Tutorial: Flat & Belt Friction P8.133 Engineering 25 Tutorial: Flat & Belt Friction P8.133 Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu

P8-133 → SelfSupporter The uniform 50-lb plank beam is supported by the rope which is attached to the end of the beam, wraps over the rough peg, and is then connected to the 100-lb block. If the coefficient of static friction between the beam and the block, and between the rope and the peg, µs = 0.4, determine the maximum distance that the block can be placed from A and still remain in equilibrium. Assume the block will not tip.

FBD Templates

MATLAB Results Enter Plank Wt, Wp = 50 Wp = 50 Enter Block Wt, Wb = 100 Wb = 100 Enter Plank Length, WL = 10 WL = 10 Enter CoEff of Static Friction, us = .4 us = 0.4000 the distance d = 4.6340

MATLAB Code % Bruce Mayer, PE % ENGR36 * 25Nov12 % ENGR36_Flat_n_Belt_Friction_Balance_H13e_P8_133_1211.m % The uniform Plank beam of Wt Wp is supported by the rope % which is attached to the end of the beam, wraps over the % rough peg, and is then connected to the Block of Wt Wb % If the coefficient of static friction between the beam & % the block, and between the rope and the peg, µs = 0.2, % determine the maximum distance that the block can be % placed from pt-A and still remain in equilibrium. % * Assume the block will not tip. % % See paper analysis for solution % User to Enter Parametric values Wp = input('Enter Plank Wt, Wp = ') Wb = input('Enter Block Wt, Wb = ') WL = input('Enter Plank Length, WL = ') L = WL/2; % L is the half-length us = input('Enter CoEff of Static Friction, us = ') % calc 90° angle-of-wrap in Rads beta = pi/2; % use formula to Calc d d = (L/Wb)*(Wp + 2*us*Wb/exp(us*beta)); disp(' ') disp('the distance d = ') disp(d)