IB Physics Unit 1. Measurements and uncertainties- The realm of physics Notes

1 | Science Skills

IB Physics Content Guide

Big Ideas

        Units are an arbitrary construct invented by humans to communicate quantitative measurements

        All units can be made up of the 7 Fundamental SI Units

        Metric prefixes and scientific notation can be used to make large or small values easier to communicate

        Units can cancel out when being divided by like units

        Unit analysis can be used to determine the validity of a formula or determine the unit of an unknown solution

Content Objectives

1.1 – Patterns in Science

I can identify patterns and use an understanding of patterns to make predictions

1.2 – Units

I can describe the difference between quantitative and qualitative observations

I can identify the 7 Fundamental SI units

I can define and give an example of a derived unit

I can represent fractional units with negative exponents

I can convert metric units between prefixes

1.3 – Dimensional Analysis

I can convert fraction units and exponential units using Dimensional Analysis

I can use dimensional analysis to verify a formula

I can use dimensional analysis to determine the units for a solution

I can represent large and small numbers using scientific notation

I can compare quantities by orders of magnitude

 

1 | Science Skills

Shelving Guide

List the seven fundamental base units and their abbreviations:

 

Unit

Abbreviation

Length

Meter

m

Mass

Kilogram

kg

Time

Second

s

Electric Current

Ampere

A

Temperature

Kelvin

K

Amount of Substance

Mole

mol

Luminous Intensity

Candela

cd

 

Metric Prefixes – List the unit prefixes in their appropriate decimal position

Dimensional Analysis

Convert the following:

20 mi hr-1 à m s-1

0.0007 km2 à m2

or

Determine the units for Q:

Q = mc ΔT

m (mass)

kg

c (specific heat)

J kg-1 K-1

ΔT (change in temp)

K

PHYSICAL WORLD

WHAT IS SCIENCE?

Science refers to a system of acquiring knowledge. This system uses observation and experimentation to describe and explain natural phenomena. The term science also refers to the organized body of knowledge that people have gained using that system. Less formally, the word science often describes any systematic field of study or the knowledge gained from it.

 

Purpose of science is to produce useful models of reality. Most scientific investigations use some form of the scientific method.

 

Scientific method is a logical and rational order of steps by which scientists come to conclusions about the world around them. The Scientific method helps to organize thoughts and procedures so that scientists can be confident in the answers they find. Scientists use observations, hypotheses, and deductions to make these conclusions.

 

Science as defined above, is sometimes called pure science to differentiate it from applied science, which is the application of research to human needs. Fields of science are commonly divided into two major categories.
  • Natural science : The science in which we study about the natural world. Natural science includes physics, chemistry, biology, etc.  
  • Social science : It is the systematic study of human behavior and society.  

WHAT IS PHYSICS?

The word physics originates from a Greek word which means nature. Physics is the branch of science that deals with the study of basic laws of nature and their manifestation of various natural phenomena.

 

There are two main thrusts in physics :
  • Unification : In physics, attempt is made to explain various physical phenomena in terms of just few concepts and laws. Attempts are being made to unify fundamental forces of nature in the pursuit of unification.
  • Reductionism : Another attempt made in physics is to explain a macroscopic system in terms of its microscopic constituents. This pursuit is called reductionism.

 

Keep in memory
  • Information received through the senses is called observation.
  • An idea that may explain a number of observations is called hypothesis.
  • A hypothesis that has been tested many times is called scientific theory.
  • A scientific theory that has been tested and has always proved true is called scientific law.

SCOPE AND EXCITEMENT OF PHYSICS

The scope of physics is very vast. It covers a tremendous range of magnitude of physical quantities like length, mass, time, energy, etc. Basically, there are two domains of interest : macroscopic and microscopic. The macroscopic domain includes phenomena at the laboratory, terrestrial and astronomical scales. The microscopic domain includes atomic, molecular and nuclear phenomena.

 

Classical physics deals mainly with macroscopic phenomena consisting of the study of heat, light, electricity, magnetism, optics, acoustics, and mechanics. Since the turn of the 20th century, the study of quantum mechanics and relativity has become more important. Today, physics is often divided into branches such as nuclear physics, particle physics, quantum physics, theoretical physics, and solid-state physics. The study of the planets, stars, and their interactions is known as astrophysics, the physics of the Earth is called geophysics, and the study of the physical laws relating to living organisms is called biophysics.

 

Physics is exciting in many ways. Application and exploitation of physical laws to make useful devices is the most interesting and exciting part and requires great ingenuity and persistence of effort.

PHYSICS, TECHNOLOGY AND SOCIETY

Physics generates new technologies and these technologies have made our lives comfortable and materially prosperous. We hear terms like science, engineering , technology all in same context though they are not exactly same.

 

SCIENCE

  • A body of knowledge
  • Seeks to describe and understand the natural world and its physical properties
  • Scientific knowledge can be used to make predictions
  • Science uses a process–the scientific method–to generate knowledge

ENGINEERING

  • Design under constraint
  • Seeks solutions for societal problems and needs
  • Aims to produce the best solution from given resources and constraints
  • Engineering uses a process–the engineering design process–to produce solutions and technologies

TECHNOLOGY

  • The body of knowledge, processes and artifacts that result from engineering
  • Almost everything made by humans to solve a need is a technology
  • Examples of technology include pencils, shoes, cell phones, and processes to treat water
In the real world, these disciplines are closely connected. Scientists often use technologies created by engineers to conduct their research. In turn, engineers often use knowledge developed by scientists to inform the design of the technologies they create.

LINK BETWEEN TECHNOLOGY AND PHYSICS

 

Some physicists from different countries of the world and their major contributions

DOES IMAGINATION PLAY ANY ROLE IN PHYSICS?

Yes, imagination has played an important role in the development of physics. Huygen’s principle, Bohr’s theory, Maxwell equations, Heisenberg’s uncertainty principle, etc. were the imaginations of the scientists which successfully explained the various natural phenomena.

HOW IS SCIENCE DIFFERENT FROM TECHNOLOGY?

Science is the study of natural laws while technology is the practical application of these laws to the daily life problems.

FUNDAMENTAL FORCES IN NATURE

We come across several forces in our day-to-day lives eg., frictional force, muscular force, forces exerted by springs and strings etc. These forces actually arise from four fundamental forces of nature.
Following are the four fundamental forces in nature.
  • Gravitational force
  • Weak nuclear force
  • Electromagnetic force
  • Strong nuclear force
Among these forces gravitational force is the weakest and strong nuclear force is the strongest force in nature.

FUNDAMENTAL FORCES OF NATURE

Physicists are trying to derive a unified theory that would describe all the forces in nature as a single fundamental law. So far, they have succeeded in producing a unified description of the weak and electromagnetic forces, but a deeper understanding of the strong and gravitational forces has not yet been achieved.
  • Theories that postulate the unification of the strong, weak, and electromagnetic forces are called Grand Unified Theories (often known by the acronym GUTs).
  • Theories that add gravity to the mix and try to unify all four fundamental forces into a single force are called Super Unified Theories.
  • Theory that describes the unified electromagnetic and weak interactions is called the Standard Electroweak Theory, or sometimes just the Standard Model.

PROGRESS IN UNIFICATION OF DIFFERENT FORCES/DOMAINS IN NATURE

WHAT IS ELECTROMAGNETIC FORCE?

It is the force due to interaction between two moving charges. It is caused by exchange of photons (γ) between two charged particles.

NATURE OF PHYSICAL LAWS

A physical law, scientific law, or a law of nature is a scientific generalization based on empirical observations of physical behavior. Empirical laws are typically conclusions based on repeated scientific experiments and simple observations over many years, and which have become accepted universally within the scientific community. The production of a summary description of nature in the form of such laws is a fundamental aim of science.

 

Physical laws are distinguished from scientific theories by their simplicity. Scientific theories are generally more complex than laws. They have many component parts, and are more likely to be changed as the body of available experimental data and analysis develops. This is because a physical law is a summary observation of strictly empirical matters, whereas a theory is a model that accounts for the observation, explains it, relates it to other observations, and makes testable predictions based upon it. Simply stated, while a law notes that something happens, a theory explains why and how something happens

The realm of physics

1.1.1 State and compare quantities to the nearest order of magnitude.

Throughout the study of physics we deal with a wide range of magnitudes. We will use minuscule values such as the mass of an electron and huge ones such as the mass of the (observable) universe. In order to easily understand the magnitude of these quantities we need a way to express them in a simple form, to do this, we simply write them to the nearest power of ten (rounding up or down as appropriate).

That is, instead of writing a number such as 1000, we write 10.

The use of orders of magnitude is generally just to get an idea of the scale and differences in scale of values. It is not an accurate representation of a value. For example, if we take 400, it’s order of magnitude is 10, which when we calculate it gives 10 x 10 = 100. This is four times less than the actual value, but that does not matter. The point of orders of magnitude is to get a sense of the scale of the number, in this case we know the number is within the 100s.

1.1.2 State the ranges of magnitude of distances, masses and times that occur in the universe, from smallest to greatest.

Distances:

  • sub-nuclear particles: 10-15 m
  • extent of the visible universe: 10+25 m

Masses:

  • mass of electron: 10-30 kg
  • mass of universe: 10+50 kg

Times:

  • passage of light across a nucleus: 10-23 s
  • age of the universe : 10+18 s

1.1.3 State ratios of quantities as differences of orders of magnitude.

Using orders of magnitude makes it easy to compare quantities, for example, if we want to compare the size of an an atom (10-10 m) to the size of a single proton (10-15 m) we would take the difference between them to obtain the ratio. Here, the difference is of magnitude 105meaning that an atom is 10or 100000 times bigger than a proton.

1.1.4 Estimate approximate values of everyday quantities to one or two significant figures and/or to the nearest order of magnitude.

Significant figures
To express a value to a certain amount of significant figures means to arrange the value in a way that it contains only a certain amount of digits which contribute to its precision.

For example, if we were asked to state the value of an equation to three significant figures and we found the result of that value to be 2.5423, we would state it as 2.54.

Note that 2.54 is accurate to three significant figures as we count both the digits before and after the point.

The amount of significant figures includes all digits except:

  • leading and trailing zeros (such as 0.0024 (2 sig. figures) and 24000 (2 sig. figures)) which serve only as placeholders to indicate the scale of the number.
  • extra “artificial” digits produced when calculating to a greater accuracy than that of the original data, or measurements reported to a greater precision than the equipment used to obtain them supports.

Rules for identifying significant figures:

  • All non-zero digits are considered significant (such as 14 (2 sig. figures) and 12.34 (4 sig. figures)).
  • Zeros placed in between two non-zero digits (such as 104 (3 sig. figures) and 1004 (4 sig. figures))
  • Trailing zeros in a number containing a decimal point are significant (such as 2.3400 (5 sig. figures) note that a number 0.00023400 also has 5 sig. figures as the leading zeros are not significant).

Note that a number such as 0.230 and 0.23 are technically the same number, but, the former (0.230) contains three significant figures, which states that it is accurate to three significant figures. On the other hand, the latter (0.23) could represent a number such as 2.31 accurate to only two significant figures. The use of trailing zeros after a decimal point as significant figures is is simply to state that the number is accurate to that degree.

Another thing to note is that some numbers with no decimal point but ending in trailing zeros can cause some confusion. For example, the number 200, this number contains one significant figure (the digit 2). However, this could be a number that is represented to three significant figures which just happens to end with trailing zeros.

Typically these confusions can be resolved by taking the number in context and if that does not help, one can simply state the degree of significance (for example “200 (2 s.f.)” , means that the two first digits are accurate and the second trailing zero is just a place holder.

Expressing significant figures as orders of magnitude:
To represent a number using only the significant digits can easily be done by expressing it’s order of magnitude. This removes all leading and trailing zeros which are not significant.

For example:
0.00034 contains two significant figures (34) and fours leading zeros in order to show the magnitude. This can be represented so that it is easier to read as such: 3.4 x 10-4 .

Note that we simply removed the leading zeros and multiplied the number we got by 10 to the power of negative the amount of leading zeros (in this case 4). The negative sign in the power shows that the zeros are leading.

A number such as 34000 (2 s.f.) would be represented as 34 x 10.

Again, we simply take out the trailing zeros, and multiply the number by 10 to the power of the number of zeros (3 in this case).

There are a couple of cases in which you need to be careful:

  • A number such as 0.003400 would be represented as 3.400 x 10-3 . Remember, trailing zeros after a decimal point are significant.
  • 56000 (3 s.f.) would be represented as 560 x 10. This is because it is stated that the number is accurate the 3 significant zeros, therefor the first trailing zero is significant and must be included. Note that this can be used as another way to express a value such as 56000 to three significant figures (as opposed to writing “56000 (3 s.f.)”).

Rounding
When working with significant figures you will often have to round numbers in order to express them to the appropriate amount of significant figures.

For example:
State 2.342 to three significant figures: would be written 2.34.

When representing the number 2.342 to three significant figures we rounded it down to 2.34. This means that when we removed the excess digit, it was not high enough to affect the last digit that we kept.

Whether to round up or down is a simple decision:
If the first digit in the excess being cut off is lower than 5 we do not change the last digit which we are keeping. If the first digit in the excess which is being cut off is 5 or higher we increment the last digit that we are keeping (and the rest of the number if required).

For example:
State 5.396 to three significant figures: would be written 5.40. This is because we remove the last digit (6) in order to have three significant digits. However, 6 is large enough for it to affect the digit before it, therefor we increment the last digit of the number we are keeping by 1. Note that the last digit of the number that we are keeping is 9, therefor incrementing it by 1 gives 10. Thus we also need to increment the second to last digit by 1. This gives 5.40 which is accurate to three significant figures.

You might think that if a number such as 5.4349 were to be rounded to 3 s.f. it would give 5.44 as the last digit is 9 which is large enough to affect the previous digit which would then become 5. Now that 5 would be large enough to affect the last digit of the number we are keeping which would become 4 (thus 5.44). However, this is not the case, when rounding, we only look at the digit immediately after the one we are rounding to, whether or not that digit would be affected by the one after it is not taken into account. Therefor, the correct result of this question would be 5.43.

1.1.1 State and compare quantities to the nearest order of magnitude.
An order of magnitude indicates the relative size of a quantity. Long and complicated numbers can be simplified or estimated through the use of this method. For example, the number 200 is in the order of magnitude of 10^2 (100). When estimating orders of magnitude — similar to rounding — anything below 5 is the lower order of magnitude while anything above or equal to 5 is the higher order of magnitude. In this case, 500 and anything above would be in the order of magnitude of 10^3 (1000). Some common orders of magnitude include:

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Practice questions
1. Estimate the number of seconds in a human “lifetime”.
Answer: 70yrs = 2.2 * 10^9 sec, 100yrs = 3.1 * 10^9 sec, 50yrs = 1.6 * 10^9 sec, therefore the estimate of the order of magnitude is 10^9 sec.
1.1.2 State the ranges of magnitude of distances, masses and times that occur in the universe, from smallest to greatest.

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The following simulation can help you better understand the ranges in magnitude:

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1.1.3 State ratios of quantities as differences of orders of magnitude.
Orders of magnitude can be compared in order to create a ratio. For example, the size of an atom is 10^-10m whereas the size of a proton is 10^-15m. The difference between these two values is 10^-5, so the atom is 10^5 (100,000) times bigger than a proton. The ratio of the atom to the proton would be 1:10^-5.
Practice questions
1. Estimate the ratio of
a) the mass of an electron to the mass of a human
b) the radius of earth to the size of the universe
Answers:
1. a) compare 10^-30 and 10^2, 10^32 is the difference hence 1:10^32  b) compare 10^7 and 10^26, 10^19 is the difference hence 1:10^19
1.1.4 Estimate approximate values of everyday quantities to one or two significant figures and/or to the nearest order of magnitude.

Significant figures are the individual digits in a numerical value. For example, the number 20 has two significant figures. One important rule regarding significant figures is that when there are zeroes preceding the number (ie. 0.020), they are not counted, hence the value 0.020 would still have two significant figures. Zeroes after the number (ie. 20.00) or between values (ie. 201) are always counted.

In order to express significant figures as orders of magnitude, one should take all of the numbers following the amount of significant figures given and convert them to a power of 10. For example, the number 0.0030 would be 3.0 × 10^-4; the zero after 3 remains because it was significant in the original value. Sometimes a significant figure amount will be given to you, for example, “56,000 (3 s.f.)” would convert to 560*10^2 because 560 has three significant figures and that was the requested amount in the original question.

Sometimes numbers need to be rounded in order to fit a significant figure amount. If the amount of significant figures required is two and your answer is “56,000”, you should rewrite it as “5.6 × 10^4”. Similarly, if your answer is “0.0560823” and you require two significant figures, you should round it down to “0.056” or rewrite it as “5.6 × 10^-2”.

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