# Why force $F$ is $ma$ but not $md$ or $mv$? How can I observe and understand “force” in real life?

As a layman, i can calculate approx "displacement" just by observing the moving object. And accurately by using a simple "scale". Similarly, again, I can calculate angle from origin by using displacement in $x$ and $y$ dimensions. Similarly I can use a stopwatch and scale to understand velocity.

But when I read about force, first of all it confuses with the english word "force", we use in real life. To some extent I am sure, it has nothing to do with that. So exactly what is it in the real sense. How can a layman, see force as, just like he can see displacement or angle? Or force is just a quantity defined by physicists to simplify the combinations of $ma$, they might be facing every time. And thus came up with term "force" ( which is similar in spelling to english word in oxford dictionary). And lastly, why not force has just been called as something proportional to mass and it's displacement or velocity. Why something at the level of change of velocity has been used to define it.

Interestingly enough, Aristotle proposed that $\vec F=m\vec v$, for, by intuition, it is reasonable to assume that how hard something hits you depends upon how heavy something is, and how hard something is going. However, this is because of Newton's First Law, inertia, which is analogous to momentum ($\vec p=m\vec v$). Yet, mass does have to have some effect on it, for it is not the same to have a truck hit you than to have a bee hit you. Thus, we reach the conclusion that a push or pull (a force) must be affected by the mass, and some factor dependent upon the derivatives of displacement with respect to time. Yet, what makes something move is not the speed with which it is hit, as we have discussed, but the change in speed, that is to say, the acceleration. Hence, $\vec F=m\vec a$.

I understand this is not the most theoretical derivation of a formula, it is rather an intuitive one, and it is very poorly written, for I am writing it on my phone and cannot even use LaTex. So please, don't hesitate to ask if you have any other questions or want a more theoretical approach.

Hope it helped!

• Well, i understand, that i cannot debate against hundreds of years of studies developed by geniuses .. but frankly what seems more intuitive to me, is that the force with which i hit, ofcourse involves the quantities like mass and displacement. But why time is important here.. is something, i need to contemplate upon! :P – Vishwas G Nov 20 '13 at 15:14
• Well, if no one where to argue the greatest minds there would be no science :P. Anyways, regarding your question, think about it this way, displacement, velocity, and acceleration are all vector quantities dependent upon the time an object has been in motion. Graphing velocity vs time yields a certain function, the slope of said function is how fast the object moved, which yields another function itself. The slope of that function is how fast the object changed how fast it moved (that sounds fun to say), which is the acceleration vector, the one which interests us. Let me know! – Demian Licht Nov 20 '13 at 15:33
• hmm... well, yes, it was silly me, where i am not involving the importance of time. As clearly enough, if two quantities with same mass and same displacement need to be compared for the force, then it's time, which will be deciding factor, which force is gonna be greater than the other. :) Thanks for the explanation :) – Vishwas G Nov 20 '13 at 15:52
• No problem! Just remember it is not necesarilly time, but how fast the object moved in that time period. – Demian Licht Nov 20 '13 at 15:53

A force is exactly how we think of it in everyday life!

A force is any push or pull.

When you push someone, you apply a force on them. It wasn't invented to fulfil $F = ma$. That was something that they found out.

Incidentally, when the total force on some object is non-zero, it creates an acceleration. And that acceleration is dependent on the mass of the object. The more the mass, the less the resultant acceleration. Experiments verified that: $$a = \frac{F}{m}$$ Thus they got the equation $F = ma$. This acceleration changes your velocity and thus makes a still object move, creating a displacement.

Force in real life is everything to do with the force of physics.

Oxford (or any dictionary, for that matter) has various definitions of force, but they all relate to a physical push or pull.

Referring to your last question, force wasn't arbitrarily defined to simplify equations containing $ma$, I've explained above. They have defined a quantity, however, encompassing $m$ and $v$. That is momentum ($p$). $p = mv$. Here, $p$ is defined as mass multiplied by velocity since it simplifies stuff. We couldn't say that force is $mv$, that would be wrong for many reasons, most important being that it would be dimensionally inaccurate.

• So, if my velocity is constant, then i am not applying any force. How come this is similar to real life scenario ? – Vishwas G Nov 20 '13 at 14:38
• @VishwasGagrani That is true. If the velocity of an object is constant, the total force acting on it is zero. Imagine a block lying on a smooth surface with no friction. If you push it, it will keep accelerating. Then when you leave it, the acceleration will stop, and it will go on forever at a constant speed until another force is applied on it. – mikhailcazi Nov 20 '13 at 14:41
• @VishwasGagrani This doesn't happen in real life - and I believe this is where you're confused - because in real life no surface is perfectly frictionless. Every surface applies friction. That's why if you slide a block on a floor, it will ultimately stop. This is because the floor is applying friction in the direction opposite to its motion, producing a deceleration and ultimately making it stop. – mikhailcazi Nov 20 '13 at 14:43
• you can also have F = dp/dt of course, which may or may not be illuminating to the OP – jk. Nov 20 '13 at 14:56
• @VishwasGagrani Force creates acceleration. That means that if you apply a force on a body for some time ($\Delta t$), it will have an acceleration of $F/m$ for that time. The moment you leave it, there will be no acceleration. (Assuming no other force acts on the body throughout) – mikhailcazi Nov 22 '13 at 8:13

So exactly what is it in the real sense.

It is that which acts to change an object's momentum or quantity of motion.

A force is something that can modify the state of motion of a system.

If a system has a constant velocity (it means it doesn't accelerate : $\vec{a}=\vec{0}$), then no force is applied to the system ($\vec{F}=m\vec{a}=\vec{0}$).

If the system has a velocity that changes (it accelerates or turns) then the acceleration is not null. We can quantify this change, namely measure the force.

This explanation is correct to some extend. If you want more information, I can develop my answer.

First I suggest you looking at physics (Classical Mechanics) as "an observation of particles". Observation makes sense with 'expression' thereof. This expression is constrained by that we can only reliably discuss on the mass, space and time of observation of particles in a 'frame of observation'. This frame is an isolated system, graduated evenly along the xyz axes and a regularly ticking clock. Outside of the frame of reference the universe is fairly homogeneous that is to say, the every particle runs into other accelerating it which in turn collides with others, hence statistically nothing is happening. Inside the frame of reference you have a particles interacting in ways that matter.

In physics we are just trying to give rigourous meaning to the word Force. As we said we cannot express Force except in the observable terms of mass, space and time. A velocity v, is an intuitive observation of comparing the clock tick with the the particle changing its position in space. The change in velocity as it went through intermediate steps is observable as well. We just have to compare our immediate memory of arbitrary segments of space being transitioned by the body in motion. Hence acceleration is intuitive enough as the other quantities. Thus observation is not only direct measurement but also comparison. So this is just computation with a memory. Now for the second part of your question.

As we said, we are concerned with observation of particles, which would mean their interaction as well in the frame of reference. At a point when the frame of reference is created, if a body drifts into the frame of reference with a constant velocity, it is not any more considered to be active than one in rest. Hence, the velocity by itself is not indicative of any interaction. Force might be understood to be a property of the interaction ie 'elastic collisions' of the particles.

What indicates a collission has happened is that the particles involved say A and B change their velocity and directions. If we observe only one particle, we see that the particle has changed its velocity after the impact in a manner proportionate to the mass and velocity of the colliding particle. The colliding particle A has hence transferred some of its velocity to the particle B or rather the two netted their velocities and the two particle system moves in the net direction of the impact. For instance if mass of B < A, then B moves faster than it used to be and A moves slower than it used to be. Hence what is interesting from the interaction is the change in velocity as modified by the proportion of the mass of the particle of interest. Observing with respect to a particle B, we might hence say particle A interacted with particle B with a property ‘Force’ equal to the product ma.