What exactly is force? What is its source or origin? I am asking this question here after trying to do much research and study to understand it on my own first. I am not sure if I am asking a metaphysical question that really can't be answered in concrete terms but I want to give it a final try and try to see if anyone can share their understanding regarding this concept.
I am confused about exactly what is force? Specifcally, where do objects gain the capacity/ability to exert force from? Like, where does a bullet (a small object, if you think about it) get the ability to strike another object with such force and cause so many damage? Why does a hammer cause different amounts of damage depending on how fast or slow I hurl it across the wall?
Does it have something to do with speed/momentum of the bullet or hammer? If it does, then what is it about momentum that objects get the capacity to exert so much force? Would it be right to think that if an object has infinite velocity, it can have infinite force?
I am not sure if my question makes sense. But if anyone can add their bit to it, I greatly appreciate it. Thanks.
 A: A lot of examples in your question are about objects exerting force when they are stopped.  So the first part of the answer is about that.

*

*There is the impulse equation Force x time = change in momentum

$$Ft = mv - mu$$
where $v$ is the final velocity and $u$ is the initial velocity.
As you can see the change in momentum includes the mass and also the change in velocity, so a bullet when it hits something exerts a large force, but so does the more massive hammer, even when moving more slowly.
If you were wondering how the force is transmitted from the moving object to the object it hits, it's like this:  The moving object is stopped at one side first, whilst the other side keeps moving, thus the moving object is compressed.  It then pushes on the object it hits, trying to expand to its usual shape.
The force these objects exert depend on the time over which they are stopped, so a hammer landing on a mattress would on average exert less force on the mattress (but for a longer time), than if the hammer struck a wall.


*The SI definition of the Newton, the unit of force is "the force that would give a mass of one kilogram an acceleration of one metre per second per second", so it's really defined from Newton's second law $$F=ma$$


*There can be other explanations of what force is but it will get quite philosophical e.g. to define force, perhaps we need to define and understand inertia and its cause, but that's still being debated today.
A: There is a lot to unpack here, but basically there are two different phenomena at play.

*

*Energy.

Namely kinetic energy or energy acquired by an object simply because it is moving (relatively to another object). If an bject of mass $m$ moves at a speed $v$, it’s kinetic energy $E$ is:
$$ E = m .v^2$$
So the energy carried by an object, owing to its it motion or speed $v$ increases with its mass but it increases much faster with its speed:

*

*An object $10$ times more massive ($m1 = 10m$) has ten times more kinetic energy with at a given speed than an object of mass $m$.

*An object which is $10$ times faster ($v1 = 2 v$) has a hundred times more energy than an object of mass $m$:
$$ T1 = m .v1^2 = m (v.10)^2 = m. v^2 100 = 100. T$$
This is why a bullet is more harmful than a stone: its lighter, but its faster.
When an object in motion hits another object, the object which is hit slows it down and gets thereby a part of the energy of the incoming object transferred in return.
If an object is heavy and/or moves fast, it will transfer a lot of energy to the object is hits.
It is said transfer of energy which will damage the object on the receiving end, because it will absorb it.
One could explain the same thing is terms of force as well (one can demonstrate that these two explanations are equivalent mathematically speaking).
In order to accelerate an object set it in motion or increase its speed, one has to apply a force to it.
In Newton’s terms acceleration ($a$), force ($f$) and mass ($m$) are related as follows:
$$ f = m a \tag 1$$
The same is true for deceleration (which technically is the same as acceleration, just with a reversed sign).
In other words, the stronger an object is decelerated, the more force it will exert on the object decelerating it, according to Newton’s law (1), above.


*Pressure.

The second reason a bullet is potentially more harmful than a stone is: force per unit surface or pressure.
If an object exerts a pressure on another object, the larger the surface over which a given pressure is spread, the less energy it will be able to transfer energy on a precise location.
A bullet having the same mass and the same speed as a much larger rubber ball will do much more damage on impact, because its kinetic energy will be transferred onto a much smaller area. This is also why a knife or an axe have to be sharp to be effective (if not the force is spread (and hence it’s effect) over a large area).
A: Force is not the easiest concept to grasp. It's probably better to list the various properties of force rather than to try and give a snappy definition. I've tried to arrange the list so that it builds up to give a coherent overall concept of force.
• A force is a push or a pull acting on a body. Some will deride this statement as vague and tautological, but at least it rules out claims like "electricity is a force".
• A force has a direction as well as a magnitude or size. It is a vector quantity.
• A force acting on a body, A, is exerted by another body, B. [I push you, the car pulls the trailer...]
• We can say that there is an interaction between A and B. This interaction has a symmetrical effect on A and B. What this means is that...
• If a body A exerts a force on a body B, then B exerts an equal and opposite force on A. (Newton's third law of motion).
• There are different types of interaction. The force that the Earth exerts on an apple and the accompanying equal and opposite force that the apple exerts on the Earth are so-called gravitational forces. Contact forces such as the upward force that the dining table exerts on the plate and the downward force that the plate exerts on the table are fundamentally electromagnetic.
• If more than one force acts on a body the resultant force is the vector sum of the individual forces.
• Whenever there is a non-zero resultant force on a body, the body's velocity will be changing. The rate of change of velocity (that is the acceleration) is proportional to the resultant force (and inversely proportional to the body's mass). In a coherent set of units this is embodied in the famous equation, $\textbf F = m \textbf a$. [In most cases this is equivalent to the impulse equation, $m \mathbf v - m \mathbf u =\mathbf F t$.]
Let's now look at the case of your thrown hammer. Clearly the force it exerts isn't simply a property of the hammer, because if the body I hurl it at is moving away the hammer will exert less of a force on it, or perhaps no force at all. Or perhaps the target is soft, like a cushion; the force will be much smaller than if the object were rigid. In that case the hammer's deceleration (rate of change of velocity) will be small and $\textbf F = m \textbf a$ shows that the force on the cushion will be small. Remember that we have an interaction between the hammer and the body that it hits. In this interaction the hammer exerts a force on the body and the body exerts an equal and opposite force on the hammer.
Hope this has helped.
A: Force is a change in momentum. Momentum, in turn is a conserved quantity, so it cannot change in isolation. Any change in momentum for one object is associated with an equal and opposite change in momentum for some other object. In other words, momentum is transferred from one object to another, meaning that forces come in pairs.
When two objects can exchange momentum, we call that an interaction. Interactions are typically mediated by some field and a corresponding “charge”. Two objects with charges of the same type can exchange momentum by having one excite the field and then the other absorb the excitation.
Of course, this is a simplification and the details can get messy on the quantum level. There are three body interactions and the distinction between fields and objects becomes tenuous. But this gives the gist of what forces are.
In your hammer and bullet examples, those interactions are mediated by very short range electromagnetic interactions. We call such interactions “contact forces”. As a bullet or hammer exert a force on a target the momentum of the bullet or hammer decreases and the momentum of the target increases by the same amount. The damage you mention is more due to energy than momentum, but the transfer of energy is power (or work) rather than force.
A: Force comes from Energy, via Work being done.
It is the transference of Energy, which normally we cannot see and do not know exactly what "energy" is, only observe its effects on other things.
One of those effects we call force.
Others can be "transfer of heat".
When the energy transfer reaches a threshold we can observe change, often we describe some of these transfers as force; such as physical force (which is usually accompanied by elasticity), electromagnetic/magnetic, gravitational.
If you want a mind-spinner.
Ask where the force comes from if two magnets, held at different heights but near each other, and initially (t=0) restrained, with same pole face (eg N to N) then lowered onto a flat surface.  Then (t=2) the restraints are removed.
The magnets will then have freedom to move from the magnetic force applied to each from other.  They can be observed to accelerate away from each other - but where did the force come from ?    If we push one magnet towards other, they will move around, due our energy and force input.  But where did the original magnetic force at (t=2) come from - and where did the force/energy come from at all other times (t=all) where the magnetic field is continuously running.....
A: 
Specifcally, where do objects gain the capacity/ability to exert force from?

Objects gain the capacity to exert force through human knowledge.
Wait, what?!
There are a lot objects moving around in the universe.  You, as an observer of those objects, can grab a ruler and clock, and start recording their trajectories.  Applying a little calculus, you can compute from that trajectory an object's velocity and acceleration.
Sometimes, the value of this acceleration is inexplicable: if I place one piece of metal on my desk and wave another piece of metal over it, the first piece of metal leaps into my hand.   On the other hand, some are more predictable (I let go of an apple; it falls).  We call the accelerations we understand "forces" and the ones we don't "new physics."  Newton's first postulate ("there exists an inertial reference frame") says that all accelerations can be understood, if we work hard enough.  So far, it's seemed to be true.
OK, but force has different units from acceleration.
How can you be certain you understand a force?  Is it enough to just write down what values it has at what times?  (No: you've just summarized your observations and haven't really learned anything.)
Newton's third postulate says that forces come in pairs acting on different objects; you know you understand a force when you can identify the corresponding pair.  But the weird thing about Newton's third law is that the corresponding accelerations of a force pair are not equal.  So how do we know when we've identified them?
Well, each object has a specific mass, which does not change in time (unless the object itself changes), and the product of the accelerations and masses for corresponding pairs is equal.  (That's Newton's second postulate.)  So we might as well just call this conserved product the "size" of the force (and that turns out to be a fruitful choice indeed).
