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.