A plastic strip, 0.55 m wide and weighing 450 g, moves between two layers of paint. It is sandwiched between two plates with paint layer thicknesses of 4 mm on side A and 6 mm on side B. A force P is applied to move the strip at a constant speed of 4.5 mm/s. The paint has a dynamic viscosity of 7.258 N·s/m$^2$. Neglecting any friction at the top and bottom openings, and assuming a linear velocity profile through each paint layer, determine the force P required to maintain this constant speed.
P
4 mm
6 mm
0.55m