Why is F=ma? (Physics homework)

[SaifTaher]

I'm taking an AP physics course on the edx.org platform and I arrived today at the "Forces" Unit. One of the fundamental properties of force that it's equal to acceleration times mass, but I, as a curious stubborn nerd, always look for the "why's", so I thought to myself "why it's not equal to velocity times mass?" after all, it makes more sense, but science has never and never will depend on "makes sense".

Please someone explain this to me because memorizing a law and not understanding "why" is one of the most frustrating things I experience in learning science.

 

[PeroK]

Velocity is frame dependent. For example, if a car accelerates from $0$ to $10m/s$, say, then what happens if you consider the car is actually on the rotating Earth, orbitting the Sun?

Is the car really traveling at $10m/s$ or $500m/s$ or $5,000m/s$?

Acceleration, however, is independent of how you look at the car's motion. In all cases, it has changed its velocity by 10m/s in a certain direction.

Note that Newton's first law tells you that it does not take a force to maintain constant velocity. Thus was a major insight, as before Newton many assumed that it must take a force to keep an object moving.

 

[SaifTaher]

Velocity is frame dependent. For example, if a car accelerates from $0$ to $10m/s$, say, then what happens if you consider the car is actually on the rotating Earth, orbitting the Sun?

Is the car really traveling at $10m/s$ or $500m/s$ or $5,000m/s$?

Acceleration, however, is independent of how you look at the car's motion. In all cases, it has changed its velocity by 10m/s in a certain direction.

Note that Newton's first law tells you that it does not take a force to maintain constant velocity. Thus was a major insight, as before Newton many assumed that it must take a force to keep an object moving.

Thanks mate :)

 

[Delta2]

Newton's second law , F=ma, is taken as an axiom in Newtonian Mechanics. An axiom means that there is no further justification as to why it holds, we know it holds from experiments where we measure force and acceleration, we cannot break it down to more simple whys (again within the framework of Newtonian Mechanics) , as to why this law is true, it just is true.

 

[atyy]

I'm taking an AP physics course on the edx.org platform and I arrived today at the "Forces" Unit. One of the fundamental properties of force that it's equal to acceleration times mass, but I, as a curious stubborn nerd, always look for the "why's", so I thought to myself "why it's not equal to velocity times mass?" after all, it makes more sense, but science has never and never will depend on "makes sense".

Please someone explain this to me because memorizing a law and not understanding "why" is one of the most frustrating things I experience in learning science.

You can regard F=ma as a definition. By itself it is meaningless, since we must also specify F. For example, for gravity, F=GMm/r².

 

[SaifTaher]

Newton's second law , F=ma, is taken as an axiom in Newtonian Mechanics. An axiom means that there is no further justification as to why it holds, we know it holds from experiments where we measure force and acceleration, we cannot break it down to more simple whys (again within the framework of Newtonian Mechanics) , as to why this law is true, it just is true.

hmm, often when something can't be broken down into more parts it's clearer than this,
thanks :)

 

[SaifTaher]

You can regard F=ma as a definition. By itself it is meaningless, since we must also specify F. For example, for gravity, F=GMm/r².

Does that mean that mathematically F has no definition? (again, mathematically )

 

[PeroK]

Does that mean that mathematically F has no definition? (again, mathematically )

Physics isn't mathematics. You can define length, time and mass by some physical process or standard. The standard metre and kilogram are in France, for example, and the second is defined in terms of the caesium atom. Then, force can defined using the equation $F = ma$.

Note that this ties in with Length, Time and Mass being the fundamental units. Force has units of $MLT^{-2}$.

 

[Vivan Vatsa]

Listen saifTaher ,
A force is a push or pull upon an object resulting from the object's interaction with another object. Whenever there is an interactionbetween two objects, there is a force upon each of the objects. When the interaction ceases, the two objects no longer experience the force. Forces only exist as a result of an interaction.

Force is a quantity that is measured using the standard metric unit known as the Newton.

One Newton is the amount of force required to give a 1-kg mass an acceleration of 1 m/s/s. Thus, the following unit equivalency can be stated:

1 Newton = 1 kg • m/s2.

Boy see though ur question makes sense, but u cannot question out the facts of nature. Why f= ma , well no one in this world can answer that but one thing can be assured that f is something u feel. One or the other way, & that feeling is expressed as an expression.

So relax , understand & try to avoid questioning the facts.Thanks
Kind regards,
Vivan

 

[Mark44]

so I thought to myself "why it's not equal to velocity times mass?"

As already mentioned, the relationship between force and acceleration is due to Newton's Second Law.

There's another attribute that is given by velocity times mass -- momentum, as in the equation $p = mv$. See https://en.wikipedia.org/wiki/Momentum#Newtonian.

 

[CWatters]

Perhaps ask yourself why you think velocity * mass would make more sense? That would imply moving at constant velocity needs a power source.

 

[David Lewis]

The Newton (as a unit of measure) is not capitalized.

 

[Delta2]

hmm, often when something can't be broken down into more parts it's clearer than this,
thanks :)

It is quite clear to me, perhaps it isn't clear to you because you don't find it simple enough. The laws in physics aren't always simple(another profound example is the laws of electromagnetism aka Maxwell's Equations).

 

[SaifTaher]

Thanks guys, I totally get it now, together your explanations made it very clear to me