Pulley Problem

ES 301 Assignment 1

Work Problem 2.65 on Page 44 in Beer and Johnston Statics, sixth edition in the usual way. Draw two force triangles, one for each of the two solutions and derive the two expressions for tension P as a function of weight w and the angles alpha and beta. Use the symbols p1 and p2 for the two forces. Then, using either Notepad in Windows 95 or Emacs in Unix, write a Matlab program to find the angle alpha and tension p for the angle beta ranging from 5 to 25 degrees in 5-deg intervals. Also, plot both of the values of tension vs. the angle beta and include a title and labels as shown in the figure below. Be sure to program your name, date, and subject with lines such as:

    % print the results
    fprintf('\n   Pulley Problem 2.65')
    fprintf('\n   Your name, ES 301, ')
    disp(date)

(Use the word date rather than the actual date in the disp command.) Put these three lines at the end of your program, just before the lines that print the table. Define the scalar weight, w, in newtons by putting in the mass in Kg and multiplying by 9.81. Also define the conversion factor, dtor (degrees to radians) to convert angles from degrees to radians (pi/180). Since you will need the sine of beta more than once, define the vector sinebeta too. Also, be sure to use vectors for angles alpha and beta and the two resultant tensions, p1 and p2. Don't use a loop to define the vector beta or any other vector; just use a single statement. Define beta with the Matlab statement:

      beta = 5:5:25;

Write two, one-line expressions, p1 and p2 for the two resultant tensions. Since the vectors alpha and beta are both be in the denominator, you need to use ./ for division. The formula starts like this:

      p1 = w * sinbeta ./

Use the Matlab fprintf command in a loop with the f format to control the number of displayed digits. Remember, the first number after the % is how wide a column to use for the number, while the number after the point is how many digits appear after the decimal point. For example:

      for i = 1:length(beta)
         fprintf('  %2.0f  %3.0f  %6.1f

to create a table that starts like this:

      Beta  Alpha  Tension  Alpha    Tension
       Deg   Deg     N       Deg       N
   1    5    80.0   527.2   -80.0    1557.6
   2   10    69.7   539.9   -69.7    1521.1

Be sure the units are shown. Don't use the Tab key. Use one plot command like:

      plot(beta,p1,beta,p2)

and use the grid, title, xlabel, and ylabel commands. Also use the gtext command to label the two curves as in the figure. Run your program in Matlab and check that your answer for beta = 20 matches Problem 2.65. Copy the output data from the screen and paste it into the bottom of your source program. Adjust the number between the % and . in the fprint statement to align the decimal points and give no more than one digit past the decimal point. Print your source program with the appended output. Make a cover page describing the problem and showing the calculations. Staple the cover page and printout of your source code.

Pulley plot

Last revised: March 17, 2000