Statics

A Philosophical Insights

Ashal Lama
The Natural Philosopher

May 1, 2020
2
Contents

1 Misconceptions about Science 1

1.1 What people thinks about science? . . . . . . . . . . . . . . . . . . 1
1.2 Methods of Science . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Science and reality . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Can physical quantities explain the nature? . . . . . . . . . . . . . 3
1.5 Discovery and perceptions . . . . . . . . . . . . . . . . . . . . . . . 4
1.6 The nature of sound, language and words . . . . . . . . . . . . . . . 4
1.7 Science and logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.8 Science and human minds . . . . . . . . . . . . . . . . . . . . . . . 5
1.9 Take away and The Natural Philosopher . . . . . . . . . . . . . . . 5

2 Fundamental Concepts in Statics 7

2.1 Newton’s laws of motion . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Is he stupid? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 How Newton came up with such a counter intuitive laws? . . . . . . 8
2.4 Significance of Newton’s second laws of motion . . . . . . . . . . . 8
2.5 Mass measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.6 Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.7 Matter, Body, Mass and Particle . . . . . . . . . . . . . . . . . . . 10
2.8 Scalar and Vector quantities . . . . . . . . . . . . . . . . . . . . . . 10
2.9 Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.10 Effects of force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.11 Moment of Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.12 Circular motion and particles . . . . . . . . . . . . . . . . . . . . . 12
2.13 Laws of lever . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.14 Proof of Laws of lever . . . . . . . . . . . . . . . . . . . . . . . . . 13

3 Forces at a point 15
3.1 Line of action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 Stress in a body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.3 Equilibrium of two forces acting at a point . . . . . . . . . . . . . . 16

i
ii CONTENTS

3.4 Equilibrium under action of forces on beam . . . . . . . . . . . . . 16

Chapter 1

Misconceptions about Science

I do not intend to demotivate the people. I am also aware that certain ascepts
always have loop holes in them and before trying to eradicate them, we must come
up with new replacement for it and i must mention that i am not here to replace
them at all. After knowing certain ascpects of the science, people can be more
familiar with the methods of science, their weakness and strength so that they
can change the way they perceive science. There are various misconceptions which
are prevailing in science since ancient times. Science seems pretty complex and
difficult today’s in 21st century, all thanks to those misconceptions and conspiracy
that our ancestor as well as people nowadays are holding. It seems to most people
that the nature can be explored through the science and there is no denying about
it. In fact, science can only explore and percieve things in their own ways but it
is evident that they will never know the absolute and intrinsic nature of anything
that exist in the universe. and you must not be surprise that science never intend
to do so. Then you must ask yourself what science have accompolished this whole
time?

1.1 What people thinks about science?

Various people may came up with various conceptions about science. It ranges from
science is very difficult and completely different language to the science discoveries
are made by the brilliant and genius minds. The following are some of which
people around thinks about science:
• Science is very difficult language to learn
• Science is based on logic
• Genius minds are needed for the discoveries
• Learning science is so exhausting physically as well as mentally
• Science can be pretty counter intuitive

1
2 CHAPTER 1. MISCONCEPTIONS ABOUT SCIENCE

• Science makes our life better, comfortable, easier and happier than ever before
but some may argue due to the advent of technology we are prone to many
sufferings
• Science is the ultimate tools to reality

1.2 Methods of Science

The best ways to verify the above thinking is to know how science works and
you might certainly changes the way you think about the science. The method
of science is iterative process. Since science is iterative process you must ask
yourself, Is science really the tools to reality? What it implies is that reality can
be iterative for the science or you should ask fundamentally whether science seeks
for the reality or not.

Figure 1.1: Methods of science

• Observation: Science first starts with observation which rely on the five senses
and the human minds. They try to observe the relationship between certain
variables of interest.
• Physical measurement: Before measuring something, we have to first make a
standard and before making a standard, we have to give a definition based on
the relationship that exists from the defintion. It is a fact that the measure-
ment process starts with the definition that comes from the observation and
1.3. SCIENCE AND REALITY 3

perceptions. for example: To measure mass we have to know the definition of

mass i.e. what mass itself is in order to make a standard of mass.
The final principles or laws or hypothesis are the results of imitation or gener-
alization which are done from many different observations.

1.3 Science and reality

Definition: Reality is anything that is irrespective of your senses and how you
perceive them. It is something that exists in the nature in its true and intrinsic
essence.
The method of science is based on the observation and how your perceive those
observation. How we perceive things is relative to all human minds and the only
thing left is whether you are convinced by the statement itself coming from the
science. In fact, we can not form any coneption of what things really is in its
intrinsic and real essence, but only how it acts. By implying something is heavy,
we mean that when placed upon our hand, it weighs it down, that is it acts in
certain way. When we say something is malleable, it means that when the thing
is struck by hard substances it yield or flattened. The name of the properties
are only the expression of the manner in which they act under certain specified
circumstances. All we can know is how certain things acts
Note: The reader must drop any idea about the conceptions of what things in
its true essence is and should focus more on how those substances present it to us
in different circumstances. It should be worth mentioning that science is never a
tools to reality.

1.4 Can physical quantities explain the nature?

The mother nature consists of not only the physical quantities but fundamentally,
there are many non-physical quantities. As long as we are not able to measure
them, we can never seek for the reality. From atomic view, we considered matter
as containing large number of atoms which are the building blocks of matter. If
fundamentally, we are just the atoms and protons then we might question ourselves
why does human being have emotion? and how atoms leads to emotion?
Similary, the physical quantities are measured based on the comparison. What i
meant by comparison is that, if we have to know the mass of the body we just
give a number to that body which acts as a standard and with respect to that
standard, we compare whether the mass is double or triple. Hence, we can not
pursue for reality where something exists in its absolute form by the method of
comparision.
4 CHAPTER 1. MISCONCEPTIONS ABOUT SCIENCE

1.5 Discovery and perceptions

Discovery is something that is experienced for the first time. Sir Issac Newton
is appreciated for the discovery of the gravity. and one should carefully note
that gravity exist even before it is discovered. and Newton was not the first
person to discover the gravity, it was the first animals or creatures or biological
life that exist in the planet that discovered the gravity, surely that was not Newton.
Fundamentally people have been confused with discovery. What Issac Newton did
was express the gravity the way he perceived by observing the perceptions of his
ancestor. So, whatever they have been calling discovery is just a expression of the
things that is perceived by one or more human beings. That is the main reason
why science is very hard because as a human beings, we perceive things differently.

1.6 The nature of sound, language and words

Definition: Sound, language and words are approximation of reality. The ap-
proximations has different forms of which three are mentioned here.
Through the help of sound, language and words, it seems that we are able to
express ourselves. The reader must know that you can not express yourselves as
long as the listener receive the sound or words and make the meaning out of it. If
they are not able to make the meaning out of it, even though how good you are at
expressing yourselves you are never going to be successful to express yourselves.
This has deep rooted consequences: even though thousand of journals, articles,
manuscript has been published they are never able to express themselves. By im-
plying approximation of reality, i mean that you are never gonna be successful in
expressing all those situation that takes place which is the inherent problems with
sound, language and words. This has created a environment of chaos since the
principles or the laws or any other hypothesis are the results of sound, language
and words. The important thing is how close your approximation is to reality?
To ensure that there is no any communication gaps between the scientist and the
reader, it is the events itself that must be explained and try to be experienced to
the reader on how the person was able to came up with those principles which is
lacking and prevailing in the century which makes science one of the most difficult
langauge to learn. By mentioning the events itself i mean that for example: if i
am the person to give law about newton second law of motion then i would tell
that there was a debate going on about the earth rotating about its center, if earth
rotates then we might land up in different places if we jump and observing this i
concluded that no force is required for the motion just because i want to imitate
those observation i.e. curve fitting any observations. We must not forget that any
events results in certain consequences. Any finding that are made in science is a
1.7. SCIENCE AND LOGIC 5

results of events. and the most important things that is to explain the events itself
that helps in the finding must be explicitly mentioned for example: what events
leads you to the discovery of gravity or did you copied other or did you borrow
idea from someone else?

1.7 Science and logic

Misconceptions about logic: People believe that logical people have great value
in the society. You might overheard people saying in their conversation, your words
does not make any logic at all.
Definition: The process of logic is the search for meaning.
The pursuit for making meaning is important because they can help us in making
decision in our everyday life. Logic is also not a tools to reality. There are many
things for example life itself that has no meaning or we have not been able to
perceive the meaning of life itself from the methods of science, therefore it is
evident that logic has just become tools for decision making. The life itself that
has great value has no meaning which means no logic at all.

1.8 Science and human minds

Although it seems there are difference between science and human minds, one
thing is similar between the two. Science and human minds does not want chaos.
Science therefore wants to explain all the phenomenon in the nature fundamentally
i.e. to reduced the fundamental principles and explain from the least possible or
one principles the entire universe. Principles are those statement that are taken
for granted which we believe to be true or are convinced or has to be convinced.

1.9 Take away and The Natural Philosopher

Science itself is a learning process. It starts with observation and imitation. Like
any child who is born on this nature, they learn first by observing and ensuring that
the imitation follows what is prevailing, science exactly is the same and iterative
which is far from reality. Therefore, it should not bother people even though
they do not know about the absolute nature of something that exists or at least
science do not seek for absolute truth and reality. The principles are made for
human benefits and they are same as human minds wanting least things to be
remembered i.e. science wants to explain the whole universe from fundamentally
least possible principles and the principles are those which they do not know why
they happened but they take it for granted. Science is very easy to learn and while
6 CHAPTER 1. MISCONCEPTIONS ABOUT SCIENCE

studying the science, one has to always seek for those events and those observations
that leads to the final laws or equation or whatsoever and when you are following
this path, you yourself will be placed in a genearl categories of something called
‘The Natural Philosopher’.
.
Chapter 2

Fundamental Concepts in Statics

Statics deals with body at rest under the influences of the external forces acting
on them. In this chapter, we will deal with some fundamental concepts which are
important to be perceived in order to understand the methods with which we deals
with the problems under statics.

2.1 Newton’s laws of motion

There are three laws of motion provided by Sir Issac Newton in his book “Principia
Mathematica” but fundamentally there is only one law of motion and the two other
laws are just the restatement of the Newton second laws of motion.
Why should we study the laws of motion?
Since statics deals with the body under rest, any causes that is responsible for
the motion are absent in the case of body at rest which are important for the
analysis. Therefore, the laws of motion is the most which explains why things in
the universe possess motion. The three laws of motions are:
• Newton’s First laws of motion: If there is no any unbalanced force acting on the
system, the body will move either at constant velocity or remain at the same
state of rest.
• Newton’s second laws of motion: An unbalanced force is responsible to accel-
erate a body
• Newton’s third laws of motion: Every action has equal and opposite reaction

2.2 Is he stupid?
These three laws, we do not know why they are true but we considered them as
true. Hence, it acts as a principles and the only thing remains is whether you are

7
8 CHAPTER 2. FUNDAMENTAL CONCEPTS IN STATICS

convinced or not. How can you be convinced with such stupid laws of motion. The
intial reaction might be: Who is this stupid guy? He does not know the laws of
motion. The first law is implying that for uniform motion, forces are not required.
If that is true, then the world would be a better places, no any forces are required
for motion. and the Newton justification was even though no force is required
for motion, in practice we have to exert force because friction exist. Now a new
term was introduced only because he wants his theory to be true. The reader
should be convinced with this statement, else there is no any other justification.
What can be done is: in any places of pratical importance if you found that forces
are required for motion, then you have to keep in mind there is something called
resisting forces that should be balanced by your forces so that the body are set to
uniform motion.

2.3 How Newton came up with such a counter

intuitive laws?
Newton’s laws implies that no force is required for a body to set in uniform motion.
That is not possbile in the planet earth. Sometimes in the past, for now we know
for sure that Earth revolves around the sun but at past, people believe that sun
revolves around the earth because we observe that sun rise in the east and set in
the west. not only that, if eath were set in motion, then we should feel it anyway.
but time after time with different experiments and mathematics proved that earth
rotates the sun and earth rotates about its axis. The real challenges was if the earth
rotates about its axis, why we do not feel the rotation and motions. Newton and
other speculated and came up with after perceving things from different sources
with the idea of inertia. The laws of inertia tell us that no force is required to set
something in uniform motion which exactly fits the idea of observation which came
from the rotation of earth about it axis and we do not feel anything nor we land
on another places when jumped from earth surface. The entire scenario was just
to match up with one small contradictions. and thats how our ancestor manage
to imitate the observations and the final laws is as we can observe in the form of
Newton’s laws of motion.

2.4 Significance of Newton’s second laws of mo-

tion
Newton’s second laws of motion forms a basis for the measurement of mass. For
the measurement of any physical quantities, a definition has to be given and the
2.5. MASS MEASUREMENT 9

second laws forms the basis for the measurement of the mass. The Newton’s second
laws of motion is mathematically given as:

F = m.a

where, F=force, m=mass of the body and a=acceleration

If we are able to know the force and acceleration, the mass of the body can be
known but the inherent problems was acceleration can be measured but the force
can not be. It means the equation has one known and two unknown quantity.
Therefore, one of the quantities has to be calibrated and standardized. What it
means to be standardized is that we have to set one object as standard of mass
and then compare the standard with other object. If same forces are applied for
two different bodies having different masses and the ratio of their acceleration is
taken, then the ratio of their masses can be measured which means that different
units of mass can be formed. For let say we have some standard called platinum
iridium alloy rod and it is considered as a standard and the unit given to the mass
is 1 kg, then we can make different unit of mass for example 2 kg of mass and 3 kg
of mass and many more from that 1 kg by comparing the ratio of their acceleration
for same external forces. And hence the force can also be measured based on the
standard formed.

2.5 Mass measurement

It should be notated that even though the definition of mass comes from Newton’s
second laws of motion, we do not use the second law to measure the mass. Instead,
we use spring balance or beam balance to measure the mass of the body. The beam
balance works on the principle of lever. If the lever arm is same and the beam
balance is exactly balanced, the mass is considered to be same. but it should be
notated that the two masses could be different because laws of lever and Newton
laws are completely different. I can defined my own definition of mass and in any
way it should not be true that the inertial mass from Newtons definition should
fit the mass from the laws of lever but from experiment to experiment, we have
found that the inertial masses equals the mass from the laws of lever. Therefore,
we use either beam balance or spring balance to measure the mass instead of using
Newton second laws because it requires some setup and calculation.

2.6 Length
Length is the space between any two points. Length is very intuitive and it is easy
to measure. We can use graduated scale to measure the length of any objects.
10 CHAPTER 2. FUNDAMENTAL CONCEPTS IN STATICS

2.7 Matter, Body, Mass and Particle

Misconceptions about mass: Mass is not the measure of amount of some

substances or anything which it accumulates. Even if it is the measure of amount
of some substances, it has not been proven yet.
Mass can be defined from Newton’s second laws of motion. From the equation of
second laws of motion, if mass increases for the same force, acceleration decreases
and vice versa which means that the mass is a imaginary number which represents
the body resistance to motion. By motion, here we are implying the acceleration
terms. Hence, it is worthwhile to define a new concept known as something called
matter and the term can be defined as a consequences of the Newton second laws
of motion.
Definition of matter: A matter is something that offer resistance to force and
thus therefore, something in which force can be applied.
Definition of body: Seperate portion of matter
Definition of mass: Mass can now be defined as the amount of matter contained
in the body which is consistent with Newton’s second laws of motion because
matter means resistance to force.
Definition of particle: Particles are matter whose shape and size can be ignored
in the case of motion. Earth can be considered as a particle even though the size
of earth is huge in the case of dealing with the motion in the Earths orbital. The
concepts of particle is established only to ignore the moments of force for saving
the laborious calculation and will be evident later in the chapter while studying
the moment of force.

2.8 Scalar and Vector quantities

Scalar does not care about the direction but the vector quantities care about the
direction. For example: we do not care about direction when we ask about the
distance between the two places but if you are going for a trip the direction as well
as magnitude is very important. Direction certainly has impact for you. Similarly,
force is a vector quantity which means that the direction of force is very important
in the sense that the effects of force depends on direction. By implying effects, i
means the effects of the direction of force on the body can be different for example
the direction of force may results an object to bend or rotate etc. which has its
own consequences.
2.9. FORCE 11

2.9 Force

When we imagine about force, the first things that came in our mind is the mus-
cular force from our hand or leg. But one should never forget that when it came
to ourselves, that is only one of the different kind of forces that acts under certain
cirucmstances i.e. forces has different forms depending on different circumstances.
The definition of force is given by Newton second laws of motion which states that
force is the agency that will set a body into acceleration. In practical, force is said
to impart motion but care should be taken because force only set up accelerative
motion not the uniform motion. Force has magnitude, direction and line of action
of force.

2.10 Effects of force

When a force is applied on to a body which is aggregration of matter and matter

is one in which force can be applied, it produces certain effects on the body. The
different effects on the body are described below:

• Acceleration: As defined in Newton’s second laws of motion

• Moment: Defined in Laws of lever and the conservation of energy
• Stress: Forms the basis for strength of materials

2.11 Moment of Force

The turning effects of force is termed as moment of force. About a fixed point, a
body under the influence of force has a tendency to rotate in circular motion. The
moment of force is the product of force times the perpendicular direction to the
point of rotation.
Thoughts: Why should the distance be perpendicular to the direction of force?
12 CHAPTER 2. FUNDAMENTAL CONCEPTS IN STATICS

Figure 2.1: Moment of force

Any force applied to an object AB pivoted at point A which means that point A
is fixed and the only motion allowed is circular motion about A. For a circular
motion, the radius representing the object and the force acting must always be
perpendicular since the tangent to the radius of the circle is always perpendiuclar
to its radius.

2.12 Circular motion and particles

A circular motion is also a kind of motion and any motions is the results of the
force. However, it should be notated that force acting at some distance from the
point of pivot forms the circular motion. Under the consideration of Newton’s
second laws of motion the assumptions was that the body is considered to be a
particle which means that no moment is acting. Hence, a particle can be defined
as those matter in which the force can be applied but the effect is not a turning
moments but a rectilinear motion only.
Note: Moment of force is responsible for a body to rotated about a fixed axis.
2.13. LAWS OF LEVER 13

2.13 Laws of lever

The laws of lever is based on the equality of moment i.e. the anticlockwise moment
must equal the clockwise moment if the body is not rotating.

Figure 2.2: Laws of lever

Mathematically,

F orce1 ∗ AC = F orce2 ∗ CB

2.14 Proof of Laws of lever

Before the proof of law one should be familiar with certain terminology:
• Definition: A explanation of mathematical meaning of words
• Proposition: Any statement which is regarded to be true and anything is only
regarded to be true if they are convinced.
• Lemma: A short proof of something which is regarded as true
• Theorem: A statement resulting from something like proposition etc.
Proposition:
14 CHAPTER 2. FUNDAMENTAL CONCEPTS IN STATICS

Figure 2.3: Simple lever system

This is self-evident and we can experiment with it. Since, there is no any law in
particular that explains about it, we have to start from this case where C represents
the center of gravity and the total weight of 2N acts on it.

Lemma:

Figure 2.4: Different forces lever system

Chapter 3

Forces at a point

Particles is generally considered to be a point and it is evident that particle does

not takes participation in rotation. Newtons works is based on the particles and
therefore, he does not discuss about the moment of force. A seperate laws are
required of which moment of law determines the condition of rotational equilibrium
for a body.

3.1 Line of action

The line AC which is parallel to the given forces and which starts from the point
of the application of force is known as the line of action of forces under which the
same forces applied in any points on the given line does not produce any changes
in the moment is known as the line of action of forces.

Figure 3.1: Lines of action of force

15
16 CHAPTER 3. FORCES AT A POINT

3.2 Stress in a body

Two forces are said to be at stress when they lies on the same line of action
of forces but opposite in direction at certain distance. The word stress implies
that the external forces tends to break them apart and that causes stress in the
materials.

Figure 3.2: Stress

At least two forces are required for a body to be at stress. for example: To apply
5N forces on a body, a force equals and opposite to that forces must be applied at
the line of action at some distance to stress the body.

3.3 Equilibrium of two forces acting at a point

Two forces are said to be in equilibrium if the two forces acts at a point in that
direction but the two forces are opposite.

3.4 Equilibrium under action of forces on beam

It was discussed above that two forces which have same line of action of forces
and when they acts opposite of each other at the given point are said to be in
equilibrium if same magnitude of force acts on the body. But under the beam
shown below, for solving the problem we use the following relationships:

∑
Fy = 0

Which implies that P + Q + R = 0

∑
Mc = 0
3.5. HOW IS IT POSSIBLE? 17

Figure 3.3: Forces on stationary beam

3.5 How is it possible?

In the above examples, it was written that P +Q+R = 0 is used for the calculation
of the reaction forces in the beams along with the laws of moment. The reader
must be very doubtful about the equation because the three forces acts completely
on different particles or the points and even though they act at different points it
seems as thought they are acting at the same point and are being in equilibrium
since we have already defined equilibrium exist only at a point. The reader must
ask himself Does the equation stands true or not and if true how does it happens?
18 CHAPTER 3. FORCES AT A POINT