Question 1:
The capacitance of two parallel conductors of length L and radius r, separated by a distance d in air, is given by
C = Π∈L/ln[(d-r)/r]
where c is the permittivity of air (∈ = 8.854x 10-12 F/m).
Write a script file that accepts user input for d, L, and r and computes and displays C. Test. the file with the values L=1m, r= 0.001 m, and d =0.004 m.
Question 2:
Write a function that accepts temperature in degree Fahrenheit(0F)and computes the corresponding value in degrees Celsius (0c). The relation between the two is
T0C = 5/9(T0F - 32)
Be sure to test your function.
Question 3:
The height and speed of a projectile (such as a thrown ball) launched with a speed of u0 at an angle A to the horizontal are given by
h(t) = vot sin A - 0.5 gt2
v(t) = √(v2o- 2vogt sinA + g2t2)
where g is the acceleration due to gravity. The projectile will the ground when h(t) = 0, which gives the time to hit thit= 2(u0/g) sin A.
Suppose that A. 300, u0 = 40 m/s, and g = 9.81 m/s2. Use the MATLAB relational and logical operators to find times when
a. The height is no less than 15 rn.
b. The height is no less than 15 m and the speed is simultaneously no greater than 36 m/s.
c. The. height is less Man 5 m or the speed is greater Man 35 m/s.
Question 4:
Figure P20 shows a mass-spring model of the type used to design packaging systems and vehicle suspensions, for example. The springs exert a force that is proportional to their compression, and the proportionality constant is the spring constant k. The two side springs provide additional resistance if the weight W is too heavy for the center spring. When the weight W is gently placed, it moves through a distance x before coming to rest. From statics, the weight force must balance the spring forces at this new position. Thus
W=k1x if x
W=k1x+2k2(x-d)if x≥d
These relations can be used to generate the plot of x versus W.
a. Create a function file that computes the distance x, using the input parameters W, k1, k2 and d. Test your function for the following two cases, using the values k1 = 104 N/m; k2 =1.5 x 104 N/m; d =0.1 m.
W=500 N
W=2000 N
b. Use your function to pot x versus W for 0 ≤ Ws ≤ 3000 N for the values of k1. k2, and d given in part a.
Question 5:
We want to analyze the mass spring system discussed in Problem previous problem for the case in which the weight W is dropped onto the platform attached to the center spring. If the weight is dropped from a height h above the platform. we can find the maximum spring compression x by equating the weight's gravitational potential energy with the potential energy stored in the springs. Thus
W(h+x) = 1/2k1x2 if x< d
which can be solved for x as
x = [W ± √(W2 + 2k1Wh)]/k1 if x < d
and
W(h+ x) = 1/2k1x2 + ½(2k2(x - d)2 if x ≥ d
which gives the following quadratic equation to solve for x: (k1 + 2k2)x2 - (4k2d + 2 W) + 2k2d2 - 2 wh =0 if x ≥ d
a. Create a function file that computes the maximum compression x due to the failing weight. The function's input parameters are k1, k2,d, w and h. Test your function for the following two cases, using the values. K1
= 104 N/m k2 = 1.5 x 104 N/m; and d = 0.1 m.
W=100 N h=0.5 m W =2000 N h =0.5 M
b. Use the function file to generate a plot of x versus h for 0 ≤ h ≤ 2 m. Use w = 100N and proceeding values for k1, k2, k3 and d.
Question 6:
Engineers often need to estimate the pressures and volumes of a gas in a container. The van der Waals equation is often used for this purpose. It is
P = RT/V' - b = a/v'2
where the term b is a. correction for the vokene of the molecules and the term a/v^2 is a correction for molecular attractions. The gas constant is R, the absolute temperature is T, and the gas specific volume is V^. The value of is the same for all gases; it is R = 0.08206 L.atm/mol-k. The values of a and b depend on the type C4 gas. Some values are given in the following table. Write a user defined function using the switch structure that computes the pressure P on the basis of the van der Waals equation. The function's input arguments should be T, V^, and a string variable containing the name of a gas fisted in the table.
Test your function for chlorine (C12) for T= 300 K and V^= 20 Land.
|
Gas
|
a(L2-atm/mol2)
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b(L/mol)
|
|
Helium, He
|
0.0341
|
0.0237
|
|
Hydrogen, 112
|
0.244
|
0.0266
|
|
Oxygen. 02
|
1.36
|
0.0318
|
|
Chlorine, Cl2
|
6.49
|
0.0562
|
|
Carbon dioxide. CO2
|
3.59
|
0.0427
|