Block A of mass m rests against the vertical face of block B of mass 2m. B is on a smooth floor and is pulled by a hanging block C through a pulley. The coefficient of friction between A and B is μ. Find the minimum mass of C so that A remains stationary relative to B.

Question

G1 Physics · Accepted Answer

For A not to slide vertically, μN ≥ mg. Since N = ma for horizontal acceleration a, we need a ≥ g/μ. If mass of C is x, the system acceleration is a = xg/(x+3m). Setting x/(x+3m)=1/μ gives x(μ-1)=3m, so xₘᵢₙ = 3m/(μ-1).