How to interpret equations

[Strange]

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.

 

No. Force and mass cannot be equal. They are different things.

 

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.

 

This is close. As long as you remember that the magnitude for each have different units (because, as above, they are different things).

 

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)

 

True. But that is just stating one particular case and so is of no real value.

[swansont]

Again...I convey my point...

 

If a=1m/s2 in F=ma, we can write F=m...

 

 

No, we can't. Units matter.

[studiot]

 

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)

 

True. But that is just stating one particular case and so is of no real value.

 

 

 

Not true.

The fact of proportionality of the force is not contingent on the value of the acceleration, which is why we have an equation such that we have the force proportional to two independent quantities and which are multiplied together.

 

Any quantity A that is proportional to another quantity B and also proportional to a third quantity C and a fourth D and so on is given by the equation

 

A = k(B*C*D.....)

Edited June 8, 2015 by studiot

[Strange]

Fair enough. "Less value" would have been more appropriate.

[studiot]

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.

 

[Deepak Kapur]

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.

 

Hi Studiot,

 

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)

Edited June 9, 2015 by Deepak Kapur

[Strange]

Hi Studiot,

 

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

 

So, what meaning/meanings can be attributed to F=ma?

 

Maybe you could clarify what you find unsatisfactory with the explanations you have been given so far. Otherwise people will just repeat the same things...

[studiot]

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.

 

 

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

 

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

 

 

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

 

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.

Edited June 9, 2015 by studiot

[Deepak Kapur]

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.

WITH ALL THE DUE RESPECT,

 

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.

Edited June 9, 2015 by Deepak Kapur

[Strange]

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

 

How about:

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

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

 

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

1. The acceleration produced by a force is directly proportional to the magnitude of the force
2. The acceleration produced by a force is in the same direction as the net force
3. 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...

[Deepak Kapur]

 

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.'

[Strange]

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.'

 

Convoluted but accurate, as far as I can tell.

[studiot]

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?

[Strange]

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

 

Good catch!

[Deepak Kapur]

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.

[Strange]

'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. .

 

The problem with this wording (to my mind) is that it makes it sound as if force is a product of the acceleration. While there are cases where that is true, it is less obvious than the normal way of stating it.

 

 

More the mass more the force required. More the acceleration, more the force required

 

Apart from being grammatically odd this doesn't seem to add anything new. It would also be true if the force was proportional to some function such as the square of the mass. So it is too vague.

[studiot]

 

'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.

 

Yes this is just fine.

 

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

 

 

More the mass more the force required. More the acceleration, more the force required.

 

 

 

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.

[Deepak Kapur]

 

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?

[Strange]

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

 

It isn't. It is a variable.

[studiot]

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?

 

 

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?

Edited June 9, 2015 by studiot

[Deepak Kapur]

 

 

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....