Consider the stability of a ladder of mass m and length L leaning against a wall
ID: 1365257 • Letter: C
Question
Consider the stability of a ladder of mass m and length L leaning against a wall as shown in the figure below. A painter wants to be sure the ladder will not slip across the floor. He knows that the frictional force exerted by the floor on the bottom end of the ladder is needed to keep the ladder in equilibrium, and he also knows that the coefficient of static friction between the ladder and the floor mu_sf = 0.74. Assume there is friction between the vertical wall and the ladder, with mu_sw = 0.24. Find the angle phi at which the ladder just begins to slip.Explanation / Answer
Taking moment about the point where the ladder sits on the floor and using N1= mu*N2= mu*W
mu*W * L*sintheta = W*(L /2)*costheta
mu*tantheta = (1 /2)
tan theta = 1/( 2mu)
theta = tan^-1(1/2*0.79)
theta = 32.33 degree