Deepak Kapur

22 hours ago, exchemist said:

You can never make such an assumption, so this scenario can never arise. 

This is because It is never possible to prove a scientific theory true. So we can never state with certainty that there is no more to discover.

 

1. But, if ToE is formulated...won't it mean that we have reached something, which has to be taken as a 'given'.

2. If there is always something more to discover, doesn't it mean that 'the never ending exploration' is to be taken as a 'given'?

Lets consider a line of length 1m.

If space is continuous, it means there is an infinity of points in this line.

Now, size of each point=1/infinity=0

This implies that our line is of zero size because its constituents are all of zero size.

How to resolve this contradiction?

You can detect single photons and have systems where at most one photon is present. I don't see how continuity applies.

I want to say that in a ray of light there is no space between the photons that make up the ray.....so, isn't light ray continuous?

Science says that light is not continuous but discrete, as it comes in small packets called 'quanta'

I want to ask....

Is there any space between the quanta of light? If not, isn't this a continuity in its own right?

There's always more to learn.Whether you actually want to learn more is your own choice.

Does it mean that concepts like 'Fundamental Reality', Fundamental Truth'......rather 'anything fundamental' are logically impossible because such concepts also lead to further questions?

Can the enquiring spirit in us be ever quenched?

e.g.

1. Suppose, science finds the fundamental particle...next question can be...What mechanism caused this fundamental particle?....or.....How it came about? If someone says, it has been always there...one can ask...What is the mechanism through which something can be eternal? and so on....

2. Suppose, someone finds God and says that He/She/It exists eternally/necessarily...next question can be...Why only He is a necessarily existing creature and not some other one? or What mechanism leads to necessary existence? and so on....

In a nutshell, can questions ever end? Any thoughts, not necessarily serious ones....

 

 

Why do I get the impression you are trying to catch people out, rather than gain understanding?

 

By itself the question in the above quote is perfectly reasonable and understandable.

Indeed I considered mentioning this link to where mass is used as the constant of proportionality.

 

However as part of the too-clever complete post above, all it shows is that you are not thinking because one part contradicts the other.

 

If applied force is to be proportional to mass, then it must be allowable for mass to vary.

 

So mass cannot be a constant.

 

If we we are going to hold mass constant and vary the acceleration, then we can say the applied force = a constant mass times the variable acceleration (in suitable units)

 

So in those circumstances we can say that mass is the 'constant of proportionality'.

 

And yes you will find plenty of references to this as it is a way of introducing inertia or inertial mass and it is one of the great unifying triumphs of Physics that we have been able to show that the quantity 'mass' as defined in Newton's second law is the same as the quantity 'mass' as defined in Newton's Law of Gravitation.

 

This is also an equation of the form

 

[math]F = G\frac{{{M_1}{M_2}}}{{{r^2}}}[/math]

 

Would you say mass is the 'constant of proportionality here, or would you say something more complicated is going on?

I think the situation is more complex, as it shows the 'interaction' between two masses and the force that 'this interaction' creates....

 

Yes this is just fine.

 

It actually tells us what you have written after. So that part is not really needed.

 

 

It actually tells us even more than this because it says that even if a body has mass, the force applied to it is zero, if the acceleration is zero.

(Which, of course, is what we want)

And of course we don't have any accelerating bodies with zero mass in classical physics to bother with thoughts of zero mass.

 

This means that there are no additive constants in the equation.

So....you find it okay???

Well, i wanted to convey something like this only from the beginning...that force is proportional to mass..

But....

If F is proportional to mass, then why m is called the constant of proportinality in the equation F=ma?

No it is still not correct.

 

It is not correct becasue it starts with the word 'when'

 

This demonstrates that my efforts have still not been understood.

 

The proportionality of the (magnitude) of the force is totally independent of the acceleration.

 

So it is true that "when an object moves with constant acceleration....etc"

 

BUT

 

It is also true that "when an object does not move with constant acceleration....etc"

 

So what is the point of the half-a-statement?

You can reprimand me even more for what i am going to write below....but do explain why it is wrong...

'Force acting on a body is directly proportional to the mass of the body and also is directly proportional to the acceleration of the body. More the mass more the force required. More the acceleration, more the force required.

So, F=kma....k being a constant of proportionality.

 

How about:

(http://www.physicsclassroom.com/class/newtlaws/Lesson-3/Newton-s-Second-Law)

 

Is that one sentence too complex? We can break it down:

• The acceleration produced by a force is directly proportional to the magnitude of the force
• The acceleration produced by a force is in the same direction as the net force
• The acceleration produced by a force is inversely proportional to the mass of the object.

OK?

 

Actually, point 2 is only covered if you use vector notation in the equation...

Why not...

'When an object moves with constant acceleration, the magnitude of the force acting on it is directly proportional to the mass of the body. If we increase the mass keeping acceleration constant, the force also has to be increased proportinately to maintain that particular constant acceleration.'

I would more-or-less take that as the definition of a force

 

[math]\frac{dp}{dt} = F[/math].

 

Why add some constant here to make the definition more complicated?

Then...i think....it shouldnt be called a LAW..

Why didnt Newton use proportionality for this because Studiot tells me that proportionality was much prevalent those days than the concept of an equation...

 

How about:

(http://www.physicsclassroom.com/class/newtlaws/Lesson-3/Newton-s-Second-Law)

 

It is "equal" when you use a system of units that makes the constants of proportionality equal to 1.

Does it mean there is really no difference between proportinality and equality....its just a matter of convenience and perspective?

Good Morning Deepak,

 

What did you make of my post# 28. It was quite short.

 

But you have not mentioned anything about it, just repeated your earlier list of options.

 

 

Post#28 did indeed explain what was wrong, but perhaps as it was also short, it was too short.

 

It is difficult to get the length of answer right.

 

Asking questions to enable understanding is good.

But you need to ask questions about what other people as thinking and saying as well as what you are thinking.

Perhaps they can see something you haven't thought of?

 

So asking

 

 

Is just fine.

Further, and unlike some here, I am willing to discuss equations in English as well as maths.

So let's do that.

 

F = ma is a common modern statement of Newton's Second Law off Motion.

 

Newton himself did not state it this way.

In his day he (people) usually thought in terms of proportion, not equations.

Equation theory was nor really developed then, like it is nowadays.

 

Today discussion of proportion has nearly fallen into disuse, in favour of using equations, which is a pity becasue proportion is a powerful tool that can be easier to use.

 

Enough background waffle, the title of your thread is equations in general and since this subject is important for lots of equations I will use another example and then return to Newton.

Let us go back another two thousand years to Archimedes and the principle of the (simple) lever.

 

Two quite independent physical quantities determine how much turning effect or moment you can generate with a lever. Let us call this moment M.

 

You can vary the lever arm or distance from the pivot. Let us call this distance d

 

You can vary the force applied at the end of the lever. Let us call this force P (to keep it separate from other equations).

 

The key point in my post#28 is that you can vary these two quantities quite independently.

 

Now the longer the lever the greater the genrated moment or M is directly proportional to the length of the lever arm, d

 

That is M = k₁d

 

But also

 

The harder you push or pull with the same length of lever, the greater the moment.

 

That is M = k₂P

 

So we can achieve the any given value of M by changing the value of P and keeping d constant

 

or by

 

changing the value of d and keeping P constant.

 

In this situation the equation for M is

 

M = k₁k₂Pd

 

and we combine the two separate constants of proportionality into a single one and adjust the units of P and d so that k₁k₂ = 1

 

So now can you tell me why I said in my post#28 that your option 3 was wrong?

 

 

As added value, and to show how powerful the idea of proportionality is, think about this.

 

The kinetic energy of a moving body is

 

Directly proportional to the mass and also directly proportional to the square of the velocity.

 

A note on terminology.

 

Directly proportional means 'multiplied by'

 

Inversely proportional to means 'divided by'

 

But you can also have proportional to the sine of something or even the square of the sine of something, as in electrical theory.

You havent explained in SIMPLE ENGLISH ( 2 or 3 sentences) the meaning of F=ma.

and...

You havent explained in SIMPLE ENGLISH ( 2 or 3 sentences) why options 2 and 3 dont follow. ( even when magnitude of force and mass is same)

A good teacher is one who STOOPS to the level of the student, to make him understand things...so...plz do that....and dont simply say that my optoons 2 and 3 are wrong.

I myself know they are wrong ..... but why..... ( AGAIN, SIMPLE ENGLISH PLEASE)

I am sorry...THIS MUST BE REALLY PAIN & GRIEF FOR YOU.

One more thing...i fully understand what you are saying in post 28 and 32.

Newton's second law states (roughly),

The rate of change of momentum of a body is equal to the force acting on the body and is in the same direction....

Why 'equal to' and not 'proportional to'

In various other formulas we use 'proportional to' and not 'equal to'.

What's the difference?

Hi Strange,

 

This is the problem with Deepak trying to force his 'list' of views on us, instead of listening to the many who have tried to tell him the same truth.

 

I am here, again (not to annoy you...)

1. So, what meaning/meanings can be attributed to F=ma? ( IN SIMPLE ENGLISH )

And...

2. plz explain how the following are wrong ( see, i am not forcing anything, just trying to understand..)

(2.If a body moves with an acceleration of 1m/s2, then the magnitude of the force acting on the body is equal to the magnitude of the mass of the body.

3.If a body moves with an acceleration of 1m/s2, then the force acting on the body is proportionl to the mass of the body. (as Delta 1212 said in post 9)

Suppose, in F=ma

m=1kg and a=1m/s2.....then....F=1kgm/s2

m=2kg and a=1m/s2.....then....F=2kgm/s2

m=3kg and f=1m/s2.....then....F=3kgm/s2

So aren't.... 2 and 3 ....true above..

i.e the 'magnitude' of force is equal/and proportional to the 'magnitude' of mass???

( again, no enforcement of anything)

You are wasting my time and yours since you are not makeing the effort to follow what others are telling you.

 

The answer to your rephrased question is

 

 

4)Something else.

 

None of the others are actually true.

Ok, sorry...dont get annoyed ( all of you are doing a philanthropic task of spreading scientific temper...so why to annoy you people..)

I will not ask what something else is ( since you feel annoyed)

Thanks for your sincere efforts.

3. You don't know how to multiply units.

You have line with length a=3 m (in axis x)

it's straight line.

You have another line with length b=2 m (in axis z)

it's also straight line, perpendicular to first line.

m*m=m^2

Meter * meter (distance unit) = meter square (area unit)

3m * 2m = 6m^2

Then if you add yet another dimension, c=4m, axis in y:

m*m*m=m^3

Meter * meter * meter (distance unit) = meter cubic (volume unit)

3m * 2m * 4m = 6m^2 * 4m = 24m^3

Actually your room has 3rd dimension- height.

So you can actually calculate volume of your room. And also tell us how much air is there.

From it you can calculate amount of Nitrogen, amount of Oxygen, amount of CO₂, Krypton, Neon, etc.

I know all of this...anyway thanks....

My point was about repeated addition of dimensions/units...It has been explained nicely already...

It means that you have written an invalid equation.

 

Several have told you this, besides me.

 

The valid physics equation is F = ma.

 

you said (wrongly) a =1

 

acceleration can never ever be 1 in any system. of units

 

a can be 1 m/sc²

 

then F = m times 1m/sc²

 

is a valid statement.

If a body moves with a=1m/s2, then in the equation F=ma, which of the following meanings are conveyed...(points 1 to 5 of the previous post)

1. If a body moves with an acceleration of 1m/s2, then the force acting on the body is equal to the mass of the body.

2.If a body moves with an acceleration of 1m/s2, then the magnitude of the force acting on the body is equal to the magnitude of the mass of the body.

3.If a body moves with an acceleration of 1m/s2, then the force acting on the body is proportionl to the mass of the body. (as Delta 1212 said in post 9)

4.Something else.

5.Nothing.

Good morning Deepak, I really thought you had cracked this issue with your earlier thread about basically the same thing, where you answered Delta1212

 

 

But you don't seem to have been back to that one.

 

 

The point is that equations such as F = ma need all the variables to be there to make sense in the physical world because they have units or dimensions.

 

So whilst in mathematics we can write 6 = 3 * 2 and be OK, in physics we must ask

 

6 What? 3 What? 2 What?

 

In the above equation we have

 

a units of force = b units of mass times c units of acceleration

 

If we set b or c equal to 1 (as you have done in both these threads) we cannot just drop that physical quantity out of the equation.

 

the equation now becomes

 

a units of force = b units of mass times 1 unit of acceleration

 

so, whilst the number as might be equal to b in mathematics,

 

F is never equal to m in Physics

 

One further consequence is that nowadays units are arranged so that

 

If b = c =1 then a = 1

 

So 1 unit of mass times one unit of acceleration gives 1 unit of compatible force units.

It was not always so as Strange has pointed out.

I think I have not been able to convey my point...I totally agree with what you have said....but, I want to ask about the physical significance of this equation....

Again...I convey my point...

If a=1m/s2 in F=ma, we can write F=m...then, which of the following meanings are conveyed...

1. If a body moves with an acceleration of 1m/s2, then the force acting on the body is equal to the mass of the body.

2.If a body moves with an acceleration of 1m/s2, then the magnitude of the force acting on the body is equal to the magnitude of the mass of the body.

3.If a body moves with an acceleration of 1m/s2, then the force acting on the body is proportionl to the mass of the body. (as Delta 1212 said in post 9)

4.Something else.

5.Nothing.

Plz help

E=m has no physical meaning. They are not equal. They do not have the same units.

 

E=mc^2 has a meaning. Mass is a form of energy.

 

 

There are some theoretical folks who set c = 1 and ignore units, but they have had years of training to do it right. Plus, they are not doing any numerical calculations. For the rest of us, c ≠ 1

I am not talking about calculations....

What is the 'physical' meaning of E=m here,

E is equal to m....E is equivalent to m.....E is proportional to m....or something else....or no meaning at all...

It's a bit like saying that a size 5 shoe is the same as a size 5 mango.

Does this actually mean anything?

F=ma and all the various equivalent ways of writing that simply means that the acceleration that an object undergoes is directly proportionate to the force applied to it and inversely proportionate to the mass of the object.

 

It's a statement about proportional relationships, nothing else. If you set a=1 then "F=m" simply means that the force required to achieve that acceleration is proportionate to the mass. If the mass goes up, the force must go up by the same ratio. If the mass goes down, the force goes down.

If a=5, F=5m.....then also, what you said applies?

F=ma and all the various equivalent ways of writing that simply means that the acceleration that an object undergoes is directly proportionate to the force applied to it and inversely proportionate to the mass of the object.

It's a statement about proportional relationships, nothing else. If you set a=1 then "F=m" simply means that the force required to achieve that acceleration is proportionate to the mass. If the mass goes up, the force must go up by the same ratio. If the mass goes down, the force goes down.

Plz don't get irritated as I have to ask more...

1. Explain E=m also, it seems to have a different meaning than F=m.

2. If a is directly proportional to the force and inversely proportional to mass, why don't we write

a=kF/m, k= constant of proportionality???

Now, its 3 am in the morning/night here and I have to sleep...Gud night...will read responses tomorrow/today morning..

This forum seems to be better than PhysicsForums even....

 

 

It doesn't mean anything. You have units that must be used. F=ma, even when numerically the value of a is 1.

 

1 has to remain 1 regardless of units. What happens if you wanted to use cm?

Plz explain..

In E=mc2, if c=1, we get E=m and this 'means'something...so, why does F=m does not mean anything?

You are right, they are not the same thing, but the numbers are the same.

It's a bit like saying that a size 5 shoe is the same as a size 5 mango.

So, what does F=m mean in this case?

F=ma,

If I put a=1m/s2, F=m

Does it mean that when an object moves with an acceleration of 1m/s2, it's force becomes equals to its mass?

( sounds utterly absurd, how can force become equal to mass, when they are completely different entities/concepts. It is like saying mango has become equal to a shoe...)