AP PHYSICS C (Mechanics)
LAB: Hooke’s Law Orbital Motion (v3b)
NAME:______________________________
ANALYSIS PROCESS
0. Start a data analysis log, either on paper or OneNote. Document all work and calculations as you go, lebeling
all work with its corresponging item number in the run summary, below.
1. Go to the HLOM Data Archive (http://academic.greensboroday.org/~regesterj/data/rgo-HLOM/) and
save the video of your assigned run to a folder on your computer.
2. Start Tracker, open the video, and determine the start frame (when the masses are released) and the
end frame (when either of the masses hits a wall). Fill in that information in the Clip Settings dialog. Also
fill in the frame rate (300 frames/sec) and the step size (10 frames).
3. Fill in the Run Configuration section of the Run Summary. All of this information comes from the table in the
data archive where you downloaded the video. Keep in mind that the distance of a mass from the axis means
the distance of the mass’s center-of-mass to the turntable axis. The position of each mass always means the
position of its COM.
4. Set the coordinate axes, with the origin at the turntable axis and the x-axis parallel to the massspring-mass system at the moment of release.
5. Set the scale. The rotating apparatus is 0.507 m long.
6. Create a point mass. Rename the point mass appropriately: the 1 kg mass is A, 0.5 kg is B, 0.2
kg is C, and 0.1 kg is D.
7. Set the accurate mass in the mass box on the toolbar. The precise masses are 0.991 kg (A),
0.494 kg (B), 0.196 kg (C), and 0.094 kg (D).
8. Shift-click to mark the center of the mass throughout the video. Yes, it’s tedious, but do it as carefully as you
can.
9. Repeat steps 6-8 for the other mass.
10. Create a new “center of mass” track.
11. Set the track display so all the mass positions are marked, connected by lines, but
without numbers.
12. IN YOUR ANALYSIS LOG, CLEARLY DOCUMENT ALL OF THE FOLLOWING CALCULATIONS.
Items 1 & 2: Watch the video just prior to the release of the masses. Watching the video with stepsize
of 1 frame, determine how many frames it takes the apparatus to turn the last full or half turn, and use
that information to calculate the initial period and initial angular velocity of the system.
Item 3: Calculate the distance of the system COM from the COM of each individual mass.
Item 4: The initial length of the spring is the mass-mass distance, minus the COM-hook distances for
both masses.
Items 5 & 6: The “Critical RPM” is the angular velocity that would result in circular motion. Derive a
formula for this, by setting the spring force equal to the centriptal force for one of the masses, before
plugging in numbers. Once you know the critical RPM, then if the actual initial RPM is less than that, the
masses first motion after release will be inwards; if greater, then outwards.
Item 7: Calculate the kinetic energies of the individual masses; get the velocities from v=ω·r, where r is
the distance from the system COM and ω is in radians per second.
Item 8: Calculate the initial elastic potential energy of the spring, relative to its unstretched length.
Items 9 & 10: Calculate initial I and L of the rotating system.
13. Set up the Excel spreadsheet numerical model sim4b.xlsm with the parameters of your run. Check your
results of Items 3 and 5 against the spreadsheet’s calculations. By the way, the non-obvious variables used in
the spreadsheet’s formulae are:
CA, CB = the COM-to-hook distances for the two masses
L = the unstretched length of the spring
Li = the initial distance between the masses (i.e. between their COMs)
RPMo, radperseci = the initial angular velocity, in RPM and rad/sec, respectively
Cut-n-paste (or screen snip) the trajectory plot from the simulation, and paste it into the indicated spot of the
Run Summary. Do the same with the trajectory overlay of the video. Rotate the video frame so the x-axis points
to the right, aligned with the simulation trajectory plot. Paste the other indicated plots, from the numerical
model as well as Tracker, into the Run Summary.
14. Find the frame where the masses are at their minimum or maximum separation from each other,
depending on whether the first motion upon release is inwards or outwards, respectively. Fill in the
Minimum/Maximum Separation sections of the Run Summary. You will determine each of Items 11 through 20
twice, once from the simulation and once from the Tracker analysis, then calculate the % difference of actual
from the predicted values. CLEARLY DOCUMENT ALL METHODS, CONCLUSIONS AND CALCULATIONS IN YOUR
ANALYSIS LOG. Some items you will simply read off graphs in the simulation or Tracker; others will require you
to do some calculatin’. CAUTION: Sometimes Tracker uses radians for angles, and sometimes degrees, and it
doesn’t label units on the axes. Be careful.
15. Complete the Follow-up Questions.
WHAT TO TURN IN...
Print out the Run Summary, Images and the Followup Questions. Use a color printer so the screenshots look
good. Also include your data analysis log. This can be handwritten, but must be neatly and logically arranged.
Email me your TRK file, as well as this document. Your TRK file should be named FlightXRunY.trk (with X and Y
being your flight and run numbers) and the Word doc should likewise be FlightXRunY.doc.
AP PHYSICS C (Mechanics)
LAB: HOOKE’S LAW ORBITAL MOTION
ANALYSIS BY: ______________
RUN SUMMARY
RUN CONFIGURATION
FLIGHT #___ RUN #___
LARGER MASS = _____kg
SMALLER MASS = _____kg
SPRING ID _____
UNSTRETCHED LENGTH = _____m
TARGET ωo = _____RPM
initial distance from axis = _____m
initial distance from axis = _____m
SPRING CONSTANT = _____N/m
VIDEO FILENAME:
AT THE MOMENT OF RELEASE (which is at frame #_______)
1. ACTUAL ωo = _____ RPM.
2. ACTUAL To = _____ sec.
3. COM is _____ m from the larger mass and _____ m from the smaller mass.
4. INITIAL LENGTH OF SPRING = _____ m.
5. CRITICAL RPM, ωc = _____ RPM.
6. Since the ωo ____ ωc , the masses, when first released, moved ___________.
7. The initial KEtrans of the larger mass was _____ J; the initial KEtrans of the smaller mass was _____ J.
8. The initial elastic PE of the spring was _____ J.
9. The initial moment of inertia was ___________.
10. The initial angular momentum was _____________.
AT THE FIRST MOMENT OF MINIMUM/MAXIMUM SEPARATION (circle one), which is at frame #_______...
SIMULATION
distance of larger mass from COM
distance of smaller mass from COM
separation of masses
length of spring
PEelastic
KEtrans of larger mass
KEtrans of smaller mass
ω
I
L
OBSERVED
% difference*
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
*Percentage difference of the simulation relative to the observed values.
IMAGES: Cut-n-paste (or screen snip) the following items. It’s OK if this section takes several pages in the end.
SIMULATION TRACK PLOT
***paste here***
VIDEO STILL IMAGE, with points marked and axes shown, oriented as the simulation trajectory plot is.
***paste here***
SIMULATION ANGULAR VELOCITY PLOT
***paste here***
TRACKER ANGULAR VELOCITY PLOT
***paste here***
SIMULATION ENERGY PLOT
***paste here***
TRACKER ENERGY KE PLOT of mass ____
***paste here***
TRACKER ENERGY KE PLOT of mass ____
***paste here***
FOLLOWUP QUESTIONS
1. Do you think the numerical model did a good job predicting what actually happened? Discuss, including
references to your qualitative impressions as well as specific numerical comparisons.
DELETE THIS LINE & TYPE RESPONSE HERE
2. What happens to the angular velocity of the system as the masses come closer to each other? Explain why,
using physics concepts.
DELETE THIS LINE & TYPE RESPONSE HERE
3. What happens to the kinetic energy of the system as the masses come closer together? Explain why, using
physics concepts.
DELETE THIS LINE & TYPE RESPONSE HERE
4. Describe what happens to the center of mass of the system, and why?
DELETE THIS LINE & TYPE RESPONSE HERE