Is it possible to express friction force as a tensor?

In summary, the conversation discusses the possibility of expressing friction force as a tensor and determining the ranks of the tensors for mass and normal force. It is determined that friction force is already a first order tensor as it is a vector quantity, while the ranks for mass and normal force are unclear. The notation ##m_{ij}## suggests different components in different directions, but the connection between mass and normal force is unclear.
  • #1
Digital_lassitude
1
1

Homework Statement


Consider the equation for the friction force Ff = m FN. is it possible to express the friction force as a tensor? If so, what rank tensor is it, and what are the ranks of the tensor m and the normal force FN?

Homework Equations


Ff = mFN

The Attempt at a Solution

[/B]
So I know friction force is a vector quantity so this one is a rank one vector and so will the normal force. Where I’m confused is when it comes to the mass.

Can I assume that the index must be summed hence making the rank of m 2? Now I’m well aware mass is a scalar quantity, but I’m slightly confuse.

(Ff)_i = (m)_ij * (FN) _j

Can I make that assumption based on the interaction between the mass and the normal force?

Like I know that friction and normal force have different direction, this I must keep this into one direction when solving for the friction force, but I can’t make this connection for some reason
 
Last edited:
Physics news on Phys.org
  • #2
Digital_lassitude said:

Homework Statement


Consider the equation for the friction force Ff = m FN. is it possible to express the friction force as a tensor? If so, what rank tensor is it, and what are the ranks of the tensor m and the normal force FN?

Homework Equations


Ff = mFN

The Attempt at a Solution

[/B]
So I know friction force is a vector quantity so this one is a rank one vector and so will the normal force. Where I’m confused is when it comes to the mass.

Can I assume that the index must be summed hence making the rank of m 2? Now I’m well aware mass is a scalar quantity, but I’m slightly confuse.

(Ff)_i = (m)_ij * (FN) _j

Can I make that assumption based on the interaction between the mass and the normal force?

Like I know that friction and normal force have different direction, this I must keep this into one direction when solving for the friction force, but I can’t make this connection for some reason
What kind of quantity is mass here? Do you have different components in different directions as your notation ##m_{ij}## suggests?
 
  • #3
Isn't friction force a vector, which is already a first order tensor?
 

Related to Is it possible to express friction force as a tensor?

1. What is a tensor and how is it related to friction force?

A tensor is a mathematical object that describes the relationship between different physical quantities. In the context of friction force, a tensor can represent the direction and magnitude of the force exerted between two surfaces in contact.

2. Why is it important to express friction force as a tensor?

Expressing friction force as a tensor allows for a more accurate and comprehensive understanding of the force. It takes into account factors such as the orientation and roughness of the surfaces, which can greatly impact the friction force.

3. Can friction force be expressed as a scalar instead of a tensor?

No, friction force cannot be expressed as a scalar because it is a vector quantity with both magnitude and direction. A scalar only has magnitude and does not take direction into account, which is crucial in understanding friction force.

4. Are there any limitations to expressing friction force as a tensor?

While using a tensor to express friction force is more accurate, it can also be more complex and difficult to calculate compared to using simpler models. It may also require advanced mathematical concepts and tools.

5. How is a tensor for friction force calculated?

The tensor for friction force is calculated using the principles of solid mechanics and contact mechanics, taking into account factors such as surface roughness, material properties, and the applied load. It can also be determined experimentally through friction force measurements.

Similar threads

Dependence of the stress vector on surface orientation
    • Advanced Physics Homework Help
Replies
4
Views
1K
Mechanical Physics: Coefficient of Friction
    • Introductory Physics Homework Help
Replies
20
Views
2K
Normal force at the base of a ladder
    • Introductory Physics Homework Help
Replies
20
Views
374
For the friction formula when to use Fn(normal force)×mu and when F×mu
    • Introductory Physics Homework Help
Replies
17
Views
656
The Work of Friction: Explained in .32m
    • Introductory Physics Homework Help
Replies
8
Views
937
Finding Radial Force from Free Body Diagram
    • Introductory Physics Homework Help
Replies
4
Views
1K
Coefficient of Friction when Normal Force is Reduced [HS]
    • Introductory Physics Homework Help
Replies
5
Views
1K
Help Me Solve This Khan Academy Question: Friction and Initial Velocity
    • Introductory Physics Homework Help
Replies
5
Views
4K
I Transmission of torque using friction
    • Mechanics
Replies
32
Views
857
B How come friction can make a car turn?
    • Mechanics
Replies
10
Views
1K

Hot Threads

Recent Insights

Back
Top