Question

The roller in the figure below weighs 400 lb. The coefficient of friction is assumed to be the same at all sliding surfaces. a) Find the value of P which causes impending pivoting motion of the roller about the edge of the step. b) Find the minimum value of u if the roller is to pivot about the edge rather than slide in the position shown. 20° 10 in- in

Answer 1

The detailed solution is given below:

Given: W= 40016 / D= loin (AC= Rin . ppsinzoo Pcos200 co nown sino = A= # In A OAB → OA = OC-AC = $_2 = 3in1 → OB = L = sin >> AB = V0B)? (OAJ? = Ain Figo Freebody diagram OB → 0 = 36.90 #(35) Mg = 0; [EA = 50+0A = f + Ossino ] -(PCos 20°) xEA — (PSin2oº )x AB +W X A8 = 0 -( PCosco) x(5 +5sin 36.9") –(psinzo")x(4) +(400)x(4) =0 —P(7.5195) - P(1368) +1600 = 0 .: P = 180167 [Assuming, the friction force is large enough to prevent sliding ] #(0)5 M = 0;

-(P Cos20°)x 0E + F X OB = 0 – (180 Cos 20°)x 5 + FXS = 0 " E = 16916 (Friction force) # (49) < Fy = 0; Psün20°-W + Ff CoS O + N sino = 0 180 sinzo – 400 + 16900536.9°+ N Sºn36.99=0 .: N = 338.576 (Noomal force) # Ę = UN → la FE 169 = 0.419 N 338.57 .: M = 0.499