Dynamic Friction between surfaces

Laiva-59

1. The problem statement, all variables and given/known data

We have a body V1, which is in contact over body V2 over a flat (i.e. planar) surface S. (The planar approximation can be considered a good one). Body V1 is moving, V2 is stationary.

A normal force F exists between the bodies at surface S, acting in point P. This force acts along the unit normal vector N.

The body V1 is moving with a body velocity V.

Q: What is the dynamic friction force between V1 and V2?

I think I found the solution, but I'd like a double check. Or a rebuttal with correct answer...


2. Relevant equations

F_friction = mu*F, acting opposed to the relative motion of the surfaces in contact.

3. The attempt at a solution

1. We find the relative speed in the plane S.

As follows:
N = unit normal surface vector in P.
V = body velocity in point P.

U = orthonormal projection of V on plane S. I think this is the speed the surfaces slide over each other. Is this correct?

U = V - (V dot N)N


2. The components of U have dimension [m/s], but as the friction force is independent of speed, we need to normalise vector U. I.e. we only need to know which direction U has.

U_ = U/norm(U) = [U_x,U_y,U_z]


3. The components of the friction force now become

F_friction,x = mu*|F|*U_x
F_friction,y = mu*|F|*U_y
F_friction,z = mu*|F|*U_z