A 200lb weight W is bang hung from the end of a rigid 8ft ho

A 200-lb weight W is bang hung from the end of a rigid 8-ft horizontal beam of negligible weight as shown. The beam is attached to a wall by a pivot and is supported by an 8-foot long cable that is also attached to the wail at a higher point. The tension in this cable is given by the equation T = W L_c L_b/d Squareroot L_c^2 - d^2 where T is the tension in the cable, W is the weight, L_c is the length of the cable, L_b is the length of the beam, and d is the distance along the beam at which the cable is attached. Write a MATLAB code to determine distance d where the cable should be attached to die beam such that the tension T in the cable is minimized. To do this, the program should ask the user to input the weight W. lengths L_c and L_b, then calculate the tension T at regular 0.01-ft intervals for 1\' lessthanorequalto d lessthanorequalto 7\'. The program should then locate the position d that produces the minimum tension and display the result using fprintf. Also the program should plot the tension T as a function of d with appropriate title and axis labels.

Solution

Matlab codes are as follows-

%the value of d is 5.66

W=input(\'enter the weight\');
Lb=input(\'enter the length of the beam\');
Lk=input(\'enter the length of the cable\');
d=1:0.01:7;
T=W*Lk*Lb./(d.*((Lk^2-d.*d).^(1/2)));
k=1;
for i=2:601
   if(T(k)>T(i))
   k=i;
   end
end
fprintf(\'the value of d is %f \ \',d(k));
plot(d,T);
xlabel(\'distance along the beam\');
ylabel(\'Tension in the cable\');
title(\'Tension v/s distance\');