Using a computer to solve Physics problems
The computer is really good at arithmetic, so we want to reduce the problem to an arithmetic problem before we give it to the computer.
P 104 page 161
First we draw the free body diagram:
Then the sum of the forces in the xdirection (horizontal) is: F_{s}  Tsinq = 0,
While in the vertical (y) direction we have: Tcosq  mg = 0.
Now we eliminate the unwanted unknown T:
tanq = F_{s}/mg
Finally we find the spring force using the relation F_{s} = ks where s is the stretch, s = Ll and from geometry,
L=2llsinq .
Thus s = l(1sinq ). Now we can set up a spreadsheet program with the following columns:
theta (rad) 
sinq 
tanq 
Fs=kl(1sinq ). 
Fs=mgtanq 
0 




.1 




.2 




The correct value of q is the one that makes the values in the last two columns equal. We can also find the solution by plotting a graph showing the curves f(q ) = kl(1sinq ) and g(q ) = mgtanq and finding the intersection.