Assignment #13: More Logic

Transcription

1 Assignment #13: More Logic 12b The height and speed as a function of time of a projectile (such as a thrown ball) launched with an initial speed of 40 at an angle 30 to the horizontal are given by where is the acceleration of gravity, 9.81 m/s 2. The projectile will strike the ground when h(t) = 0, therefor the time to hit is 2 Create an independent vector of times with a one millisecond spacing and the corresponding heights and velocities. Find the times when the height is 15 m or greater and the speed is 36 m/s or less. Report the results with a disp([ ]) sentence. 14a Let E1 and E2 be logical expressions. DeMorgan's laws state that: NOT(E1 AND E2) if and only if (NOT E1) OR (NOT E2) NOT(E1 OR E2) if and only if (NOT E1) AND (NOT E2) Use these laws to find the equivalent expression for each of the following expressions ~( x<10 & x>=6 ) ~( x==2 x>5 ) 14b Use x = 1:11 to verify that each original expression matches your equivalent expression. 15a These expressions are not equivalent, prove using a counter example. For example, if A=5, find values for B and C so that one expression is true and the other false. 1. A==B & (B==C A==C) 2. A==B (B==C & A==C)

2 Assignment #14: If Constructs 17 Rewrite the following statements to use only one if statement. No test run needed. if x < y if z < 10 w = x*y*z end end 18a Write a script that accepts a numerical input value from 0 to 100 and computes a corresponding letter grade. Display the results in a sentence such as: Your score of has earned a grade of B. You may use any grading scale you wish and any series of if statements (nested, sequential, elseifs ). Be sure there are no gaps in the computation, needs to get a grade as well. Show your code and a test run. 20a The diagram below shows a mass-spring model used in packaging systems and vehicle suspensions. The springs exert a force proportional to their compression, with the spring constant k. The outer springs apply additional force when the weight is too heavy for the middle spring. W = k1x W = k1x + 2k2(x-d) if x d if x d Create a function that computes the distance x, based on input arguments for W, k1, k2, and d. Test your function for k1 = 10 4 N/m, k2 = 1.5 ˣ 10 4 N/m, d = 0.1 m, and two possible W values: W = 500 N and W = 2000 N.

3 Assignment #15: Switches and Menues 40 A human player makes the first move against the computer in a game of Tic-Tac-Toe, which has a 3X3 grid of squares. Write a function that chooses a computer response to that first move. The function's input is a number from 1 to 9 corresponding to the human's first in the 3X3 grid of squares. The first column of squares are numbered 1,2,3 (heading down), the second column are numbered 4,5,6 and the third column 7,8,9. The function's output will be the computers responding first move. Use a switch construction to select the computer's responding first move and output it from the function. 42 The height and speed as a function of time of a projectile (such as a thrown ball) launched with an initial speed of at an angle to the horizontal are given by where is the acceleration of gravity, 9.80 m/s 2. The projectile will strike the ground when h(t) = 0, therefor the time to hit is 2 Write a script that uses a menu and a switch so the user can choose to compute and report one of the following three pieces of information: The maximum height, the minimum velocity, or the time to hit.

4 Assignment #16: Menu & Lookup Computations 41 The table below give the approximate values of the static coefficient of friction µs for various contacting surfaces. To start a weight W moving on a horizontal surface, you must push with a force F, where F = µsw. Write a script that has a cell array containing a column for the contacting material descriptions and another column for the friction coefficients. Use input() to allow the user enter the weight W and a menu() for them to select the contacting materials. The script should echo the contacting materials to the screen as well as the required force to get the weight moving. Should be done without a switch or if statement. Contacting Materials µs Metal on metal 0.20 Wood on wood 0.35 Metal on wood 0.40 Rubber on concrete Engineers sometimes use the van der Waals equation shown below to estimate the pressures and volumes of gasses in containers. P is the pressure in atmospheres, R is the universal gas constant L-atm/mol-K. T is the absolute temperature in Kelvin, and is the specific volume L/mol. a and b are adjustments that depend on each gas's molecular attraction and molecular size. The table below shows the adjustment constants for various gasses. Gas Symbol Attraction (a) Size (b) (L 2 -atm/mol 2 ) (L/mol) Helium He Hydrogen H Oxygen O Chlorine Cl Carbon dioxide CO Write a script that contains a 5x4 cell array with the text and data for the 5 gasses. Use input() to collect entries for and temperature. Use menu() to allow the user to select the gas. Compute the pressure. Test your script for Chlorine with = 20 L/mol at a temperature of 300 K.

5 Assignment #17: For Loops 47 The problem asks you to simulate financial accumulation in bank accounts with regular deposits and a yearly transfer to a CD (certificate of deposit) to earn extra interest. The account starts with a zero balance. The first 12 months of deposits are $300 each month. At the end of each month, add interest to the savings balance of 4% (0.04 divided by 12 months). At the end of each year in which the savings account balance is at least $3000, withdraw $2000 and add it to your CD balance. Each year, the CD balance earns 6% (this will need to be added in before making the Dec 31 transfer so that you don't get interest the same day you add a deposit). Your monthly deposits increase using the following table: Year Monthly Deposits Write a script with all the data loaded into variables (no input() functions needed). The program uses nested for loops to run through the 12 months X 5 years and compute the money accumulated in the savings and CDs. ENGR 6 MATLAB Assignment #18: While Loops 34 Write a script that uses a while loop to determine how long it will take to accumulate 1 million dollars in a bank account if you start with $10,000 dollars and deposit $10,000 at the end of each year. The account pays 6% annual interest.

6 Assignment #19: 2D Plot Chapter 5 2 A marketing engineer at a paint production company is looking to maximize the profitability of the company's efforts by setting the wholesale price. Years of experience and modeling has developed an equation that relates the millions of gallons sold Q to the sales price P. That equation is Q = P. So if we give it away we sell 6 million gallons, and if we charge $6 a gallon, no stores will order it. We have fixed costs of $2.045 million per year and variable costs of: Materials: Energy: Labor: 62 cents per gallon 24 cents per gallon 16 cents per gallon Make a script that generate a vector of the reasonable prices to the nearest cent, computes the net profits, and makes a plot of profit vs. price. The script should automatically add the standard axis labeling, title, name, date, course & college. The script should also scan to get the break-even price points and the max profit price. Edit the plot to add annotation for the break-even & max points and a text box that shows the unique equation and costs data. ENGR 6 MATLAB Assignment #20: Optimization 29a A company has the choice of producing up to four different products with its lathes, grinders, and milling machines. The number of hours on each machine required to produce a product is given in the following table, along with the number of hours available per week on each type of machine. Assume the company can sell everything it produces. The profit per item is also shown. Product Hours available Hours Required Lathe Grinder Milling Unit Profit ($) Determine how many units of each product the company should make to maximize its net profit, and compute the profit.

7 Assignment #21: 3D Plot Chapter 5 36 The electric potential voltage V at a point due to two charges is given by: where and are the charges on the particles in coulombs (C), and are the distances of the charges from the point in question (in meters), and is the permittivity of free space /. Use meshgrid() and mesh() to generate a 3D surface plot showing the voltage over the ranges x 0.25 and y The charges of 2 10 and 4 10 are located at (0.3, 0) and (-0.3,0) respectively. Add all appropriate annotation to the plot.