Reference no: EM131684519
Assignment -
Write one MATLAB program and make use of the MATLAB's menu command that creates three (3) interactive menu buttons to solve the following 3 problems.
Problem 1: A truss is a structure made of members joined at their ends. For the truss shown in the figure, the force in the 9 members are determined by solving the following system of 9 equations (attached):
![342_figure.png](https://secure.expertsmind.com/CMSImages/342_figure.png)
Write the equations in matrix form and use MATLAB matrix to determine the forces in the members. A positive force means tensile force and a negative force means compressive force. Display the results in a table where the first column displays the member name, the second column displays the corresponding force, and the third column shows the type of tensile or compressive force.\
Problem 2: A ball thrown up falls back to the floor and bounces many times. For a ball thrown up in the direction shown in the figure, the position of the ball as a function of time is given by:
x = vxt y = vyt z = vzt- ½gt2
The velocities in the x and y directions are constants throughout the motion and are given by vx = v0sin(θ)cos(α) and vy = v0sin(θ)sin(α). In the vertical z direction the initial velocity is vz = v0cos(θ), and when the ball impacts the floor its rebound velocity is 0.8 of the vertical velocity at the start of the previous bounce. The time between bounces is given by tb = (2vz)/g, where vz is the vertical component of the velocity at the start of the bounce. Make a 3-D plot (shown in the figure) that shows the trajectory of the ball during the first five bounces. Take v0 = 20 m/s, θ = 30o, α = 25o, and g = 9.81 m/s2.
![1322_figure1.png](https://secure.expertsmind.com/CMSImages/1322_figure1.png)
Problem 3: The flow Q (m3/s) in a rectangular channel is given by the Manning's equation:
Q = kdw/n(wd/w+2d)2/3√S
where d is the depth of water (m), w is the width of the channel (m), S is the slope of the channel (m/m), n is the roughness coefficient of the channel walls, and k is a conversion constant (equal to 1 when the units above are used). Make a 3-D plot of Q (z axis) as a function of w (x axis) for 0 ≤ w ≤ 8 m, and a function of d (y-axis) for 0 ≤ d ≤ 4 m. Assume n = 0.05 and S = 0.001 m/m.
![325_figure2.png](https://secure.expertsmind.com/CMSImages/325_figure2.png)
Attachment:- Assignment File.rar