING EXISTS
3. The universe is full of undetectable particles

The logical flow should be:

Given two theories, how do we choose between them? a) Find an experiment to distinguish them or b) Choose the simpler (???????) which is known as Occam's Razor

e.g. Aristotle

• Motion can be divided up into "Natural" and "Unnatural"
• e.g. it is natural for a stone to fall, and a force must be supplied to stop it
• It is natural for a ball to stop rolling, and so a force must be supplied to keep it moving, so the motion is "unnatural"
• 

• SIMPLER??

• All forms of motion are the same
• e.g. A stone has a gravitational force that acts on it and causes it to fall. To stop it falling , an equal upward force must be applied
• A ball has a frictional force which slows it down: to overcome this force, a force in the direction of motion must be applied.
• Theory makes more predictions

• Aristotle: Heavy objects fall faster than light
• Galileo/Newton's: All things should fall at same speed

Models

Life is Difficult (usually too difficult!)

Ball will have air resistance, gravity will vary, sun and moon will attract ball, ball won't be a perfect sphere.................

• Model is

  Note that the world has become an infinite flat plain,we have ignored air-resistance, the child is irrelevant.....

Note that, although you have to be careful in choosing the model, you don't have to have the same model in two different calculations.

• e.g for a satellite in orbit, we need to consider the earth as a perfect sphere, 6500 km in radius

e.g for the earth in orbit around the sun, we need to consider the earth as a point with some mass

• Note that these models for the earth are not only different, they are not even consistent! The earth cannot be an infinite flat plane, a sphere and a point at the same time!

What is an electron?

What is an electron?

1. I have no idea
2. A very small negatively charged particle
3. It's a very stupid question
4. A wave that moves around a nucleus

What is an electron?

e.g

• What colour is an electron?
• What shape is an electron
• Is soft or hard?
• How big is it?

• e.g What colour is an electron? Colour comes from reflected light: an electron is too small (actually, it reflects light of all colours, so ....)
• What shape is an electron? To decide what shape something is, we need to "see' it
• Is soft or hard? What can we "poke" it with?
• How big is it? Depends on how you measure size; best assumption is that it's a point.

• "What is an electron?" is not a good question
• How does an electron behave?
• It behaves like a solution of the Dirac Equation

• But for a model of an electron:: A model is a spinning ball of negative charge

• Note: this is not reality, but a convenient crutch for thinking!!!!

Measurement and Units

Measurements originally defined for trade e.g.

• foot : obvious
• Babylonic Inch : 25 barleycorns
• Bushel : Amount man could conveniently carry ~56lbs (but bushel of corn is different from bushel of barley)
• Yard is distance from tip of Henry 1st's nose to end of his index finger
• Acre is area a man could plough in a day

Unification of measurements possible when it was realised that (e.g.) length and area are related

Hence 1 acre = 1 furlong x 1chain (!). It also happens to be the area that a man can easily plough in a day

Unification of measurements Then need smaller units 1 rod/pole/perch = 1/4 chain = 5 1/2 yards (!!) Then rationalise: Define

• 3 ft = 1 yd
• 12" = 1 ft
• 8 furlongs = 1 mile

• But............ This leads to more problems: circumference of earth differs at various places,....rotation speed of earth varies...
• Need reproducible unit, so any lab can measure it
• Define time via the oscillations of a caesium atom 1 s = 9,192,631,770 f
• Distance used to be via wavelength of red line from Kr⁸⁶ light ( 1 m = 1,650,763.73 l)
• but now speed of light (c) is much better measured, so 1 m = distance travelled by light in 1/299,792,458 s
• Foot-Pound-Second system still used sometimes but in this course we will always use .........

S. I. units

Accuracy and Significant Figures

e.g. A car travels 2 km at 47 km/hr. How long does it take?

• Ans:
  

  t = 2/47*60 = 2.553191489 mins = 153.1914894 s
  

• No Problem!!
• Wrong! 9 significant figures implies that you are measuring the time to .0000001s.
• Use the same number of sig figs as in the least accurate number in the question.
• When in doubt, use 3 sig. figs. t = 154 s

Order of Magnitude

(no, its not a foreign decoration)

Very often want to be able to guess an answer before we do a detailed calculation. e.g.

• How many lightbulbs are sold in Canada in one year?
• How many do we each buy ?
• 1 < n < 20

• Hence N~ (no. of people in Canada) x n
• N ~20x10⁶x10~10⁸
• Note that in order of mag. calcs, want nearest factor of 10 only

• e.g. My calculation says that the volume of an atom is 10²⁰ m³.
• It's very small, so it must be correct?
• O.K. , I did it again and got 10^-20 m : that really is very small, so it must be right???

• Turn Off Your Taps! If a tap is left dripping just once a minute, it can waste enough water in a month to fill 20 baths. Source: Ottawa Citizen (Ontario Ministry of the Environment)
• ........Wait a moment.......!!!!!!!!!!!!

How big is a drop?

What is the approximate volume of a drop of water?

1. 10^-2 m³
2. 10^-5 m³
3. 10^-8 m³
4. 10^-11 m³

Dimensional Analysis

e.g. Wallpaper

• My room is 8' x 10' x 15'. How much wallpaper do I need?
• 8x10x15 = 1200.
• 1200 what?
• 1200 square feet, obviously. (????????)
• This works out to cu. ft, not sq. ft.
• Always check that units are consistent: we cannot have an equation with kg = m . Never substitute numbers into formula until the last step

Always check that units are correct at the end of a calculation.

Never substitute numbers into formula until the last step.

Can also use this to guess formulae sometimes e.g a body falls under gravity: how fast is it going after falling s feet?

• g is the acceleration due to gravity. v = g s ?

• Dimensions [s] = L [g] = LT-2 [v] = LT-1 so

  [v] = [g ] [s] -⇒ LT-1 = L T-2. L = L2T-2

• NO WAY!!!: however we can now guess the right answer

   [v]  =  ([g ] [s])1/2      ⇒
  LT-1 = (L T-2. L)1/2
        = LT-1
  

• so v = (g s)^1/2 would at least be dimensionally correct. Correct answer is

  v = 2(g s)1/2
  

• Can never get the constant (2 in this case) by dim. analysis.

Pendulum

How long does a pendulum take to swing? A pendulum consists of a weight on a string of length l, and mass M. There is an acceleration due to gravity given by g. (Acceleration has units of Length/Time² or LT^-2). Which of the following expressions could be correct for the time it takes to swing?

1. t = gl
2. t = g/l
3. t = (g/l)^1/2
4. t = (l/g)^1/2