The critical buckling length for a column under its own weight, with mass density , area A, and moment of inertia I, is given by the formula
Say this buckling mode limits the weight of collars that can be stacked on a drill bit in a drill string. Determine the maximum force that the weight of stacked collars can exert on a drill bit, without the string of collars buckling. Take the steel collars to have an outer diameter of 7 in. and an inner diameter of 2.81 in.