1. Tutorial: Flat & Belt Friction P8.133
Engineering 25
Tutorial: Flat & Belt Friction P8.133
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer

2. 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.

3. FBD Templates

7. 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

8. 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)