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The Realm of Physics

IB-physics Unit 1

Keith Herold

on 11 August 2016

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Transcript of The Realm of Physics

Measurement in Physics

Chapter 1
Physics & physical measurement
Mechanics: kinematics, gravity
Thermal properties of matter
Oscillations and waves
Electricity and Magnetism
Circular motion and gravitation
Atomic, Nuclear, and Particle Physics
Energy Production
[HL]: wave phenomena, fields, electromagnetic induction, quantum & nuclear physics
[OPTION-everyone]: Astrophysics
**We need a system to talk about units that are standardized...=The SI system. Seven basics units to describe measurements.
1. meter....m
2. kilogram...kg
3. second...s
4. ampere....A
5. kelvin.....K
6. mole....mol
7. candela...cd
We need to use the SI units to describe:
electric current
quantities of tiny things such as atoms or molecules
luminous intensity
What is a derived unit?
-------->well....it is when you need to use a combination of more than one unit.
e.g. : velocity is total displacement(s) per time(t) or V=s/t [which yields meters/sec or m/s]
Many of these derived units have their own name.... e.g. : the Newton (N)=Kgm/s^2
-this is a force that is = to a (kilogram)x acceleration=(meter per second squared). ms^2
N=kg*m sec^-2
Weight is a force in N's not kg.
Mass is in kg, the force pulling it down is the mass(kg) times the acceleration due to
You need to know some names associated with quantities. See page 7 ...fig. 4 Metric multipliers
But the main ones are:
centi vs. hundredth
milli vs. thousandth
deci vs. tenth
micro vs. mega {millionths 10^-6, million 10^6}
nano vs. giga {billionths 10^-9, billion 10^9}
pico vs. tera {10^-12 & 10^12}
femto vs peta {10^-15 & 10^15}
The 4-Fundamental Forces of the universe in physics:
1. gravitational
2. electromagnetic
3 & 4. strong & weak nuclear forces
2. ELECTROWEAK [weak nuclear+electromagnetic]
3. Color [strong nuclear force]
*Nb: throughout the year I will say there is four but be aware of the new classification.
You must be familiar with geometry and trigonometry to solve problems in physics! Also a sound general mastery of algebraic manipulation of numbers is very important.
Textbooks skip steps. You can solve using different approaches but......
soh cah toa
Uncertainties & Errors
There are two types of error:
1. random error
2. systematic error
random error:
characterized by the fact that it is the error associated with every time you measure something.
Random errors are reduced by averaging repeated measurements.
An example of a random error would be: "reading errors". The instrument is fine and has no problems. But with an analog reading such as a meter stick, you might select the final digit (aka-the estimated digit of uncertainty) digit slightly off.
Systematic error: those not apparent until you change or remove the insulting device. This could be a badly made ruler stick or a non calibrated digital analytical balance (scale).
{the systems devices are poor or inaccurate}
One must always remember that every time you measure something there is error. Also error begins to get large if there are lots of instrumental measurements. All recorded uncertainties accumulate during an experiment and must be taken into consideration= "propagation of error"
Accuracy vs. Precision
I like the dart board classic example to explain the difference between accuracy and precision.
---->the area of the dart board in the center or "bull's eye".
Here we have all three darts hitting the bulls eye. Very accurate and each time getting the same result=precision
Poor accuracy & poor precision
Precision is great because the darts all hit the same spot....but........they didn't hit the bulls eye so the accuracy is poor!
You can't have answers that are more significant than the least significant figures used in a calculation!!!!!
The use of standard form scientific notation is used in the sciences...
i.e.: #'s between 1 & 10 for very small numbers less than 1/100th and greater than 100. So the previous example of 269. could be shown as 2.69E2 g/cm^2. You will see exceptions throughout physics.
eg: .000235=2.35E-4 and 4,003,759=4.003759E6 but if wanted three sig figs then 4.00 E6
*Measurements are accurate if the systematic error is small.
*They are precise if the random error is small.
If you multiply 6.3875 X 42.3 you will get the answer = 270.19125 but.......this is more significant than my least significant number. Answer: 2.70 X 10^2 or 2.70E2
Nb: these are end result answers and not steps. In physics don't round off and follow this rule until the answer is needed.
Line of best fit...
Here we have some data plotted but it isn't showing what the error is in each measured point called the +- uncertainty. The largest error bar is consistently used here.
Assumptions are often made about finding a reasonable solution to a physics problem. eg: assuming there is no friction with pushing something across the floor.
If there are assumptions though, one should be able to justify why some factor is not used in the solution of the problem. eg. Assume the falling object is accelerated due to gravity and there is no air resistance. {*the air resistance may be too difficult to ascertain because of shape, etc.. but in a short fall the object's air resistance may be considered negligible. Therefore we assume no air resistance}.
Vectors and Scalars
Vectors have direction and magnitude. eg:
velocity, acceleration, force.
scalars only have magnitude
eg. speed, temperature mass, distance, time.
*see a more complete list of scalars and vectors on table shown on page 11 of Pearson's handout.
The length of the vector is the magnitude. Vectors can be added and subtracted.
resultant vector = sum of the vectors
----->parallelogram method
----->head to tail method (see page 22-Tsokos)

Subtraction of vectors:
vector a-b becomes a+(-b)
---so reverse the vector b's direction. Next draw a new vector tip of vector b to the tip of vector a. *go through problem Q4 Tsokos page 24 to see how this looks on your own*
Components of a vector
Components of vectors are usually considered the x-axis and the y-axis measurements. Angles are measured from the x-axis in the counter clockwise fashion. Vectors should be moved in a parallel fashion to the origin of the Cartesian coordinate system.
Some of the vector rules probably are confusing. As we go through problems in Physics more of the solution ability will come to you. You can always google for rules and tutorials.
Go to page 25 Tsokos Example problem. (Next slide/frame is the problem)
This is a good example to see what I meant in the last prezi frame/slide. Lets do this one on the board to refresh our Trig.-skills and realize some relationships about the neg. or pos. answers for a vector.
I am sure you noticed that the quadrant labeling follows from the X-axis in quadrant #1
Graphical Analysis and Uncertainties:
Section 1.5
The common logarithm is the logarithm with base 10
The natural logarithm is the logarithm to the base e, where e is an irrational and transcendental constant approximately equal to 2.718281828
The natural logarithm of a number x is the power to which e would have to be raised to equal x. For example, ln(7.389...) is 2, because e^2=7.389...i.e.::(2.718E2=7.389)
To simply state: sometimes we want to change the exponential curve into a straight line. Logs are often used to simplify this...
Propagation of errors:
Repeating measurements will decrease the random error as the misreading should begin to blend out or average out....
e.g.: 5.00cm, 5.01cm, 5.00cm, 7.00cm

*from inspection you can see 7 is out of the ordinary measurement of the same distance...So if you repeated the experimental measurement many times the average would be closer to the true value!
Go to page 36 Tsokos and see graph showing the uncertainty with the extremes. This illustrates the point/concept that uncertainty in measurement makes a difference!
....In my class I want a specific way to solve problem in homework, quizzes, tests and IBDP final exams. You must show skeleton equations, plugged in #'s in the second step, and then solutions boxed off with units.
This shows a logical sequence of events to solve problems and makes it easier for an examiner to know what and how you are solving the problem at hand.
The concept of
surfaces throughout physics.
Estimating very large and very small quantities often use the power of 10 that is close.
A skill of understanding the quantity.
e.g.: the magnitude of the diameter of the nucleus of a hydrogen atom is in the order of:
A. 10^-9 m B. 10^-15 m C. 10^-23 m D. 10^-30 m
*really only wanting you to understand the relative size in this example.
answer: B (femto meter)
52.9 +/- .5 mL uncertainty
13.37 seconds +/- .01 uncertainty
digital ! not analog
Now a more difficult way to think about orders of magnitude. One order of magnitude difference is = 10^1, two orders= 10^2 or one hundred , three orders of magnitude 10^3 or 1000.
Dickinson example page 1: resting mass of proton vs. electron respectively:
1.67 x 10^-27 and 9.1 x 10^-31 What is the magnitude difference?
Next slide frame but first you discuss it...
-27- -30 =
3 orders of magnitude
, which is a 1000 time greater for the mass of the proton. Note Nb: 1.67 is far away from 10 so 1.0x10^-27 kg and electrons 9.1 almost 10 so change the ten power to a larger number (E-31) to -30 so 1x 10^-30.
In a calculation, lets say a derived value such as density where density=mass/vol. & the mass is 14.0 gms and the volume is 0.152 cm^3.
14.0/0.152=92.10526316 g/cm^3
What is the correct way to show the answer?
Nb: each has 3 sig figs. answer should be to three sig. figs! therefore = 92.1 g/cm^3
So how do we get the error bar length?
For the axis in question it depends on the amount of values or trials to get that point.
*You will need to work on making graphs with Microsoft excel on your own. Hopefully you have some background. In lab write-ups, you will be expected to give graphs on your data collected and show uncertainty error bars. Best line fit & two extreme lines usually required. As the previous two frames with tutorial on graphing, you can see that it is possible to be taught the method via youtube and other tutorials...
---Grapher for Mac's and Graphmatica for windows have been suggested as alternative programs. I can't endorse any of these, you must check them out. ------

IB syllabus 1.2.10: State uncertainties as absolute, fractional, and percentage uncertainties.
1.2.11: Determine uncertainties in results.
1.2.12: Identify uncertainties as error bars in graphs. [total absolute uncertainties is addition of fractionals]
Absolute uncertainty: e.g.: use of stop watch to the hundredths of a second. =+/- 0.01 s

fractional uncertainty: = absol. uncer./recorded value

percentage uncertainty: fract.uncert.x100
Best to follow the standard deviation method described and illustrated on the board. *see Tsokos..............page 9...the next slide is that area
It is called the "unbiased estimate of the standard deviation.
parallelogram method

green is resultant vector; the brown & green=head to tail method.

*we are not too concerned with logarithmic function graphs at this point but beware what they are used for...
IN TSOKOS page 36.
Let us take an example of volume, like what
you are going to calculate soon in a lab.
LxWxH=vol. {Note vol. is a product}
3-measurements each with an absolute uncertainty value.
+/- .1 cm each
5.01, 6.80, and 7.85 cm respectively for the sides of a rectangular block.
??What is the answer for volume???
Addition of the % uncertainties is the rule for units with procedures of: multiplication, divisions, powers, and roots.

Graphs use the total absolute uncertainties for the error bars. Always use the largest error bars for your values. If I had one point and the measurement is 267.4 cm. and the % uncertainty in that measurement is 5% then I would multiple 0.05 time the measurement. This is approx. +/- 13 cm. This is the error bar.
If I was calculating density (as you will be doing shortly with several blocks of wood), you will note density equation is derived from mass/volume. Therefore each point plotted for density would have the addition of the mass relative %'s plus the volume relative % of 5%. If each mass had a absolute error of +/- 0.01g, you would need to first change to relative % error. If given the mass of a block at 48.00 g and the +/- 0.01 the fractional uncertainty is .01/48=0.0002 or less than 2 hundredth of a percent. So insignificant with added to 5% and doesn't change the total % error.
**Need two extremes as well!
nb: I showed the answer as "E". For steps this is OK but for the final answers show as X10^power.
Note: two extremes
are not shown...

Decimal multiples and submultiples of SI units can be written using the SI prefixes listed in the table below:

Factor Name Symbol Factor Name Symbol

10^1 deca da 10–1 deci d
10^2 hecto h 10–2 centi c
10^3 kilo k 10–3 milli m
10^6 mega M 10–6 micro µ
10^9 giga G 10–9 nano n
10^12 tera T 10–12 pico p
10^15 peta P 10–15 femto f
10^18 exa E 10–18 atto a
10^21 zetta Z 10–21 zepto z
10^24 yotta Y 10–24 yocto y

A googolplex is the number 10googol, or equivalently, 1010100. Written out in ordinary decimal notation, it is 1 followed by 10100 zeroes, that is, a 1 followed by a googol of zeroes.
???what is the smallest
cm. marking??? 1/10 or .1cm
The digit of Uncert. therefore is .05 cm
So lets say the measurement is exactly 6cm. How do I record this? 6.00 +/- .05 cm.
Digit of uncertainty
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