# Why is F=ma? (Physics homework)

1. Dec 25, 2017

### SaifTaher

• Member advised to use the formatting template for all homework help requests
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.

2. Dec 25, 2017

### 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 travelling 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.

3. Dec 25, 2017

### SaifTaher

Thanks mate :)

4. Dec 25, 2017

### 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.

5. Dec 25, 2017

### atyy

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.

6. Dec 25, 2017

### SaifTaher

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

7. Dec 25, 2017

### SaifTaher

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

8. Dec 25, 2017

### PeroK

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 $MLT^{-2}$.

9. Dec 25, 2017

### Vivan Vatsa

• Member advised that the use of "text speak" is not allowed in posts.
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

10. Dec 25, 2017

### Staff: Mentor

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.

11. Dec 25, 2017

### CWatters

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

12. Dec 25, 2017

### David Lewis

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

13. Dec 26, 2017

### Delta²

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).

14. Dec 27, 2017

### SaifTaher

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