In high school, we used to draw a free diagram, and we are asked what are the forces acting on the object. When we represent these forces, we represent them using vectors going out from a point called point of application. So all forces in newtons law are point forces in such case?
How can we understand physically the difference between a force and a point force, knowing that force itself doesn't exist, no?
Newtons law do not only work with point forces, It works with all forces associated with a vector field. Finding the force to a non point object requires integration.
The most standard way a force is exerted is through the electromagnetic force. But instead I'll work with force per unit volume ($\vec{f}$)
Newtons laws work with point forces, However it is common to deal with vector fields, aka, a vector attached to every point in space
$\vec{f} = f_x(x,y,z) \hat i + f_y(x,y,z) \hat j + f_z(x,y,z) \hat k$
Point forces can be moddeled using vector fields aswell
Forces acting on the whole body :
If a body has some volume, the body at each point in space experiences some force, in relation to a force field, we assume the body is rigid, and thus the sum of these forces acting on the whole body constitutes as the "net force" on the body.
$\vec{f}$ has units force per unit volume, and therefore:
The force on an infinitesimal volume is therefore $\vec{f} dv$
To find the total force acting on a body we integrate. $\iiint \vec{f}dv$
Point forces:
This models the force being concentrated in some location. Such that at that point of contact, $\vec{f}dv = \vec{F}$ where $\vec{F}$ is the chosen force.
The vector field associated with a point force located at $r_{0}$ is
$\vec{f} = \vec{F}\delta^3(\vec{r}-\vec{r}_{0})$
When $r ≠ r_{0}$ then $\vec{f} = 0$
When $r = r_{0}$ then $\vec{f} = \infty$
Such that $\iiint \vec{f} dv = \vec{F}$ for any volume containing $\vec{r}_{0}$
Torque and point forces:
Others have said that it doesn't matter where the force is applied, aslong as the body is rigid. But that is not necessarily true. The location of the force matters, as this influences the net torque, the same force applied to different areas can change the torques value. The total force being the same if e.g it was a point force,or spread out equally, does not mean the torque is the same.
In most problems in high school we assume the body as rigid,so it doesn't make any difference if the force is point load or a distributed load.
But if you see in practice the point load will cause deformation(take a sponge and apply load on it by your finger and observe the effect,try applying force on sponge by a wooden block or other object with distributed area)
An object, or a body, consists of particles. You can think of body as a collection of particles. Each particle has its mass and its coordinates in respect to origin of chosen coordinate system. Body has its center of mass, which position is calculated as a mass weighted average position of particles. So, while body is a collection of particles, it is equivalent to a particle with a mass M which is the sum of all particles. This means that when some external force acts on a body, and that body moves accordingly, it moves just as though all of the masses of other particles were concentrated at the point of center of mass.
If you have a symmetrical body with uniformly distributed mass, such as a billiard ball, its center of mass is the same as its geometric center. Other bodies may not be symmetrical nor have a uniformly distributed mass. In school, you usually have these symmetrical bodies as examples, so when drawing a force diagram, its convenient to draw it as a force acting from a point that's center of a body.
