Question

please solve question A, solve part B with Matlab and explain why does part C can not generate graph

5 ft A 1 ft B A) Determine the position x and the tension in the cable that is required for equilibrium. B) Use Matlab or Excel to show how tension in the ABC cable changes by changing the load from 5 lb to 50 lb at 5 lb increments. Generate the following graph and describe your observations: a. Cable tension versus load C) Use Matlab or Excel to show how tension in the ABC cable changes by changing x from 0.5 ft to 5 ft at 0.5 ft increments. Generate the following graph and describe your observations: a. Cable tension versus x-position

Answer 1

M A a 5-X B W

A) Let the rope subtend an angle, $\theta$ with the vertical at equilibrium. If T is the tension in the rope and W is the weight. The force balance in the vertical direction will give

=W Cost

T 2cose

From the

AABM

5 x MB = tane

also

MB 1 tane

5 1+ tane tanf

tan 5-2

so the will be

cos e

cose 2x)21 (5

Putting the value of cos$\theta$ in tension gives

(5 2x)21 T

This is how the tension will depend on the load and the position x.

2T )2 1) = (5 2

this is how the position will vary with load W

B) MATLAB Program to generate the required T versus W graph for a fixed value of x

clc;clear;
x= 1 %% fixed value of x
W = 5:5:50 %%%% variation of weight from 5 to 50 in interval of 5
T = (W/2)*sqrt((5-2*x)^2+1) %%% calculation for tension
plot(W,T)

The Output plot

80 at x 1 70 60 40 30 20 10 F 0 5 15 35 40 45 10 20 25 30 Load 50 415 50 Tension

C) MATLAB Program to generate the required T versus x graph for a fixed value of W

clc;clear;
W = 50; %% fixed value of x
x = 0.5:0.5:5 %%%% variation of x from 0.5 to 5 in interval of 0.5
for i = 1: 10
T(i) = (W/2)*sqrt((5-2*x(i))^2+1) %%% calculation for tension
end
plot(x,T)

Output curve of the program

140 at W 50 lb 120 100 80 60 40 20 0.5 1.5 2 4,5 1 2.5 3 3.5 5 X Tension