Who is Right?

When I talk with my friends, somewhat the topic gets deviated from Physics to Philosophy. I am a lot used to relate physics with philosophy. But my friend is good at pure philosophy.

         

We were discussing about Relativity and the concept of reality. I said the Physical reality is not true. Everything we observe in our real life is not the absolute truth. But it is only true with respect to someone or something. The concept of absolute can never be reached.

         

The world of a blind will be completely different from the world of ours. So, what you believe to be true is only true with respect to your mind. Thus I argued nothing is a perfect one and No one is absolutely true. I said everything is relative.  

         

But he explained it in a different manner with pure psychology.

He said no one is correct and a perfect decision can never be made in any situation. He also gave an example. And I love that example.

         

Let us take a debate between two groups of people. One group is supporting for an idea and arguing that it is good. The other is opposing that idea by stating it as bad.   

Let say, both of the groups went to a common person to ask for a decision.

Now can anyone decide whether the idea is really good or bad as a common person?

But the condition is, “The decider should not be in either of the groups because he should be a common one”.

The answer is no. “The decision cannot be made by a common person”. The argument is as follows,

Let us take some number of people. In this total, a group is supporting an idea. The great thing is that, it also implies that the people who are not in the first group automatically allocated into the opposing group.

You can say, some of the people may be common, who supports for both 50-50.       
But think..

There is no use of the common people in this task. We need a decision. 

        When you need to take a decision, you don’t need a common person.

A common person is one who supports both groups 50-50 is moreover equivalent to a person who doesn’t support both of the groups. Simply they are useless in the debate. We don’t need to consider them.

Thus if you ask for a common person to make the decision, and suppose if he take a decision, "by the time he takes a decision, he will be allocated to either one of the groups". If the decision is to support, then he will be allocated to first group. Otherwise he will be classified to the second group. 
Thus he will be no more a common person. And his decision is useless, because he is on one side. 
The condition is that we need the decision from a common man.

So what is now? Again we are in a debate. 

It is always the ideas of one group will be against to the people in other group. And the common people are useless.

Thus we can come to the conclusion that "any decision can never be made as the truth".

Then what we think as the truth in our real life is “the idea of the majority ones”. The idea agreed by most of the people is considered to be the reality. Similar to the idea of the physical world. 
The world seen by most of the people was considered as the real and not the world of a blind or the world of snake (full of infrared things).

Thus the ultimate truth can never be achieved.  

Then who is right?

The Reason for the dot product in work done definition

It was defined the work as

W                =                Fext * d

You can see here that, there is no need of vector products here, because the displacement by the net external force will always be in the direction of the Net external force.  Then what is the problem?

The problem arises when the body is already in motion or already acted by an external force.

First we will take the case of most usual one i.e. pushing an object on Earth where the object is initially at rest.  

When you try to move an object in earth by pushing at an angle θ the object will move only in the horizontal direction.

Don’t think that Newton’s law is not valid here.

You may think that the net external force is not in the direction of the motion. But it is really in the direction of the motion.

What happens here is that the perpendicular component of the applied force would be canceled out by the Normal force from the ground.

Normal force is just the electrostatic repulsion forces between various objects which prevent one object move into another.

So, the net external force will only be in horizontal direction.

The problem of direction is not essential, if you again consider the work in terms of the net external force. But you cannot always consider the Normal force separately. 

We simply know that nothing is going into the Earth. So, all perpendicular components of the force should be canceled out.

It shows that the net external force is not important, but the component of the force along the direction of the motion is important.

Then,

W = Force along the direction of the motion * displacement

Now, we will go to the second case where the object itself initially moving at some velocity.   

Take an example of a projectile motion. 

When the object is thrown with an initial velocity, due to the net gravitational force acting downwards the projectile will take a parabolic path.

Though the projectile takes a curved path, you will consider only the displacement along the direction (vertical direction) of the net external force when you need to calculate the amount of work done. 

The effects in horizontal direction is not considered since there is no external force in that direction. 

It is used only the amount of work done in the direction of the force and that will only change the energy of the particle. Energy in other components of direction wouldn’t be affected.

Then,

W = Force* displacement along the direction of the force

For the sake of simplicity we just redefined the work as follows,

W = F*d*cos θ

Now this definition is suitable for all the cases. The angle  “θ” is defined from the directions of the force vector and the displacement vector by joining the tails of the both vectors.

Only to find the value of “cos θ”, we need the directions of Force vector and the displacement vector. And that is why, the work done is simply written using the vector notation as,

W = F⃑    . d⃑   = F*d*cos θ

Note: "F*d*cos θ" is only translated as  the dot product - F⃑    . d⃑   

and not F⃑    . d⃑   is translated as "F*d*cosθ". 

*There is a difference.

where “F” and “d” are respectively the magnitudes of the force and displacement vector. And the work done is just a magnitude. It can have either positive or negative values depending on the directions of force and displacement vector.

A simple analysis about why this formula is perfect as follows,

If an object is moved perpendicular to the direction of the force then the work done by that force on that direction is zero. The reasoning is simple,

“If I moved you, you will move only in the direction of my force or its component direction”. But you will never move in a direction perpendicular to my force. The perpendicular motion is independent from the force applied. The force will not be anyway responsible to the motion of the object in perpendicular direction.  

Don’t consider the example of doing work by placing a stone at your head and standing for a long time. With respect to Physics, it is not a work, because all the physics things defined for point particles. And you are not a point particle. 

Work

Everything in Physics was created just to explain the phenomenon in real life. Anybody can explain it any manner. But the explanation that satisfies most of the people will be considered as the good one.

          Dot product and cross product is one of them. It is used to be taken in such way that it already exists in Nature.

It is used to define the work done by a force with dot product and the torque of a rotating object using cross product.

  

But the most essential thing that is to be noted is that,

“Work is not defined from the dot product but the dot product only was defined from Work and vice versa the Torque”.

First we will give a look to “What is meant by Work”.

Work:

When an object is moved by an external force up to a distance “d”, some kind of change is happening in the motion of the body. The change can be described the change in the velocity of that object. But to measure this change, we need to make a relation of measurable quantities with this change.

It was noticed that, “the Change is high when the force acting on the object is high”

It can be written simply as

The change is proportional to the Net external force applied on the object.

Second, it can be observed that the change is high when the displacement is high. Here displacement refers to the displacement during the force acting on that object.

So,

The change is proportional to the displacement during the force on the object.

Now, to avoid these long statements Scientists made a very small statement using specific words,

The change is described by the word – W - Work [Energy]

Work and Energy are not different. They are distinguished only by the way we look at it.

And the force acting on the body is represented by “F” and the displacement during this force is “d”

W                α                Fext * d

Taking out the proportional constant to be one   [ask Why?]   

                   W                =                Fext * d

·       In this first equation, there is no vector symbol or dot product or cross product.

The role of direction comes into play only when you deal with multiple things.

Note: The proportionality constant comes when you deal with Gravitation is different from the proportionality constant comes here in the definition of Work and the Newton’s first law. 

Importance of the Newton’s first law

Discussion helps you to understand a concept better than thinking it one’s own self. I always like to study science with historical continuity which helps me to think in a different way. I got new friends in that journey of different way of scientific discussion. Giving and sharing improved my understanding of physics in a way completely different from text books.

          First I want to talk about the very basic Newton’s three laws.

Law means an abstract from the Nature. You cannot prove it but you can just observe. We don’t know the answer of why to these laws. It is given by the Nature to deduce the Nature.

          A law is something that is followed by Nature itself. And Newton gave us three laws that tell about the movement of objects in real life.

Newton’s first law states that,

          Every object in the universe continues to be in same state of rest or uniform motion until it is acted upon by an external force.

And the second law states that,

          The net external force acting on an object is proportional to change in momentum of that object.

          p – momentum = m*v

m – mass

v – velocity

                            

                                      Fext  = dp /dt

Don’t you think there is a waste here?

          The second law itself is going to give information about the first law as follows,

                  

          When Fext  = 0 it implies p – momentum is a constant.

If mass is constant then “v – velocity” is also a const. The second law itself gives that when there is no net external force acting on a body, the velocity of the object is going to be constant. The constant can be either zero or some finite velocity.

Then why do we need the first law as a separate statement?

Scientist never waste time by writing same thing in two different ways since science is the method of minimum laws. You can suspect the first law but the answer we know.

It has to be something different kind of information should be there in the first law.

         

Let see what it can be?

The answer is there in your bus travel. When you travel in bus near the window seat in constant velocity, you can see through the window, how trees, houses looks moving at constant velocity.

                   

Let assume that the bus window is too small so that you can only see through small holes. You can’t realize whether the bus is moving or the trees are moving.

         

When you suddenly stop, you can see trees and houses and all the things stops moving.

         

With respect to your point of vision, you see all things came to a

sudden halt or stop. But there is no force acting on those things. Then how did these came to a halt.

          If Nature follows only the second rule, then

Fext  = 0 then Velocity should be a constant. But here velocity is changing but without any external force. Does it mean Nature don’t follow Newton's second law?
         

But Newton is very clever. He solved this by simply arguing that, “It is second law. Nature should follow also the first law then only second law would be valid”.

         

          First law says that “No object would change its velocity by itself but will change only when it is acted by net external force”.

          Nature should follow this rule. So Newton formulated a new force called “Pseudo force”.

Pseudo forces are the forces made to explain non inertial reference frames.

He explained that Pseudo force made the trees and house and all the things to stop instantaneously.

          Now you can apply the second law to Pseudo force and it is perfectly applicable.

          Pseudo forces are not only present in the trees and outer environment but also in your bus. If there is an object with low friction with surface is there in your bus, when you accelerate you can see the object moves in the opposite direction to the acceleration. And this was explained by Pseudo forces.  

          Thus we understood the importance of the first law in Newton’s laws of motion.