# Measurement3

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```							                        Physics
 What is physics?

 Measurements in physics

- SI Standards (fundamental units)
- Accuracy and Precision
- Significant Figures
- Uncertainties and Mistakes

 Language of physics
- Mathematical Expressions and Validity
 What is physics?

- A way of describing the physical world
6th Century B.C. in the Greek city of Miletus (now in Turkey) a group of men
comes from the Greek “physis” meaning “nature” and the Latin “physica”
meaning natural things

- Physics is understanding the behavior and structure of matter
- It deals with how and why matter and energy act as they do

- Energy is the conceptual system for explaining how the universe works
and accounting for changes in matter

- The word energy comes from the Greek “en”, meaning “in” and “ergon”,
meaning “work”. Energy is thus the power to do work. Sounds weird!!

- Although energy is not a “thing” three ideas about energy are important

1. It is changed from one form to another (transformed) by physical events
2. It cannot be created nor destroyed (conservation)
3. When it is transformed some of it usually goes into heat
-Areas within physics studied this year:

Mechanics – Motion and its causes

Thermodynamics – Heat and temperature

Vibrations and Waves – Periodic motion

Optics – Behavior of light

Electromagnetism – Electricity, magnetism and EM waves

Atomic – Structure of the atom, energy associated with atomic changes

Nuclear – Structure of the nucleus, energy associated with nuclear changes
 The Power of Physics

Physics predicts how nature will behave in one situation based on the
results of experimental data obtained in another situation.

Mechanics → Newton’s Laws          → Rocketry

Electromagnetism → Maxwell’s Equations → Telecommunications
 What is physics?

- Investigations in physics generally

Observations + initial data collection
formulation and testing, interpret
results + revise hypothesis if
necessary, state conclusions

Some hypotheses can be tested
by making observations.

Others can be tested by building a model
and relating it to real-life situations.
- Physics uses models to simplify a
physical phenomenon

They explain the most fundamental features of
a phenomenon.
Focus is usually on a single object and the
things that immediately affect it. This is called
the system

Lord Kelvin, who lived in England in the 1800s, was famous for
making models.

To model his idea of how light moves through space, he put balls into
a bowl of jelly and encouraged people to move the balls around with
their hands.

Kelvin’s work to explain the nature of temperature and heat still is
used today.
-Models help:

identify relevant variables and a hypothesis worth testing
guide experimental design (controlled experiment)
make predictions for new situations

Today, many scientists use computers to build models.

NASA experiments involving space flight would not be practical
without computers.

An airplane simulator enables pilots to
practice problem solving with various
situations and conditions they might
encounter when in the air.

This model will react the way a plane
does when it flies.
Measurements in physics

Physics experiments involve the measurement of a variety of quantities.

These measurements should be accurate and reproducible.

The first step in ensuring accuracy and reproducibility is
defining the units in which the measurements are made.
Measurements in physics
- SI Standards (fundamental units)

Fundamental units:     distance – meter (m)         time – second (s)
mass - kilogram (kg)         temperature - kelvin (K)
current – ampere (A)
luminous Intensity - candela (cd)
Amount of substance – mole (mol) – 6.02 x 1023

Derived units:         combinations of fundamental units

speed (v) = distance/time                   units: m/s
acceleration (a) = velocity / time          units: m/s/s = m/s2
force (F) = mass x acceleration             units: kgm/s2 = N (Newton)
energy (E) = force x distance               units: kgm2/s2 = Nm = J (Joule)
charge (Q) = current x time                 units: As = C (Coulomb)
Measurements in physics
- Precision and Accuracy

“It’s better to be roughly right than precisely
wrong”

– Allan Greenspan, U.S. Federal Reserve Chairman (retired)
Measurements in physics
- Precision

The precision of a series of measurements is an indication of the
agreement among repetitive measurements. A “high precision”
measurement expresses high confidence that the measurement lies
within a narrow range of values.

Precision depends on the instrument used to make the measurement.
The precision of a measurement is one half the smallest division of the
instrument for analogue and one least significant digit for digital.

The precision of a measurement is effected by random errors that are not
constant but cause data to be scattered around a mean value. We say that
they occur as statistical deviations from a normalized value.

Random variations can be caused by slight changes in pressure, room
temperature, supply voltage, friction or pulling force over a distance.
Human interpretation is also a source of random error such as how the
instrument scale is read between divisions.
 Measurements in physics
- Significant Figures

Significant figures reflect precision. Two students may have calculated the
free-fall acceleration due to gravity as 9.625 ms-2 and 9.8 ms-2 respectively.
The former is more precise – there are more significant figures – but the
latter value is more accurate; it is closer to the correct answer.

General Rules:
1. The leftmost non-zero digit is the most significant figure.

2. If there is no decimal point, the rightmost non-zero digit is
the least significant.

3. If there is a decimal point, the rightmost digit is the least
significant digit, even if it is a zero.

4. All digits between the most significant digit and the least
significant digit are significant figures.
 Measurements in physics
- Arithmetic with Significant Figures

cannot be more precise than the least precise measurement.

Add:   24.686 m + 2.343 m + 3.21 m           Answer: 30.24 m
3.21m has the least dp’s

When multiplying or dividing measurements the factor with the least
number of significant figures determines the recorded answer

Multiply: 3.22 cm x 2.1 cm                   Answer: 6.8 cm2
2.1 cm has only 2sf

Note significant digits are only considered when calculating with
measurements; there is no uncertainty associated with counting. If you
counted the time for ten back and forth swings of a pendulum and you
wanted to find the time for one swing, the measured time has the
uncertainty but the number of swings does not.
 Measurements in physics
- Dealing with uncertainties

If you measured a length of string to be 24.5 cm long this is called a
“raw value” because the string is not perfectly straight and there is
some interpretation of the scale involved at each end of the ruler. So
next you need to estimate the “absolute uncertainty” which could be
0.2 cm.

Because repeated measurement or a more precise measurement
might reveal the string’s length to be slightly longer or slightly
shorter than the initial value we must express the uncertainty as
“plus or minus the absolute uncertainty”.

Therefore:        l  l   = 24.5 cm  0.2 cm = (24.5 0.2) cm

Rules:
1. When adding experimental uncertainties to measured or calculated
values, uncertainties should be rounded to one significant figure.
2. The last significant figure in any stated answer should be the same
order of magnitude (in the same decimal position) as the uncertainty
 Measurements in physics
- Dealing with uncertainties

Suppose you have the following repeated measurement of a measured
length. Which measurement is the right one?

Clearly the data falls within  0.07 cm of the mean
Trial       Length        So you might think length = 25.43  0.07 cm
(cm)
1         25.45         But… There is uncertainty in the tenths place - it
2         25.40         varies from 3 to 5 so back off and write…
3         25.50                       length = 25.4  0.1 cm
4         25.42
But… the measurement 25.50 cm looks out of place
5         25.38
with the rest of the data so it we ignored it and ran the
average again we could get a more precise
Mean         25.43         measurement….
value
length = 25.41  0.04 cm
 Measurements in physics
- Pure Numbers

Lets say you measure the thickness of 100 sheets of paper (26  1mm)
and want to know the thickness of a single sheet.

Rule: When you multiply of divide by pure numbers you multiply
or divide the absolute uncertainty by the pure number.
So one sheet is (0.26  0.01)mm

Now lets say you measure the diameter of a circular object (D = 4.6
 0.2 cm) and want to determine the circumference using c = 2r.

r = D/2   so   r  r = (2.3  0.1) cm and c = 2r

c  c = 2 (rr) = 2 (2.3  0.1) cm

c  c = 14.4513 cm  0.6283 cm = (14  1) cm
 Measurements in physics
- Combining uncertainties in calculations:

If you multiply or divide, find difference between the actual
and the maximum and minimum calculated values using
the absolute uncertainties.
A rectangular metal plate has length, L = (363)mm and width, W = (18 1)mm
what is its circumference?

Cabsolute = 2L + 2W = 2(L+W) = 2(36mm + 18mm) = 108mm

C = 2(L + W) = 2(3mm + 1mm) = 8mm

C = (108 8)mm

What is the area of the plate?

Aabsolute = L x W = 36mm x 18mm = 648 mm2
Amax = Lmax x Wmax = 39mm x 19mm = 741 mm2
Amin = Lmin x Wmin = 33mm x 17mm = 561 mm2
A / 2 = 741 – 648 = 93
A / 2 = 648 – 561 = 87
A = Aabsolute  A = (648  93)mm2 = 650  90mm2 = (6.5 0.9)x102 mm2
 Measurements in physics
- Accuracy and systematic uncertainty

The accuracy of a measurement is its relation to the true, nominal,
or accepted value. It is sometimes expressed as a percentage
deviation from the known value. The known or true value is often
based upon reproducible measurements.

Instruments might not be accurate. A two-point calibration can be
used to check. Does the instrument read zero when it should and
does it give a correct value when it is measuring an accepted value

Systematic uncertainty effects the accuracy of a measurement because it
comes from a source of error that is constant throughout a set of
measurements. The measurements are consistently shifted in one
direction.
A common source of systematic error is not zeroing your measuring
instrument correctly so that all data is constantly shifted away from the true
value. This can give high precision but poor accuracy.
 Measurements in physics
- Accuracy and systematic uncertainty
- Percentage Deviation

The accuracy of a measurement is sometimes expressed as a
percentage deviation from the known value. The known or true
value is often based upon reproducible measurements.

Percent Difference                                     100%
Actual value

For example, if a student determines experimentally the acceleration due to
gravity is 9.5 m/s2 but the known value is taken as 9.8 m/s2 then …..

9.5 - 9.8
Percent Difference                 100%  3.1%
9.8
 Measurements in physics
- Mistakes

Mistakes on the part of the individual such as..

• Misreading scales (using equipment incorrectly)
• Poor arithmetic and computational skills

• Wrongly transferring raw data to the final report

• Using the wrong theory and equations

These are a source of error but ARE NOT considered a source of
experimental error
 Language of physics
- Mathematical Expressions and Validity
Physicists use the tools of mathematics to describe measured or
predicted relationships between physical quantities in a situation.

A physical equation is a compact statement based on a model of the
situation
Like most models, physics equations are only valid if they can be used to
make predictions about situations. Physical expressions can be checked
for validity a number of ways;

1. through an experiment
2. through dimensional analysis
3. by order of magnitude estimation

Lets say that you are trying to find the mass of an object using, M = V / 
Dimensionally:    m3 / kg/m3 = m3 m3 / kg = m6 / kg not kg
So the variables are in the incorrect order! (M = V )

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