(1). The weight of an object can be found using

\[w = m \times g\]

where,

\(w = \text{weight }(N)\)

\(m = \text{mass of the object (kg)}\)

\(g = \text{gravity }\left( \text{m/sec}^{2} \right)\)

Write an m-file to find the weight of a 30 kg Martian on earth (g=9.8 m/sec2) and on Mars (g=3.7 m/sec2). Make sure to suppress intermediate outputs and write comments in the m-file.

  

(2). You are asked to find the volume of a cylindrical storage tank. You know that the interior diameter is 3 feet and the length is 5 feet. Write a MATLAB m-file that finds the volume of this tank. Your boss needs the Command Window to look nice, so be sure to suppress intermediate outputs and only show the final answer in the Command Window.

  

(3). Congratulations! You’ve just been hired at The Pressure is on Us, Inc. Your first assignment is to write a MATLAB program that finds the pressure inside a cylindrical storage tank. You know that the tank has a 2.15 m interior diameter and is 4.55 m in length. You also know that the tank will hold 215 kg of an ideal gas at 400 K. The pressure in the tank can be found using:

\[p = \frac{mRT}{V}\]

where,

p is pressure (Pa)

m is mass (kg)

V is volume (m\(^3\))

T is temperature (K)

R is the ideal gas constant, \(287.05\ \displaystyle\frac{\text{N}\cdot \text{m}}{\text{kg}\cdot \text{K}}\)

Follow the expected rules of display of Command Window and comments in m-file.

  

(4). A 12-volt battery and a switch are placed in parallel with the primary windings of a transformer. The secondary windings are placed in parallel with a resistor (See Figure A). Find the current traveling through the resistor after the switch is closed.

You may use

\(\displaystyle\frac{n_s}{n_p} = \frac{V_s}{V_p}\), and \(\displaystyle I = \frac{V}{R}\)

where,

\(n_s=\text{number of secondary windings}\)

\(n_p=\text{number of primary windings}\)

\(V_p=\text{primary voltage (V)}\)

\(V_s=\text{secondary voltage (V)}\)

\(I=\text{current (A)}\)

\(R=\text{resistance}\ (\Omega)\)

Figure A: Electrical Schematic for Exercise 4.

  

(5). The applied normal stress on an object is, in general, defined as the force acting on the object divided by the area the force is acting on. Assuming that a force, \(F = \text{252.2 lbs}\) is acting in the direction as shown (see Figure B), find the normal stress in the body that has the top cross-sectional area of \(a = 2\text{ i}\text{n}^{2}\).

figure22e_stress

Figure B: Object with a force acting on its top face.

  

(6). When a normal axial load is applied to a thin plate with a hole, the nominal stress at the hole is amplified by a factor called the stress concentration factor, \(k_t\). The maximum stress \(\sigma_{\max}\)is given by

\[\displaystyle\sigma_{max}=k_t\sigma_{nom}\]

where,

\(\sigma_{max} =\) the maximum stress in the body,

\(k_t =\) the stress concentration factor

\(\sigma_{nom} =\) the nominal stress.

For a thin plate with a center hole, the stress concentration factor \(k_t\) is

\[k_{t} \approx 3.0039 - 3.753\frac{D}{W} + 7.9735\left( \frac{D}{W} \right)^{2} - 9.2659\left( \frac{D}{W} \right)^{3} + 1.8145\left( \frac{D}{W} \right)^{4} + 2.9684\left( \frac{D}{W} \right)^{5}\]

where,

\(W\) is the width of the plate

\(D\) is the diameter of the hole

If a force, \(F\) of 1230 lbs is applied to a thin plate (see Figure C), find the peak stress in the plate. The width of the plate is 30 inches, the diameter of the hole is 1.25 inches, and the plate thickness is 1.25 inches.

figure23e_wholestress

Figure C: Thin plate shown with applied load, F for Exercise 6.

Hint: To find the nominal stress you may use,

\(A_{nom}=(W-D)\times T\)

\(\sigma_{nom}=\displaystyle\frac{F}{A_{nom}}\)