# How to interpret equations

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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...)

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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.

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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?

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

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?

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Well for a start the force is not its force.

The force is the external force required to accelerate it at 1m/sc2.

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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?

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so, why does F=m does not mean anything?

Because it doesn't. Nor is it a correct equation, since you deliberately missed something out.

What do you think that might be?

Edited by studiot

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The short answer is that the units need to work out as well.

1 Newton = 1 kg * 1 m/s2

or

It takes a Newton of force to accelerate a kilogram of mass at a meter per second2.

http://en.wikipedia.org/wiki/Newton_%28unit%29

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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.

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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....

Edited by Deepak Kapur

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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?

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

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

Why is that any more concerning with a = 1 m/s/s than, say, a = 0.5 m/s/s and getting F = 0.5 m ? (The mix of m for mass and m for metre is odd here. Sorry.)

The formula F=ma relates Force on one side to mass and acceleration on the other. What's extra mystifying about the case where any one of those values happens to be 1?

(

I know I'm not answering your question here, I'm more getting at the meta-aspect of it; why is that one case worrying you?

)

Perhaps what this really shows, is the beauty of having a decent (e.g. S.I.) set of Units that makes things consistent and relatable.

(e.g. Look at pounds vs slugs.)

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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?

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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???

You can write that, if it is acceleration you are calculating. (And k = 0.)

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

Again, you're ignoring units.

Mass m has unit kg,

Energy E has unit J = Joule = kg*m^2/s^2

and force F has unit N = Newton = kg*m/s^2

You can't just assign F=m, because these variables have different units, and there will be mismatch of units between sides of equation.

there is still acceleration there, but normalized to 1.

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???

I don't understand..

That k would have to have value of 1, no?

Otherwise old equation would not be satisfied, no?

Then why to introduce constant, that's always 1, in the first place.. ?

You can write that, if it is acceleration you are calculating. (And k = 0.)

If k will be 0, then a=0, or I am missing something.. ?

Edited by Sensei

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I don't understand..

That k would have to have value of 1, no?

Otherwise old equation would not be satisfied, no?

Then why to introduce constant, that's always 1, in the first place.. ?

It might not be 1; it depends what units you are using. If you measure weight in pounds, force in newtons and acceleration in furlongs per fortnight per hour then ... [working out the value of k is left as an exercise for the reader].

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...however....I will think over this..

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.

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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...

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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...

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.

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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.

Hi there,

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.

Does the same thing apply to F=m, Why...why not...?...plz take pains to explain.. Edited by Deepak Kapur

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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.

Edited by studiot

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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.

Ok, forget about the notations at the moment...

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.

Edited by Deepak Kapur

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

4)Something else.

None of the others are actually true.

Edited by studiot

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

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)

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The 1 is a coefficient.

That is a simple number, like 2,3, 4 etc.

so if we have 2kg of mass the 2 is a coefficient (of mass)

So if we have an acceleration coefficient of 4 and a mass of 2kg the equation says that

(The coefficient of force) x Force = {(The coefficient of mass) times mass} times {(The coefficient of acceleration) times acceleration}

So the coefficient of force is 2 x 4 = 8

But the force is 8 Newtons.

Does this make it any clearer?

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