# Defining Force

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Issac Newton not only introduced the concepts of velocity and acceleration, which can be measured by measuring distances and time, but also introduced the concepts of mass and force. So, technically, is the oldest equation in Physics. However, putting the definition of mass across, the other day a friend asked how did Newton know that exactly , and why did he not just define the force to be . So I have made this thread to see what others think.

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#2

(Original post by

Issac Newton not only introduced the concepts of velocity and acceleration, which can be measured by measuring distances and time, but also introduced the concepts of mass and force. So, technically, is the oldest equation in Physics. However, putting the definition of mass across, the other day a friend asked how did Newton know that exactly , and why did he not just define the force to be . So I have made this thread to see what others think.

**Absent Agent**)Issac Newton not only introduced the concepts of velocity and acceleration, which can be measured by measuring distances and time, but also introduced the concepts of mass and force. So, technically, is the oldest equation in Physics. However, putting the definition of mass across, the other day a friend asked how did Newton know that exactly , and why did he not just define the force to be . So I have made this thread to see what others think.

Isaac Newton did not come out with .

The modern

*F=ma*form of Newton's second law nowhere occurs in any edition of the

*Principia*even though he had seen his second law formulated in this way in print during the interval between the second and third editions in Jacob Hermann's

*Phoronomia*of 1716. Instead, it has the following formulation in all three editions:

*A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed.*In the body of the

*Principia*this law is applied both to discrete cases, in which an instantaneous impulse such as from impact is effecting the change in motion, and to continuously acting cases, such as the change in motion in the continuous deceleration of a body moving in a resisting medium. Newton thus appears to have intended his second law to be neutral between discrete forces (that is, what we now call impulses) and continuous forces. (His stating the law in terms of proportions rather than equality bypasses what seems to us an inconsistency of units in treating the law as neutral between these two.)

The above paragraph is taken from https://plato.stanford.edu/entries/n...pia/#NewLawMot

If I don’t remember wrongly,

*F = ma*is from Euler.

https://en.wikipedia.org/wiki/Euler%27s_laws_of_motion

Hope it helps.

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(Original post by

Isaac Newton did not come out with .

The modern

The above paragraph is taken from https://plato.stanford.edu/entries/n...pia/#NewLawMot

If I don’t remember wrongly,

https://en.wikipedia.org/wiki/Euler%27s_laws_of_motion

Hope it helps.

**Eimmanuel**)Isaac Newton did not come out with .

The modern

*F=ma*form of Newton's second law nowhere occurs in any edition of the*Principia*even though he had seen his second law formulated in this way in print during the interval between the second and third editions in Jacob Hermann's*Phoronomia*of 1716. Instead, it has the following formulation in all three editions:*A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed.*In the body of the*Principia*this law is applied both to discrete cases, in which an instantaneous impulse such as from impact is effecting the change in motion, and to continuously acting cases, such as the change in motion in the continuous deceleration of a body moving in a resisting medium. Newton thus appears to have intended his second law to be neutral between discrete forces (that is, what we now call impulses) and continuous forces. (His stating the law in terms of proportions rather than equality bypasses what seems to us an inconsistency of units in treating the law as neutral between these two.)The above paragraph is taken from https://plato.stanford.edu/entries/n...pia/#NewLawMot

If I don’t remember wrongly,

*F = ma*is from Euler.https://en.wikipedia.org/wiki/Euler%27s_laws_of_motion

Hope it helps.

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#4

**Absent Agent**)

Issac Newton not only introduced the concepts of velocity and acceleration, which can be measured by measuring distances and time, but also introduced the concepts of mass and force. So, technically, is the oldest equation in Physics. However, putting the definition of mass across, the other day a friend asked how did Newton know that exactly , and why did he not just define the force to be . So I have made this thread to see what others think.

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#5

(Original post by

Thank you for your response! I always took for granted that F=ma was credited to Newton, but it's also interesting that what he said is his Principia as a law of motion i assume could be written as , ...

**Absent Agent**)Thank you for your response! I always took for granted that F=ma was credited to Newton, but it's also interesting that what he said is his Principia as a law of motion i assume could be written as , ...

*Principia*, so I don't really know if the assumption is valid.

To my limited knowledge, I am not sure did Newton "define" motion in

*Principia*and it seems that Newton never presented the “three laws of motion” in the form of equations.

(Original post by

… but Euler seems to have derived F=ma from first principles.

**Absent Agent**)… but Euler seems to have derived F=ma from first principles.

ma. Thanks.

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Actually,for constant mass,accelaration is always exactly in direct relation with the force applied.Thus,Newton took F=ma instead of F=m+a.

**muhammad hasnain**)Actually,for constant mass,accelaration is always exactly in direct relation with the force applied.Thus,Newton took F=ma instead of F=m+a.

(Original post by

I had not read

To my limited knowledge, I am not sure did Newton "define" motion in

**Eimmanuel**)I had not read

*Principia*, so I don't really know if the assumption is valid.To my limited knowledge, I am not sure did Newton "define" motion in

*Principia*and it seems that Newton never presented the “three laws of motion” in the form of equations.*"The motion of a body is the sum of the motions of the parts; and therefore in a body with double quantity, with equal velocity, the motion is double; with twice the velocity, it is quadruple."*

I have difficulty understanding whether that definition has got anything to with his second law, but it seems that taking F=m+a assumes that a mass with it's acceleration would not be "conjunct" quantities. As a result, according to F=m+a, a body of a certain mass with zero acceleration would have require force for its state of motion (F=m+0).

*Attachment 709102*

In fact, Newton seems to refer to motion as the quantities of mass and velocity, but I don't know if he also means the product of mass and velocity.

(Original post by

Again, I am not sure about this. If you can support it with reference(s), I would be glad. I would really like to know how did Euler arrive F =

ma. Thanks.

**Eimmanuel**)Again, I am not sure about this. If you can support it with reference(s), I would be glad. I would really like to know how did Euler arrive F =

ma. Thanks.

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#7

Actually Newton wrote:

F = dp/dt

Given p = mv and a = dv/dt

--> F = d (mv)/dt

F = m dv/dt

F = ma

F = dp/dt

Given p = mv and a = dv/dt

--> F = d (mv)/dt

F = m dv/dt

F = ma

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#8

(Original post by

Actually Newton wrote:

F = dp/dt

Given p = mv and a = dv/dt

--> F = d (mv)/dt

F = m dv/dt

F = ma

**williamnguyen**)Actually Newton wrote:

F = dp/dt

Given p = mv and a = dv/dt

--> F = d (mv)/dt

F = m dv/dt

F = ma

Note that F = ma is not from Newton but from Euler. This is a fact. And Newton never presented the “three laws of motion” in the form of equations.

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#9

(Original post by

Well, in both cases, acceleration is directly proportional to the force.....

**Absent Agent**)Well, in both cases, acceleration is directly proportional to the force.....

Not really. When we say one quantity

*y*is

**proportional**to another quantity

*x*, it means

*y*=

*kx*. When we write

*y*=

*kx*+

*c*, it means

*y*varies linearly with respect to

*x*.

(Original post by

... Well, I thought the link to Wikipedia you provided in your first post also contained derivations of Euler's laws, ...

**Absent Agent**)... Well, I thought the link to Wikipedia you provided in your first post also contained derivations of Euler's laws, ...

It contains the derivation but how did Euler derive F = ma is another story. Did Euler extend the work of Newton or did Euler derive F = ma independently?

(Original post by

... but I really cannot make sense of them.

**Absent Agent**)... but I really cannot make sense of them.

It depends on what level of physics you are doing. The derivation is for rigid bodies instead of point particle. You need vector analysis and vector calculus to appreciate the maths.

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