FORCE  TABLE   (VECTORS)  for PhysMoVan  Students
                                  (Prof. Julia Thompson, May 3, 2003)

Vectors are all around us, and important  for making many things in our lives work.

A few examples are:

   Holding up bridges, so they don’t fall down. 

   A  wheel  rolling down an incline.

   Planes or boats travelling in an air or water current.


With  this force table we can study vectors, and learn a little about  them.  We will also 
learn about  how to calibrate equipment, and about drawing graphs.  This lab can be done
in two ways.  The first way assumes that students have already learned trigonometry.  The
second does not.   But to begin with, both ways are the same. 

Step 1:  Calibrate your springs.  Adjust them so that they read zero when no force is applied.
Then,  put the one marked  “1”  along zero degrees, and the one marked “2” opposite it.
Secure the “1”,  and pull  “2”  until  they balance.  Pull until  “1”  reads 100 g,  200 g,  300 g,
and 400 g. Make a table of the results.  Now do the same thing  for “1” and  “3”. 
Read the values on the springs as well as you  can and put down  your  estimate of  the uncertainty.
In order to complete the lab,  you will  need this uncertainty.   You can judge the uncertainty
Either by re-doing a measurement, or by having first you, then your partner make the measurement.
Be czreful  of  “parallax”,  which is the effect that if you tilt your head at different angles, you may
find that the value of the reading changes.

Step 2:  If  the vectors are all at equal angles from each other (in our case 120 degrees), and the system 
is in equilibrium,  the magnitudes of  the vectors will  be equal.    (Those of you who have had 
trigonometry can prove this; others may be able to think it makes sense using  the idea of 
“symmetry”… if one is larger than the others, which one could it be?  Check this configuration for your 
setup.  Does the  conclusion hold?  Be sure to take uncertainty in your readings into account, and also, 
if necessary, your calibration curves: it may be that 150 g. on one spring  corresponds to 152 g  (eg) on 
another spring.

Step 3:  Put one spring at zero  degrees, and put the other two at +/- the same angle wrt. 180 degrees. 
(We would try putting them both at 180 degrees next, but the springs are too bulky, and won’t fit).
Here is where the students who have had trigonometry and have not will do something different.  One 
can show, using trigonometry, that if A is along  zero degrees, then B and C should  have equal values.
(if  you have had trigonometry,  your instructor will  work with you to show this).  But both  groups 
can check this result as in Step 2, again taking your calibration curves and uncertainties into account.

Step 4:  If  you have had trigonometry,  you can show that A = 2 B cos(theta),  where theta is the angle 
between B and 180 degrees.   If you have not had trigonometry,   you can still use the formula, and  
your instructor will help you find the cosine of  theta.  Check this condition as in steps 2) and 3),  again 
taking  your uncertainties  (in both the angle and magnitudes of the vectors) into account.

Step 5:  DID IT WORK?  CONGRATULATIONS?  IF NOT… RECHECK YOUR CALIBRATION 
CURVES,  MEASUREMENTS,  AND UNCERTAINTIES! ( it will work in  the end, if you get them 
rigtht)