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Deepak Kapur

Force and Mass

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Hi all,

 

F=ma

 

If a=1, F=m

 

How can force and mass be equated and become equal. They are different entities.

 

It' s same like saying wood=iron

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Hi all,

 

F=ma

 

If a=1, F=m

 

How can force and mass be equated and become equal. They are different entities.

 

It' s same like saying wood=iron

F=ma means "The amount of force is directly proportional to the amount of mass times the amount of acceleration."

 

In your scenario, the equal sign means "the amount of force is directly proportional to the amount of mass" not "force and mass are the same thing."

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In this and similar examples, you have to take care with the units. You have set a = 1 m/s/s or what ever units you are using.

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Hi all,

 

F=ma

 

If a=1, F=m

 

How can force and mass be equated and become equal. They are different entities.

 

It' s same like saying wood=iron

Setting a=1 doesn't get rid of its units of measurement. If a is measured in m/s/s, setting it to 1 means 1m/s/s.

 

Force is not a fundamental dimensional unit of measurement. the fundamental units are length, mass and time. Force and is a derived measurement. meaning that it is actually made up of a combination of fundamental dimensional units.

 

In the CGS system, the fundamental units are centimeters, grams and seconds.

 

In this system a is c/s/s, and force is measured in gc/s/s (grams x centimeters per second per second), called a dyne.

 

So F=ma in fundamental units is

 

[math] \frac{gc}{s^2}= g \left ( \frac{c}{s^2} \right )[/math]

 

By setting a=1, what you are actually doing is saying that the part in the parenthesis is equal to 1c/s/s.

 

Another way to look at it is that if you strictly say that c/s/s =1, it has to do so on both sides of the equation. Thus the c/s/s on the left(force) side of the equation must also go to 1 and you end up with

 

grams = grams.

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It' s same like saying wood=iron

Actually both wood and iron are made of protons, neutrons and electrons. Simply their configurations are different.

 

There is no two pieces of irons with equal structure (due to f.e. contamination).

and there is no two pieces of woods with equal structure.

They are just more or less similar, but never equal. Like finger prints.

 

Hi all,

 

F=ma

 

If a=1, F=m

 

How can force and mass be equated and become equal. They are different entities.

First of all, you should start from analysis of what acceleration and velocity is.

 

Velocity is change of position of measured object over time.

 

f.e. we measure object to be at locations:

at t=0 x=0

at t=1 x=10

at t=2 x=20

at t=3 x=30

 

We can subtract locations of object at different times

x(t1)-x(t0)

to receive distance object traveled (in meters).

If we will then divide it by t1-t0 (in seconds),

we will receive velocity (in meters per seconds).

 

v=(x(t1)-x(t0))/(t1-t0)

 

so position of object at time t is x(t)=x(0)+v*t = x(t0) + (x(t1)-x(t0))/(t1-t0) * t

 

Velocity is constant in this example. Thus acceleration is 0, and force is 0.

 

 

Acceleration can be calculated by taking two velocities at two different times:

Imagine measured data:

t=0 v=0

t=1 v=1

t=2 v=2

t=3 v=3

 

Velocity is increasing over time.

 

Acceleration is

a=(v(t1)-v(t0))/(t1-t0)

 

Velocities in meters/seconds divided by seconds, gives acceleration in meters/seconds^2.

 

If v(t1) is equal to v(t0), velocity is constant, and we have no acceleration.

 

Force in Newtons is mass in kilograms multiplied by acceleration in meters per seconds^2.

 

Momentum is p=m*v [kg*m/s]

 

So force will be also F=(p(t1)-p(t0))/(t1-t0)

Change of momentum over time.

Edited by Sensei

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F=ma means "The amount of force is directly proportional to the amount of mass times the amount of acceleration."

 

In your scenario, the equal sign means "the amount of force is directly proportional to the amount of mass" not "force and mass are the same thing."

 

I think here 'equal' means really 'equal' and not just 'proportional'

In this and similar examples, you have to take care with the units. You have set a = 1 m/s/s or what ever units you are using.

 

I take a similar example.

 

F=ma

 

Put a=3

 

F=3m

 

or

 

F=m+m+m

 

(i.e the force acting on a body = adding mass of a body to itself 3 times)

 

In other words, when this Force acts on a body, does the body's mass really become triple its previous mass?

Actually both wood and iron are made of protons, neutrons and electrons. Simply their configurations are different.

 

There is no two pieces of irons with equal structure (due to f.e. contamination).

and there is no two pieces of woods with equal structure.

They are just more or less similar, but never equal. Like finger prints.

 

 

First of all, you should start from analysis of what acceleration and velocity is.

 

Velocity is change of position of measured object over time.

 

f.e. we measure object to be at locations:

at t=0 x=0

at t=1 x=10

at t=2 x=20

at t=3 x=30

 

We can subtract locations of object at different times

x(t1)-x(t0)

to receive distance object traveled (in meters).

If we will then divide it by t1-t0 (in seconds),

we will receive velocity (in meters per seconds).

 

v=(x(t1)-x(t0))/(t1-t0)

 

so position of object at time t is x(t)=x(0)+v*t = x(t0) + (x(t1)-x(t0))/(t1-t0) * t

 

Velocity is constant in this example. Thus acceleration is 0, and force is 0.

 

 

Acceleration can be calculated by taking two velocities at two different times:

Imagine measured data:

t=0 v=0

t=1 v=1

t=2 v=2

t=3 v=3

 

Velocity is increasing over time.

 

Acceleration is

a=(v(t1)-v(t0))/(t1-t0)

 

Velocities in meters/seconds divided by seconds, gives acceleration in meters/seconds^2.

 

If v(t1) is equal to v(t0), velocity is constant, and we have no acceleration.

 

Force in Newtons is mass in kilograms multiplied by acceleration in meters per seconds^2.

 

Momentum is p=m*v [kg*m/s]

 

So force will be also F=(p(t1)-p(t0))/(t1-t0)

Change of momentum over time.

 

Thanks for the clarification.

 

 

Do you mean that in this example 'mass' and 'acceleration' interact with each other?

 

I think, 'mass' and 'acceleration' are properties/quantities of the same object/body.

 

Objects can interact, how can the quantities interact?

Edited by Deepak Kapur

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In other words, when this Force acts on a body, does the body's mass really become triple its previous mass?

No, the mass remains the same. What you do know in your example is that the numerical value of the force is three times the numerical value of the mass in the units you have chosen.

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Units units units. They're not just there for a laugh they are important. A measurement without units is completing useless. (Measurements of ratios excepted of course)

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...

I take a similar example.

 

F=ma

 

Put a=3

 

F=3m

 

or

 

F=m+m+m

 

(i.e the force acting on a body = adding mass of a body to itself 3 times)

 

In other words, when this Force acts on a body, does the body's mass really become triple its previous mass?

...

If you kick a ball, you apply a force to it. That accelerates it, and it ends up moving at some speed. The formula F=ma shows the relationship between the force and the acceleration - and the mass of that ball.

 

If you kick the ball with 3 times the original force, it'll get 3 times the original acceleration. Makes sense doesn't it? Kick the ball harder, it'll go faster (and further).

 

If you kick another ball that has 3 times the mass of the first ball, you'll have to kick it with 3 times the original force, to accelerate it as much as the first ball with the first kick. Makes sense doesn't it? Kick a heavier ball, and it'll need a harder kick to accelerate as much as a lighter ball.

 

If you want to kick a ball with 3 times the mass of the first ball, and you want to give it 3 times the acceleration that you gave that first ball with that first kick, you'll need to kick it 9 times as hard as the first kick. (That's the a x m coming into it).

 

 

Maybe to give you a totally different (or not?) example:

 

Say you work at a shop where you get paid $5.00 an hour and you work 8 hours a day. What do you earn in a day?

 

Days pay = Hourly rate x Hours worked per day

 

Days pay = $5.00 x 8 = $40.00

 

Now, that's not saying that the concept "day" equals the concept of "dollar". The hourly rate of 5 isn't making the hours you work in a day 40 ... it's still 8. The formula is just relating the values.

 

Someone earning $10 dollars an hour, would only have to work 4 hours to earn as much. Someone earning $2.50 an hour would have to work 16 hours, to earn as much.

 

The unit analysis works out, too.

Days pay unit is dollars per day; Hour rate unit is dollars per hour; Hours worked per day = hours per day; so ...

 

dollars per day = dollars per hour x hours per day

dollars per day = (dollars x hours) per (hour x day)

dollars per day = (dollars x hours) per (hour x day)

dollars per day = dollars per day

 

... the units always need to balance; try that with F=ma.

Edited by pzkpfw

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If you kick a ball, you apply a force to it. That accelerates it, and it ends up moving at some speed. The formula F=ma shows the relationship between the force and the acceleration - and the mass of that ball.

 

If you kick the ball with 3 times the original force, it'll get 3 times the original acceleration. Makes sense doesn't it? Kick the ball harder, it'll go faster (and further).

 

If you kick another ball that has 3 times the mass of the first ball, you'll have to kick it with 3 times the original force, to accelerate it as much as the first ball with the first kick. Makes sense doesn't it? Kick a heavier ball, and it'll need a harder kick to accelerate as much as a lighter ball.

 

If you want to kick a ball with 3 times the mass of the first ball, and you want to give it 3 times the acceleration that you gave that first ball with that first kick, you'll need to kick it 9 times as hard as the first kick. (That's the a x m coming into it).

 

 

Maybe to give you a totally different (or not?) example:

 

Say you work at a shop where you get paid $5.00 an hour and you work 8 hours a day. What do you earn in a day?

 

Days pay = Hourly rate x Hours worked per day

 

Days pay = $5.00 x 8 = $40.00

 

Now, that's not saying that the concept "day" equals the concept of "dollar". The hourly rate of 5 isn't making the hours you work in a day 40 ... it's still 8. The formula is just relating the values.

 

Someone earning $10 dollars an hour, would only have to work 4 hours to earn as much. Someone earning $2.50 an hour would have to work 16 hours, to earn as much.

 

The unit analysis works out, too.

Days pay unit is dollars per day; Hour rate unit is dollars per hour; Hours worked per day = hours per day; so ...

 

dollars per day = dollars per hour x hours per day

dollars per day = (dollars x hours) per (hour x day)

dollars per day = (dollars x hours) per (hour x day)

dollars per day = dollars per day

 

... the units always need to balance; try that with F=ma.

 

I know what I am saying is annoying because I also know what the 'correct' interpretation is.

 

I just want to say that do we have to cherry pick our conclusions from any equation, when it offers other possibility/possibilities?

 

F=ma very well conveys the idea that Force is proportional to mass,as pointed out by Delta 1212. Doesn't it mean, greater the force, greater the mass? Why?

 

I don't get the idea behind 'units' because they can be set in different ways and in every system of unit, the idea that 'force is proportional to mass' will be there.

 

If you say its the numerical value of force that is proportional to numerical value of mass, again it means greater the force greater the mass.

 

Plz take pains to see the equation from my point of view ( even if it is wrong).

 

 

In the example of wages, it is the 'pay' that is proportional to the 'no. of hours worked'. This is different from F=ma situation.

Edited by Deepak Kapur

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What is the mass of an object when there are no resultant forces?

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I know what I am saying is annoying because I also know what the 'correct' interpretation is.

 

I just want to say that do we have to cherry pick our conclusions from any equation, when it offers other possibility/possibilities?

 

F=ma very well conveys the idea that Force is proportional to mass,as pointed out by Delta 1212. Doesn't it mean, greater the force, greater the mass? Why?

That all depends on context. Unless you are talking relativity, kicking a ball harder, doesn't give it more mass, it gives it more acceleration. It's (your green bit) more the reverse, the greater the mass, the greater the force needed (to give the same acceleration). You're confusing yourself by picking a parameter to change, without thinking about what that change really means.

 

I don't get the idea behind 'units' because they can be set in different ways and in every system of unit, the idea that 'force is proportional to mass' will be there.

Only if the units make sense. Force has certain units, mass has certain units and acceleration has certain units. It doesn't matter which set of units you are using (e.g. slugs or kilograms) as long as they are all consistent. It's bad to use metric for one thing and imperial for another; it's even worse to measure Force in tulips and mass in whales per second. The units have to make sense for the formula to make sense.

 

If you say its the numerical value of force that is proportional to numerical value of mass, again it means greater the force greater the mass.

 

Plz take pains to see the equation from my point of view ( even if it is wrong).

Well, in a way it's true. If the acceleration stays the same, a greater force will kick a ball of greater mass.

 

That doesn't mean the force is creating or changing the mass.

 

If you kick a ball with some force, you will accelerate it by some amount. If you kick the ball with more force, you won't change it's mass - you'll give it more acceleration.

 

In your example you arbitrarily chose to triple the acceleration. For F=ma to still balance, that would mean kicking a less-mass ball with the same force, or a same-mass ball with more force.

 

Edit: and it's not "... the numerical value of force that is proportional to numerical value of mass", it is "... the numerical value of force that is proportional to numerical value of acceleration x mass". You can't just ignore one parameter. If you choose to keep acceleration fixed, a greater force will accelerate a greater mass. Like kicking a heavier ball, harder, to get the same acceleration. The harder kick is not creating more mass - kick a ball of the same mass, with greater force won't give the same acceleration. You can't have your cake and eat it too.

 

In the example of wages, it is the 'pay' that is proportional to the 'no. of hours worked'. This is different from F=ma situation.

 

No. The example was pay per day, and that's proportional to hourly rate and hours worked per day.

 

It's a direct comparison.

Edited by pzkpfw

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That all depends on context. Unless you are talking relativity, kicking a ball harder, doesn't give it more mass, it gives it more acceleration. It's (your green bit) more the reverse, the greater the mass, the greater the force needed (to give the same acceleration). You're confusing yourself by picking a parameter to change, without thinking about what that change really means.

 

 

Only if the units make sense. Force has certain units, mass has certain units and acceleration has certain units. It doesn't matter which set of units you are using (e.g. slugs or kilograms) as long as they are all consistent. It's bad to use metric for one thing and imperial for another; it's even worse to measure Force in tulips and mass in whales per second. The units have to make sense for the formula to make sense.

 

 

Well, in a way it's true. If the acceleration stays the same, a greater force will kick a ball of greater mass.

 

That doesn't mean the force is creating or changing the mass.

 

If you kick a ball with some force, you will accelerate it by some amount. If you kick the ball with more force, you won't change it's mass - you'll give it more acceleration.

 

In your example you arbitrarily chose to triple the acceleration. For F=ma to still balance, that would mean kicking a less-mass ball with the same force, or a same-mass ball with more force.

 

Edit: and it's not "... the numerical value of force that is proportional to numerical value of mass", it is "... the numerical value of force that is proportional to numerical value of acceleration x mass". You can't just ignore one parameter. If you choose to keep acceleration fixed, a greater force will accelerate a greater mass. Like kicking a heavier ball, harder, to get the same acceleration. The harder kick is not creating more mass - kick a ball of the same mass, with greater force won't give the same acceleration. You can't have your cake and eat it too.

 

 

 

No. The example was pay per day, and that's proportional to hourly rate and hours worked per day.

 

It's a direct comparison.

Thanks for elaborate reply.

 

I don't want to argue, I just want to clarify things :)

 

1. Suppose I apply such a huge force to a ball that its speed approaches the speed of light. In this case It would mean 'more the force, more the mass'.

 

I know you would tell me that I am confusing things and a separate equation is needed for such a scenario.

 

 

My 2nd point is as follows.......

 

 

2. If we need a second equation this time, does it mean that,

 

'an equation does not only describe nature but it describes our view point (thoughts, mind) as well?'

 

Thanks.

 

 

BTW, I have been banned by 'Physics Forums' over and over again . I tried different 'avatars' but they found it every time and closed my account.

 

 

So, don't ban me. It's they who directed me here.

Edited by Deepak Kapur

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So, don't ban me. It's they who directed me here.

If you obey the rules then you won't get banned. Principally, be polite, ask questions and take in what people say. Don't just soapbox and disregard all of known physics.

 

I see where you are coming from with your question, but i) what is the mass of an object when it is not acted upon by any forces? ii) take care with your units, this seems to be one issue.

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Deepak Kapur, do you saw Newton's cradle?

 

 

http://en.wikipedia.org/wiki/Newton's_cradle

 

It costs less than $10 in western countries, and allows visualizing conservation of momentum (while interaction) between objects with the same mass, or conservation of momentum between objects with different masses, etc. etc.

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I numbered your questions for ease of answering them.

 

F=ma very well conveys the idea that Force is proportional to mass,as pointed out by Delta 1212.

1. Doesn't it mean, greater the force, greater the mass? Why?

 

I don't get the idea behind 'units' because they can be set in different ways and in every system of unit,

2. the idea that 'force is proportional to mass' will be there.

 

If you say its the numerical value of force that is proportional to numerical value of mass,

3. again it means greater the force greater the mass.

 

1. No. What is means is that if you have two masses, the larger one requires more force to accelerate, assuming they accelerate at equal rates.

 

2. Your units should always be consistent, as was already pointed out. Both sides of the equation should use units from the same measuring system. This doesn't change the inherent relationship between the values themselves.

 

3. No, it means the greater the mass, the greater the force for equal acceleration. As has already been pointed out, Force is a derived unit, not an inherent one. It is possible (in theory at least) for an object with substantial mass to have an F of 0. Mass determines force, force does not determine mass. Force can be used to calculate mass, but that's a different kettle of fish all together.

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BTW, I have been banned by 'Physics Forums' over and over again . I tried different 'avatars' but they found it every time and closed my account.

 

 

So, don't ban me. It's they who directed me here.

!

Moderator Note

What happened elsewhere doesn't matter in that you start here with a clean slate. Probably better not to have not brought it up; it's entirely off-topic. Follow the rules and things will be fine.

 

But, as an aside and fair warning: "I know what I am saying is annoying because I also know what the 'correct' interpretation is." sounds awfully troll-ish.

 

Please don't respond to this modnote

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