Why does a body accelerate when there is a force applied to it?

Question

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

How force acts upon things to make them accelerate?

Answer 1

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.

Answer 2

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.

Answer 3

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…

Answer 4

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.

Answer 5

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.

Answer 6

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.

Answer 7

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.

Answer 8

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.

Answer 9

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.