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 x-direction (horizontal) is: Fs - Tsinq = 0,

While in the vertical (y-) direction we have: Tcosq - mg = 0.

Now we eliminate the unwanted unknown T:

tanq = Fs/mg

Finally we find the spring force using the relation Fs = ks where s is the stretch, s = L-l and from geometry,

L=2l-lsinq .

Thus s = l(1-sinq ). Now we can set up a spreadsheet program with the following columns:

 theta (rad) sinq tanq Fs=kl(1-sinq ). 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(1-sinq ) and g(q ) = mgtanq and finding the intersection.