1. The problem statement, all variables and given/known data An AFM tip has a spring constant k, a colloidal bead with radius r is glues onto the cantilever tip. Derive an expression and plot the deformation of the cantilever spring, Δx, as a function of distance the tip of the cantilever is moved towards another bead of the same radius. 2. Relevant equations The cantilever tip can be treated as a Hookean spring. So Fspring = -kΔx The non-retarded Van der Waals interaction free energy between two spheres of the same radius is: W = -AR/(12D) where D is the distance between the spheres, R is the radius of the spheres, and A is the Hamaker constant. The Van der Waals force is simply the derivative of the potential w.r.t. D: Fvan = AR/(12D2) 3. The attempt at a solution The question seems fairly straight forward. At equilibrium, Fspring = Fv, so -kΔx = AR/(12D2) we can say D is the distance the cantilever tip is manual moved (z), plus the distance the spring is stretched because of VDW interaction. -kΔx = AR/(12(z+x)2) For some reason, I can't solve for Δx as a function of z. I feel like I'm missing some trivial step, and would appreciate any help with a solution. Thanks in advance.