PASCO ME-9502 Statics System - Manual (Page 26)

S t a t i c s S y s t e m E x p . 4 : T o r q u e — P a r a l l e l F o r c e s
®
22 012-12876B
Procedure: Equal Distance, Equal Mass
Position one of the protractors near one end the beam and tighten its thumbscrew to hold it in place. Adjust the
position of the other protractor until the beam is perfectly balanced, and then tighten its thumbscrew to hold it in
place.
1. Measure d
1
and d
2
, the distances
from the pivot to the center of each
protractor.
• d
1
= _______________
• d
2
= _______________
2. Add a 50-gram mass to each mass
hanger.
• Is the beam still balanced?
3. Add an additional 20-gram to one of the mass hangers.
• Can you restore the balance of the beam by repositioning the other protractor and mass hanger?
Procedure: Unequal Distance, Unequal Mass
Position one of the protractors approxi-
mately halfway between the pivot point
and the end of the beam and tighten its
thumbscrew to hold it in place. Add 75
grams of mass to the mass hanger, M
1
.
Place various masses on the other mass
hanger (M
2
) and slide it along the beam
as needed to rebalance the beam.
1. At the first balanced position, measure the total mass, M
1
and M
2
, on each side of the pivot (protractor, mass
hanger, added masses) and record the masses in the data table.
2. Measure the distances, d
1
and d
2
, between the centers of the protractors and the pivot and record the values in
the data table.
3. Take measurements for five more different values of M
2
and record your results in the data table. Be sure to
include the units of your measurements.
4. If there is time, vary M
1
and repeat the procedure.
• Reminder: For accurate results, include the mass of the protractor, mass hanger, and added masses when mea-
suring M
1
and M
2
.
Calculations
Calculate the gravitational force (weight = mg) produced by the total mass on each side of the beam for each case.
Calculate the torques,

1
and

2
, on each side of the beam for each case. Remember, torque,
, is the cross product
of the net force and the lever arm. Since the distance and the direction of the force are at right angles in this exper-
iment, the torque,
, is F d (where F
g
= mg). Record your calculated values of weight, F
g
, and torque,
, for each
balanced position of the beam.
d
1
d
2
M
1
M
2
Figure 4.4: Measuring Torques
center of
protractor 1
center of
protractor 2
pivot
M
1
M
2
d
1
d
2
Figure 4.5: More Torques
center of
protractor 1
pivot
center of
protractor 2