Original Post
Say you have two beams at different height and a plank with length L and a centre of gravity that is fL where f is a fraction. Both the beams have variable coefficients of friction, u1 and u2. How can i figure out the angle of the plank where it starts to slip? Heres what I have so far: The mass needs to be distributed across the two beams. So beam one has (1 - f)*mass resting on it and beam two has f*mass resting on it. The maximum static friction forces are given by u1*mgcos(theta) and u2*mgcos(theta) for each of the beams, where m depends on the beam (as above). The force pulling in the other direction is mgsin(theta). So the the system slips when mgsin(theta) > u1*mgcos(theta) + u2*cos(theta) So that means I have to differentiate somehow to get the maximum value for theta. Am I on the right track or missing something completely?