Dynamic Friction between surfacesby Laiva59 Tags: amontons' law, contact surfaces, coulomb, dynamic, friction 

#1
Jul511, 07:45 AM

P: 6

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 


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