Using Matlab In case the pictures arent showing correctly Pa

Using Matlab

In case the pictures aren\'t showing correctly

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A train leaves Philadelphia traveling towards DC at 62 mph. A train leaves DC traveling towards Philadelphia traveling at 85 mph. Washington DC and Philadelphia are 140 miles apart. How far from Philadelphia are the trains when they meet? Write a program that solves the above problem by creating a matrix equation. Call your function file ELEE2040_ps8_ql_lastname.m. Truss System. The following figure shows a truss system supporting the three loads indicated by arrows. The truss system is supported by a fixed point at D and a rolling support at F. Each truss supports a force along its axis and the problem is to find the force along each truss. The truss is assumed to not be moving, so all forces must balance at every point. At each intersection, two equations can be written for the balance of forces in the x and y directions. Furthermore, we assume that all forces are compressive forces, i.e. towards the intersection point. Intersections A, B, C, and E contribute two constraint equations each. Because D is a fixed point, the support provides forces in the horizontal and vertical direction that balance the truss forces; thus including the equations at D would provide two additional constraint equations but also two additional unknowns so we don\'t include the constraint equations at intersection D. Similarly, for the vertical direction at F, there are forces from the support, and we don\'t include this constraint equation. Thus there are 9 equations and 9 unknowns and the force in each truss can be found. The nine equations are From point A (vertical) 1/2 F_1 + 1/2 F_2 = 15000 N

Solution

A=zeros(9,9);
A(1,[1 2])=[1/2 1/2];
A(2,[1 2])=[sqrt(3)/2 -sqrt(3)/2];
A(3,[4 5 1])=[sqrt(3)/2 sqrt(3)/2 -1/2];
A(4,[4 5 1 3])=[1/2 -1/2 -sqrt(3)/2 -1];
A(5,[6 7 2])=[sqrt(3)/2 sqrt(3)/2 -1/2];
A(6,[6 7 2 3])=[1/2 -1/2 sqrt(3)/2 1];
A(7,[5 6])=[sqrt(3)/2 sqrt(3)/2];
A(8,[8 5 9 6])=[1 1/2 -1 -1/2];
A(9,[7,9])=[1/2 1];

b=zeros(9,1);
b([1 3 5],1)=[15000 5000 5000];
F=A\\b

%output

F =

1.0e+004 *

    1.5000
    1.5000
   -0.5774
    1.4434
    0.0000
   -0.0000
    1.4434
   -0.7217
   -0.7217