# 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.

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Last revised: March 17, 2000