Field of contact forces

[Manish_529]

Homework Statement

Can the contact forces like the Tension, Friction, and Normal have a field?

Relevant Equations

The field of force is a region of space at whose each point a particle experiences a force varying regularly from point to point.

Since contact forces are a manifestation of fundamental electromagnetic interactions at a macroscopic scale. They should possess a field whose effect is so small for regular bodies that are not in contact that it can be neglected? But when the bodies come in contact, this force cannot be neglected?

 

[ergospherical]

All the phenomena you listed are treated differently. For elastic materials, you will learn that we can come up with a stress tensor field $\boldsymbol{\sigma}(\mathbf{x})$, such that the traction (force) on an "imaginary" internal surface in the continuum with normal $\mathbf{n}$ is given by $\mathbf{F}(\mathbf{x};\mathbf{n}) = \boldsymbol{\sigma}(\mathbf{x}) \mathbf{n}$. There's a sensible way to assign a stress -- in this case, a 3x3 matrix -- to each point in the continuum.

Friction and contact forces are macroscopic phenomena arising due to electromagnetic interactions. They depend on the local geometry of the contact surfaces, etc. There's no sensible way to bundle this into a field: the interactions between the bodies are discrete. But at the microscopic level, you are dealing with electric and magnetic field.

 

[Steve4Physics]

Homework Statement: Can the contact forces like the Tension, Friction, and Normal ...

There may be a misunderstanding of the terminology. My understanding is this...

A contact force between two separate objects arises because of the interaction between the electrons at the two surfaces in contact. At a simple level a contact force can be attributed to electron-electron repulsion but it is really a consequence of the Pauli excursion principle.

The component of contact force perpendicular to a surface is referred to as the normal force on that surface.

The component of contact force tangential to a surface is referred to as the friction force on that surface.

Tension exists only inside an object and doesn’t directly exert a force on another object. For example if two people hold the ends of a rope and have a ‘tug-of’war’ competition, the rope exerts frictional forces on their hands. The magnitude of tension equals the magnitude of the frictional force, so we would generally say 'tension acts on each person' - this is incorrect but convenient.

 

[Manish_529]

Thanks!

 

[Manish_529]

All the phenomena you listed are treated differently. For elastic materials, you will learn that we can come up with a stress tensor field $\boldsymbol{\sigma}(\mathbf{x})$, such that the traction (force) on an "imaginary" internal surface in the continuum with normal $\mathbf{n}$ is given by $\mathbf{F}(\mathbf{x};\mathbf{n}) = \boldsymbol{\sigma}(\mathbf{x}) \mathbf{n}$. There's a sensible way to assign a stress -- in this case, a 3x3 matrix -- to each point in the continuum.

Friction and contact forces are macroscopic phenomena arising due to electromagnetic interactions. They depend on the local geometry of the contact surfaces, etc. There's no sensible way to bundle this into a field: the interactions between the bodies are discrete. But at the microscopic level, you are dealing with electric and magnetic field.

Thanks!

 

[Manish_529]

All the phenomena you listed are treated differently. For elastic materials, you will learn that we can come up with a stress tensor field $\boldsymbol{\sigma}(\mathbf{x})$, such that the traction (force) on an "imaginary" internal surface in the continuum with normal $\mathbf{n}$ is given by $\mathbf{F}(\mathbf{x};\mathbf{n}) = \boldsymbol{\sigma}(\mathbf{x}) \mathbf{n}$. There's a sensible way to assign a stress -- in this case, a 3x3 matrix -- to each point in the continuum.

Friction and contact forces are macroscopic phenomena arising due to electromagnetic interactions. They depend on the local geometry of the contact surfaces, etc. There's no sensible way to bundle this into a field: the interactions between the bodies are discrete. But at the microscopic level, you are dealing with electric and magnetic field.

Please correct me if I am wrong. In the real world, aren't all the solid bodies elastic or show deformations, and it's only due to the rigid body approximation that we neglect the deformations of a body in classical mechanics?

 

[Manish_529]

All the phenomena you listed are treated differently. For elastic materials, you will learn that we can come up with a stress tensor field $\boldsymbol{\sigma}(\mathbf{x})$, such that the traction (force) on an "imaginary" internal surface in the continuum with normal $\mathbf{n}$ is given by $\mathbf{F}(\mathbf{x};\mathbf{n}) = \boldsymbol{\sigma}(\mathbf{x}) \mathbf{n}$. There's a sensible way to assign a stress -- in this case, a 3x3 matrix -- to each point in the continuum.

Friction and contact forces are macroscopic phenomena arising due to electromagnetic interactions. They depend on the local geometry of the contact surfaces, etc. There's no sensible way to bundle this into a field: the interactions between the bodies are discrete. But at the microscopic level, you are dealing with electric and magnetic field.

Also, how do we measure the strength and flux of this field? Like in the usual gravitational/electric fields, we get the strength by dividing the force of the field by a scalar quantity like mass/charge, depending on the field. And secondly, can this field exist independently, like a gravitational field exists independent of the presence of any particle to act on and so does the electric field??