Dynamic Friction between surfaces

[Laiva-59]

Homework Statement

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...

Homework Equations

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

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

 

[KataKoniK]

I think your solution is correct. The formula you have used for the friction force is the correct one, where mu is the coefficient of friction (which can vary depending on the materials in contact). The direction of the friction force will always be opposite to the direction of motion, so your calculations for the components of the force are also correct. However, I would recommend double checking your calculations to ensure that your final answer is correct. Also, keep in mind that the coefficient of friction can sometimes be a range of values, so you may need to use the average or maximum value depending on the situation. Overall, it seems like you have a good understanding of the problem and have used the correct approach to find the solution. Good job!