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Why does a body accelerate or changes velocity when a force is applied on it?

How force acts upon things to make them accelerate?

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – ACuriousMind
    Dec 7, 2021 at 0:24

9 Answers 9

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Force BY DEFINITION is $\frac{\partial p}{\partial t}$ Thus $\int_{t_{0}}^{t_{1}} \frac{\partial p}{\partial t} dt $ = Change in $ p$

The application of a force for a time changes the momentum of a body,

$p= mv$

$\frac{\partial p}{\partial t} = ma$

Thus if I apply a force, I will get an acceleration,

Acceleration is the rate at which the velocity changes with respect to time.

It is all about defining a quantity that is useful. We can measure acceleration, velocity, distance. So defining a quantity that changes those values in some way, can be used as a tool to predict and understand nature.

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    $\begingroup$ "When we push wall, we say that there is a force applied on wall, it can be clearly seen that there is no change in momentum or velocity of wall" - is that force term apllicable here too? Why $\endgroup$ Dec 4, 2021 at 15:18
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    $\begingroup$ The NET force on a body is the thing that contributes to its change in momentum, when I push on a wall, the internal structure of the material produces a force that counteracts this applied force, Once the applied force exceeds the materials ability to resist it there is a change in momentum. Aka "breaking things" $\endgroup$ Dec 4, 2021 at 15:35
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    $\begingroup$ I disagree with this answer. $F = dp/dt$ is definitely not a definition. Among my several objections to this claim, one of them is: how am I supposed to understand forces on objects in equilibrium using this definition? I stand on the floor, the Earth pulls down on me, and the ground pushes me up. There are obviously forces acting on me, but your definition doesn't allow me to say anything about what those forces are. $\endgroup$
    – d_b
    Dec 5, 2021 at 1:01
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    $\begingroup$ Well defining a force as the rate at which momentum changes with respect to time , can allow you to say what those forces are. dp/dt is a vector you can specify what that vector is, If they are equal but opposite in magnitude then dp/dt = 0 Just as you DEFINE a force, you can equally define the rate of change of momentum. This is exactly how Newton himself defined force. Newton said F is proportional to dp/dt, then made units to N to make them equal. Newton didn't write f=ma $\endgroup$ Dec 5, 2021 at 1:09
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    $\begingroup$ @jensenpaull I’m just saying this is Newton’s definition of net force. Your whole answer is only valid for net force, not any force such as friction, stress, pressure… I’m perfectly fine with that definition of net force, but I think the "net" should be mentioned ;) $\endgroup$
    – Didier L
    Dec 6, 2021 at 13:53
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As others have pointed out, $F=ma$ is a definition of force (and mass for that matter). The reason we invented the concept of force, as defined by this equation, is because it makes things very simple and elegant. We want to understand how things move. We note that objects usually move we constant velocity. The special circumstance is when an object deviates from constant motion. Therefore, whenever an object deviates from constant motion, we say that, by definition, it is being acted on by a force. Then, it turns out, in our universe, we can describe all kinds of phenomena with only a couple of simple fundamental forces.

Note, we could just as well try to define a "velocity force" by the equation $F_v=mv$. You could, technically speaking, build a complete theory of classical physics using "velocity forces" (just use $F_v=\int_{t_0}^t Fdt+mv_0$). However, such a system would be extremely inelegant. The "velocity force" would have to depend on the entire history of the interactions of the particle.

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  • $\begingroup$ +1. This is the best answer I have come up for with this perennial problem. F=ma because we found that, if we measure 'm' and 'a', declare F to be their product, then F has a whole lot of nice properties which make it very easy to understand how things move in complex situations. $\endgroup$
    – Cort Ammon
    Dec 6, 2021 at 17:55
  • $\begingroup$ @CortAmmon this definiton would not be enough to explain the equilibrium situations. This is only apllies for net force. But for example force that you aplly on ground and that what ground apllies upon you don't have any affects but still there is something there called force. $\endgroup$
    – user316791
    Dec 6, 2021 at 19:24
  • $\begingroup$ @ArsenalCreation True. Those would be the nice properties I mentioned. But it is nice to find that the equations that work in non-equilibrium situations also work in equilibrium. In these situations you have matching forces which, if the scenario is suddenly changed in a multitude of ways which leave them imbalanced, the result is always physically consistent. $\endgroup$
    – Cort Ammon
    Dec 6, 2021 at 23:10
  • $\begingroup$ Incidentally, this is a major safety thing. A steel cable can be under an astonishing amount of tension (force), but be completely at equilibrium. But should something happen to that cable, the fact that everything was under tension suddenly becomes very important as that cable becomes incredibly dangerous. Perhaps a selling point is that the concept of force could show the terror in the deep. $\endgroup$
    – Cort Ammon
    Dec 6, 2021 at 23:39
  • $\begingroup$ @ArsenalCreation $F=ma$ defines the net force. From situations where only one type of force (e.g. electrostatic, gravitational, etc.) is present, we can infer simple laws describing the forces of these interactions. Then, for situations where multiple interactions are present, we find that, in our universe, the net force can be found by summing the forces that we would have gotten by considering the interactions one at a time (which is very convenient). This is where the concept of equilibrium forces comes from. $\endgroup$
    – Yachsut
    Dec 7, 2021 at 4:19
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Force is defined as an interaction that changes the motion of an object (look at Newton‘s laws for example). A change in motion means that the object which experiences the force is accelerated.

That should be in every physics textbook…

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  • $\begingroup$ When i think about why objects accelerate, the reason that comes to my mind is because there is a force applied. But at sudden it hits me with another question- What is force? Why does it change motion of objects? Your answer is not talking about "why". $\endgroup$ Dec 4, 2021 at 15:21
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    $\begingroup$ @PredakingAskboss I understand why those questions might come up. However, I think you are overcomplicating things. I gave the answer to what force is and why it changes motion of objects: because that's how force is defined. Seems like a chicken-and-egg problem... Maybe you meant to ask something like: Why can the motion of an object be changed? $\endgroup$ Dec 4, 2021 at 17:35
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Frame challenge: Your question doesn't make sense; nor can it be readily answered in words

cause i am from another world and i don't know about these things

One thing that we assume for physics is that the laws of physics (such as we understand them) apply everywhere. Time and space may behave differently around mass, sure, but that's still following the same laws on Earth as elsewhere. So wherever you are in the universe, you understand pull or push.

All that you don't understand is the words. You say "explain pull or push". I physically grasp your body, and pull and push. Now you understand pull and push.

Words are merely descriptive of a physical action. At some point, the physical action must be observed in a way we both agree on. Adding extra words does not help explain this.

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  • $\begingroup$ " I physically grasp your body, and pull and push. Now you understand pull and push." What i would feel is just a compression on my body. You yourself said that you can't explain these terms. But what i think is that these are very important terms and create base of physics so we need to make a proper defintion for them in physics that can explain them clearly at all stages. $\endgroup$
    – user316791
    Dec 6, 2021 at 19:17
  • $\begingroup$ @ArsenalCreation Certainly it can be explained in units for physics. Google SI units, and honestly if you haven't already then you don't know enough to have a conversation about physics. If you want to explain the underlying concept to someone though, words aren't going to help. $\endgroup$
    – Graham
    Dec 6, 2021 at 20:23
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The first step to fully understanding the stature of classical forces is to categorically separate models and their features from reality itself. Our models strive to describe reality, but ultimately we must recognize that concepts like velocity, momentum, and force are defined in the context of a model, not unequivocal features of reality. Reality gives us intuition for our models and vice versa, but they are distinct.

Now, the statement $\vec F=\frac{d \vec P}{dt}$ is a loaded one. It is the core postulate of a model of dynamics, a model that postulates quite a few things in order for the statement to have meaning.

A fundamental force or fundamental interaction in physics is any interaction between matter that cannot be reduced to more basic interactions. This is not so edifying a definition from the perspective of this question, namely because it's unclear how these must impact motion. This was a necessity for generality because key measures of "motion" like position and velocity aren't necessarily meaningful in fundamental physics. When we restrict our scope to classical physics, however, where the most basic objects in the model are particles with well-defined positions (be it in Einsteinien spacetime or Galilean Euclidean space), it's simply an assumption of the model that all such interactions impact particle motion according to Newton's second law, and part of this assumption is that associated to each fundamental interaction there is a vector force on each of the interacting particles entirely encapsulating its effect. Think of the Coulomb force between charged particles, or more generally the Lorentz force.

When we put forward $\vec F = \frac{d \vec P}{dt}$ as a means of modelling classical dynamics, then, we are postulating that matter is comprised of particles with well-defined momenta; we are postulating that there exists some collection of fundamental interactions of matter, and that to each of these there is associated a vector $\vec F_i$ ($i$ indexing over the interactions), called its force, on every particle of matter; furthermore (in a Galilean context), we are postulating that there exists a family of reference frames, called inertial frames, within which the equation $\sum_i \vec F_i = \frac{d \vec P}{dt}$ is true for every particle of matter (and hence for systems composed of them). By observing real-world dynamics, we hypothesize what the fundamental interactions are and what the vector force associated to each is. We then put these into our model $\vec F = \frac{d \vec P}{dt}$ and see how well it predicts what we see.

All of that to say: "push" and "pull" are heuristics capturing what we want "force" to mean in reality, but definitionally a force is a modeled manifestation of a fundamental interaction of matter, and we say that forces cause acceleration because our model of their doing so works extremely well in predicting what we see in the real world.

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In the end it's all fields that want to reach some optimal state of lowest energy: In our macroscopic world it's electromagnetic and gravitational fields. On the particle level you have additionally weak and strong forces.

Everything tends to go "downhill" (to some minimum) as long as the forces aren't balanced.

When that minimum— equilibrium — is reached there are only internal forces left. The atoms in crystals are experiencing enormous electromagnetic forces which only become apparent when we try to disturb the equilibrium. Whether those forces, which perfectly cancel each other out, are actually there is in the eye of the beholder.

As another example, many glass artifacts are under internal stress that only becomes apparent when a crack emerges and ends the balance of forces. We typically ignore internal forces until the equilibrium is disturbed, as in the mentioned glass, or a bridge in Genoa, or when it's up to us to keep up the equilibrium. Just ask Atlas, or St. Christopher.

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  • $\begingroup$ The idea that things "want to reach some optimal state of lowest energy" seems incorrect to me. Things want to reach the state of highest entropy, which is sometimes (at low temperature) the same as the state of lowest energy. When we can transfer energy to the environment, the system tends toward minimum free energy F_sys = E_sys - T S_sys, which is always equivalent to maximizing the entropy of the both the system and its environment but only equivalent to minimizing the energy of the systm when T=0. $\endgroup$ Dec 6, 2021 at 16:48
  • $\begingroup$ @WaterMolecule Entropy is an emergent behavior of collectives while energy states concern microscopic systems as well. I think they are orthogonal. $\endgroup$ Dec 6, 2021 at 18:10
  • $\begingroup$ Then in what sense do things "want to reach some optimal state of lowest energy"? If we are talking about a closed microscopic system, energy is conserved, so there is no lower or higher energy. Forces act to accelerate particles (or degrees of freedom) toward a local minimum of potential energy, but this is not guaranteed to be "optimal" and the particles cannot stay there due to the kinetic energy they acquired on the way. Optimization requires dissipation and dissipation is by its nature a collective process. $\endgroup$ Dec 6, 2021 at 19:10
  • $\begingroup$ @WaterMolecule Masses and charges are pulled in the direction of their respective fields, where the field energy would be minimal. That is what we perceive as force. At his level, it has nothing to do with entropy. Particle energy can be shed by emitting a photon (not sure with gravity). $\endgroup$ Dec 6, 2021 at 20:47
  • $\begingroup$ I agree that the force points toward some local minimum of the potential energy. I was objecting to your use of "optimal," which implies some kind of global minimum. $\endgroup$ Dec 6, 2021 at 21:09
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In Newtonian mechanics that is the definition of a force: F = M A, where M is the mass, and A the acceleration. So why doesn't my car accelerate if I lean on it? Isn't that a force? There is friction of the tyres against the ground, and friction in the transmission, so the nett force is zero (unless I push really hard).

Newtonian mechanics is a big conceptual jump from Aristotelian mechanics--see The Invention of Science: A New History of the Scientific Revolution, by David Wootton. In many ways Aristotle's theory is more intuitive: it just doesn't give rise to a means of calculating motion that works.

If you persist with the "why" questions, you may find yourself going outside of Newtonian mechanics, and into relativity and quantum mechanics. Reputedly Einstein asked himself why he was exerting a force (weight) on his chair, which was balanced by an equal force from the chair on his tuchis. His answer was general relativity.

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    $\begingroup$ The equation you wrote is not true in general. $\endgroup$
    – Osmium
    Dec 5, 2021 at 2:21
  • $\begingroup$ Why do you think that the second law of motion isn't true in general (whatever that means))? Please bear in mind that it is a definition. Leonard Susskind pointed out that it isn't useful (or even meaningful) to ask whether a definition is "true": ask whether or not it is useful. $\endgroup$ Dec 5, 2021 at 5:54
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    $\begingroup$ @Simon_Crase By the comment, I meant that this is true only for a particle or system of particles having constant mass. The second law, in general, is $F=\frac{dP}{dt}.$ $\endgroup$
    – Osmium
    Dec 5, 2021 at 7:20
  • $\begingroup$ "Why does a body accelerate or changes velocity..." -- a body, IMHO, is a good example of "a particle or system of particles having constant mass." $\endgroup$ Dec 5, 2021 at 9:13
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There are quite satisfactory answers to this question. Most of them are using Newton's force equation $$\text{Force}\rightarrow \text{Acceleration}\rightarrow \text{Change in Velocity}\rightarrow \text{Change in Displacement}$$

But there can also be possible explanations from a microscopic point of view. One can argue that Since there's a lot of space in there in a body. Why not when I push a body, I simply go through it instead of displacing it from its position. I don't think, Newton's equation takes that possibility.

This is because of Pauli exclusion principle which says that the electron doesn't like to be squeezed together. So when electron cloud from your hand tries to squeeze with some other body. You get repulsion. Of course, a fair amount of electromagnetic interaction also going in there. But the sole reason is exclusion principle.

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    $\begingroup$ I don't think the Pauli exclusion principle is the reason solid matter can not "overlap". That's regular electromagnetic forces. $\endgroup$ Dec 5, 2021 at 23:36
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I don't know how far i am wrong or correct but what i think about force is that-

Force is a try to accelerate something and when that "something" accelerates and an another thing obstructs its path like a ball(when pushed with hand) there comes interia, the fundamental law, which tries to make the ball to maintain its motion without changing. But the acceleration of hand moves the ball too. We can feel this as force cause we are sensitive to this. But on the other hand the ball accelerates with our hand too. That interia of ball reduces the acceleration of our hand. So we are actually trying to accelerate our hand with more fsater rate than it is actually at. Which makes us feel that force too.

A hand accelerating at $6m/s^2$ with mass 5kg has rate of change in momentum = $30kg m/s^2$

A ball of mass 1kg adds to hand and gives a total mass of 6kg

But since the energy supply or rate of momentum change remains same we get acceleration = $30kg m/6kg s^2 = 5m/s^2$

Balls is getting force = $5m/s^2 × 1kg = 5N$

Reduction in acceleration of hand = $1m/s^2$

Force on hand = Reduction in acceleration × mass of hand = $ 1m/s^2 × 5kg = 5N$

Here force apllied is 5M and the force felt is 5N.

So here it is also explaining why there is a reaction force.

Cause we can define the force as something that is opposed by inertia which is actually a change in motion. Since objects have mass too, it's mass times acceleration that fights with inertia. We call this as force.

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