Lab deck: Multiple
Johann Alcaraz
Mary Regacho
Mariah Barrera
Lab #38: The pit and the pendulum
Purpose
Apparti
Theory
Methods
Data Table
Analysis
Conclusions




To use the Datastudio program to record data and analyze data
To understand the centripetal force in a pendulum
To gain a better understanding of simple harmonic motion
To compare the measured force from that calculated force depending on the
radius and speed of the pendulum
 To measure the centripetal force on a swinging pendulum from tangential speed,
mass, and rad
 To find the source of centripetal force for a pendulum
Centripetal force consists of mass,speed,and radius of
motion.
The theory of this lab is that an object moving in a continues circular path is showing
centripetal force.
Example: Gravity orbiting the Earth; a car going around a curb; a pendulum swinging
back and forth really fast.
The lab group followed this provided set of procedures as
accurately as they could with a few minor changes in that
they repeated a few of the steps. All in all, these
procedures were their guides.
Setup
1.
2.
3.
4.
5.
collect materials and settle at lab deck
organize jobs for each person
read through lab and understand basic concepts
Set up the PASCO Interface and computer and start DataStudio.
Open the DataStudio file: 38 Centripetal Force.ds.
o
The DataStudio file has graph displays of Angular Velocity (rad/s) versus
Time and Force versus Time and a table display of Angular Position. Both
sensors are set to record at 50 Hz and the Rotary Motion Sensor is set to
record at 1440 Divisions/Rotations.
6. Set up the Force Sensor and Rotary Motion Sensor with the Centripetal Force
Pendulum.
7. Measure the mass of the two-piece clamp-on mass and record the mass.
8. Put the Force Sensor cable into the cord clip. Use the brass thumbscrew to attach
the cord clip to the adapter rod and slide the adapter rod into the front center hole
on the Force Sensor. Tighten the Force Sensor thumbscrew onto the adapter rod.
9. Screw the lightweight pendulum rod into the end of the Force Sensor. Secure the
clamp-on mass to the end of the pendulum rod.
10. Measure the length of the pendulum from the axis of rotation (center of adapter
rod) to the center of the clamp-on mass and record the length.
11. Slide the Force Sensor with adapter rod onto the Rotary Motion Sensor shaft.
Tighten the brass thumbscrew on the end of the adapter rod to secure the Force
Sensor.
12. Use a table clamp and rod to mount the Rotary Motion Sensor to the edge of a
table.
13. Connect the Force Sensor and the Rotary Motion Sensor to the PASCO Interface.
14. Adjust the Force Sensor cable in the cord clip so there is about as much cable
looped on one side of the clip as the other.
Procedure
1.
2.
3.
4.
5.
6.
7.
8.
make sure everyone understands their assigned jobs
tare the measuring device
make sure computerist and person handling the experiment are ready
Zero the Force Sensor with the pendulum at rest. Click ‘Start’ to begin recording.
Displace the pendulum about 30˚ from equilibrium and let it go.
Click ‘Stop’ to end data recording after a few oscillations.
copy and paste data from run onto a word document
get ready to perform next step of the experiment
Repeat the procedure for two other angles (e.g., 45˚ and 60˚).
Analyze
9. Examine the graph to determine the maximum force and the maximum angular
velocity.
10. Use the ‘Statistics’ in the table to determine the maximum angular position.
11. Use your results to answer the questions in the Lab Report section.
Item
Mass
Value
.1003 kg
Length
.455 m
Item
Run #1
Run #2
Run #3
Angular Velocity,
max.
1.85 rad/s
2.73 rad/s
4.25 rad/s
Force (measured)
.12 N
.47 N
1.03 N
Angular Position,
max.
1.8544 rad
2.9452 rad
4.5815 rad
Item
Run #1
Run #2
Run #3
Force (calculated)
.156 N
.340 N
.824 N
Percent difference
23 %
38%
25%
Calculation
Fc = mv^2 / r = mr(w^2)
FORCE (Fc) CALCULATED:
Run 1
Fc = (.1003 kg)(.455 m)(1.85^2) = .156 N
Run 2
Fc = (.1003 kg)(.455 m)(2.73^2) = .340 N
Run 3
Fc = (.1003 kg)(.455 m)(4.25^2) = .824 N
% diff = [ |T-A| / A ] 100%
PERCENT DIFFERENCE CALCULATED
Run 1
[ |0.156-0.12| / 0.156 ] 100% =23%
Run 2
[ |0.340-0.47| / 0.340 ] 100% =38%
Run 3
[ |0.824-1.03| / 0.824 ] 100% =25%
LINE GRAPH
Questions
12. How close are the values of the calculated centripetal force and the values of
measured force?
-- They were close, the range of inaccuracy was between 23%-38%
13. Did the force increase, decrease, or stay the same for larger angles of the
amplitude? Why?
-- The force increased with larger amplitudes because more centripetal force is required
to for the pendulum to pass the equilibrium point.
14. What are possible sources of error in this activity?
Possible sources of error in this activity are:
o
o
human error
 stress (w/ deadline)
 drifting into lala land
limitations of equipment
JOHANN'S CONCLUSION
Results
The data indicates that as the centripetal force on the pendulum increases, the
maximum angular velocity also increases. This is shown in that the force increased for
larger angles of the amplitude. Each successive run had in increase in angular
displacement, and the graphs appear to have a greater increasing change in values for
each successive run. Therefore, it is seen that there is a direct relationship between the
three variables.
Purposes
1. To use the Datastudio program to record data and analyze data.
-- This was done in efficiency and proficiency. Datastudio automatically recorded the
data and through analyzation, the results were formed.
2. To understand the centripetal force in a pendulum.
-- I understand that centripetal force in a pendulum leads to its exhibition of simple
harmonic motion (see below).
3. To gain a better understanding of simple harmonic motion.
-- SHM is illustarted in this lab as needing a fixed point, a medium, and a mass (i.e., the
pendulum). Through this, the pendulum is able to swing in the manner that it does.
4. To compare the measured force from that calculated force depending on the radius and
speed of the pendulum.
-- With the use of the equation mr(w^2) with m being the mass, r being the radius,
and w being the angular speed of the pendulum, a simple plug-and-chug / plug-and-pray
was all that was required of this purpose.
5. To measure the centripetal force on a swinging pendulum from tangential speed, mass,
and rad
-- I don't recall doing this with tangential speed. Hmmm...
6. To find the source of centripetal force for a pendulum.
-- In discussion with Mary over the phone, it was decided that acceleration from the point
of displacement as well as the force of tension were sources of the centripetal force. We
decided on the foce of tension rather than weight because centripetal force is inwardseeking, meaning towards the fixed point.
Knowledge
This was definitely the most productive lab. The group got it done efficiently and
proficiently, as I had already mentioned. Outside research was minimal on my part, but
the concept of the lab was grasped by all members of the group. The tasks were divided
up well and everyone worked cooperatively and communicated. Although this was the
third lab experiment done, I think the time availability allowed the group to really make
sense of the procedures and graphs. Consequently, this is by far the most completed lab
write-up out of the four.
Working with two new people was definitely a big change. I've worked with Earnest
Salgado in all the previous labs, and from that, we've established a stable duo together in
lab work, with adjustments to our third lab member. However, we decided to 'spread the
wealth' and part paths. My new group consisted of mary Regacho and Mariah Barrera.
Although communication is again at a loss, we were able to at least meet the basic
minimum level of collaboration. A new change was in for me as well: Mary took on the
"backbone of the lab" - the template, which I am so accustomed to doing. Adaptation was
difficult, but at least 1 out of 4 labs was done completely. Right now however, I'm
wondering when choosing a permanent triad to work and STICK with will come into
play. Changing partners with every lab does not seem to be a very succesful transition for
me.
As completed as this lab seems, I did not go into depth with my analysis. I was focused
on getting it done and moving onto the next. It's true that partial blame goes towards me
and my lack of preparation, but then again, even as an AP class, the lab set was
overwhelming a bit. But then again, when the group is put into consideration, working
smarter is still a MUST-DO on everyone's list.
Mary’s conclusion
Results

The data collected shows that as amplitude is increased, centripetal force also
increased. The force over time plot and angular velocity plot gave sinusoidal graphs
that got bigger from run to run as we increased the amplitude. More force would be
required to pass the equilibrium point at a faster pace, and this would cover a larger
angle. When the angle from where the pendulum was released was large the
amplitude and centripetal force increased along with it.
Purposes
The first purpose was completed by utilizing the Datastudio program and sensors to
record the data.
The second purpose was fulfilled by understanding that the centripetal force, in
simple harmonic motion, keeps the pendulum moving. The greater the centripetal force
the faster the greater the velocity and the larger the amplitude.
The third purpose was not fulfilled because the lab did not unveil new knowledge on
simple harmonic motion.
The fourth purpose was accomplished by answering question number 1. It showed
that we had a range of error between 23%-35%.
The fifth purposed was completed by collecting the data during the experiment
through the Datastudio program and the Pasco sensors.
The sixth purpose was solved by sitting down and actually wondering where the
centripetal force was coming from in a pendulum. My lab partners and I sat down
together and decided the swing from the part where we let go of the pendulum
combined with gravity and the rod connected to the bar were all a source of centripetal
force.
Knowledge
I learned that centripetal force and amplitude have a direct relationship, when one
increases so does the other. In order to better understand the lab I read up on the Hewitt
book for a simplified version of circular motion and simple harmonic motion. Despite
our percent of error, which was pretty large for my standards, I felt we as a group were
very meticulous with our process, we followed the procedures, dotted our I’s, the whole
nine yards, but it is still a bit of a mystery to me as to why our data was off by that great
of a percentage. If we had more time, it would have been nice to change the length of
the pendulum and see what happens when the radius is changed. Or we could have
possibly added more weight. This would help us gain a better understanding of the
centripetal force on a pendulum, and give us a broader scope to see how all the factors of
mass and radius affect a pendulum; so we can better understand why we got oddities in
our graphs.
Mariah's Conclusion
Results: