01 Jul VECTOR ANALYSIS
Vector Analysis
A. At equilibrium, the ring moves to the center of the force table without touching
the table, with the pin out. (It can touch the top of the center pin.)
a. Mount a pulley on the 0º mark on the force table and suspend a total of
200 grams on it.
b. Mount a second pulley on the 90º mark and suspend a total of 200 grams
on it.
c. Experimentally find the magnitude and position of a third force required
to achieve equilibrium.
d. Assume the masses have 1% uncertainty, and calculate the uncertainty of
your angular position.
B. At equilibrium, the ring moves to the center of the force table without touching
the table, with the pin out. (It can touch the top of the center pin.)
a. Mount a pulley on the 20º mark on the force table and suspend a total of
300 grams on it.
b. Mount a second pulley on the 170º mark and suspend a total of 200
grams on it.
c. Experimentally find the magnitude and position of a third force required
to achieve e quilibrium.
d. Assume the masses have 1% uncertainty, and calculate the uncertainty of
your angular position.
C. At equilibrium, the ring moves to the center of the force table without touching
the table, with the pin out. (It can touch the top of the center pin.)
a. Mount a pulley on the 120º mark on the force table and suspend a total
of 100 grams on it.
b. Mount a second pulley on the 30º mark and suspend a total of 100 grams
on it.
c. Mount a third pulley at 90º with 150 grams on it.
d. Experimentally find the magnitude and position of a fourth force required
to achieve equilibrium.
e. Assume the masses have 1% uncertainty, and calculate the uncertainty of
your angular position.
Analysis:
Note: Though the theory section talks about forces, it is much easier to use the masses
on the hang ers for the magnitudes of the vectors.
1. Sketch the vectors for each setup and show the vector addition graphically. This
does not need to be perfect, but try to get the scales for the vectors and the
angles close to right.
a. These sketches must appear in your informal lab report
2. Calculate the force vectors using the vector addition rules (see the equations
below).
3. Compare the experimentally obtained equilibrium force vector with a calculated
force vector . Calculate the percent difference for both the magnitude and
direction.
4. Give the reasons for the differences between the calculated values and
experime ntally measured ones. Suggest ways to improve the sensitivity of the
apparatus. (DO NOT SAY HUMAN ERROR)
Uncertainty
This is a very difficult lab to do uncertainty on, so were going to cheat a bit on
uncertainty. Were going to ignore the uncertainty propagation in the calculation of the
resultant vector.
a. First of all, create an uncertainty budget with a mass uncertainty for each
mass (both the given masses and the balancing masses).
b. Youll get the same angle uncertainty for all angles, so give it only once.
c. Determine if e ach calculated resultant vector falls within the uncertainty
for your measured resultant vector. Remember to compare both the
magnitude and direction.
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