Is it possible to express friction force as a tensor?

[Digital_lassitude]

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

 

[fresh_42]

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?

 

[Chestermiller]

Isn't friction force a vector, which is already a first order tensor?