Question

A ladder of mass m = 15 kg and length L = 2.0 m leans at an angle theta = 30 degree against frictionless wall. Coefficient of friction between ladder and grand is mu = 0.40. draw diagram of all forces acting on ladder calculate magnitude of each force max angle such that ladder will not slip?

Answer 1

mass = 15 kg length = 2.0 m theta = 30 degree mu = 0.40 figure shows all forces acting on the ladder in equilibrium position means not sliding total there are forces acting on ladder. at point A: - N_A is normal force only flow on ladder mu F_n as ladder tend to slide towards -ve X axis to friction force will act on +ve X axis direction w = mg will acting vertically downwards will break into w sin theta and w cos theta at point B: - wall is frictionless so no force will act on that N_B will be normal force by will Now in equilibrium position Sigma F_X = 0 all forces acting in X direction should be zero \r\n mu F_n - N_B = 0 - 1 Now Sigma F_y = 0 N_A - w = 0 N_A = w = m times g = 15 times 9.8 N = 147 N N_A = 147 N Now from equation 1 mu F_n = N_B