Bungee-Jump Accelerations
Purpose
The acceleration of a falling mass tethered to a rubber band is measured to analyse the
complicated motion of this model “bungee jump”. Learn how to analyze complicated motion by
decoupling it into simpler motions.
Apparatus
Ring stand, meter stick, stop watch, rubber bands, various masses, Vernier® low-g
accelerometer, PC running LoggerPro® software, LabPro® interface.
Pre-Lab Exercise
Consider the following two idealized cases:
1. A mass is hanging from an ideal spring (i.e., obeying Hooke’s law) at vertical position y = 0.
The mass is then lifted to y = h and held there at rest. At time t = 0 the mass is released.
2. A mass is hanging from a very flexible, light, nearly un-stretchable string at vertical position
y = 0. The mass is then lifted to y = h and held at rest. At time t = 0, the mass is released.
For each case, sketch the position y, the corresponding velocity v and acceleration a of the
mass for t ≥ 0.
Your sketches should include at least one period of any oscillatory motion. Make sure your
sketches of y, v and a are all on the same page with matching time axes.
Part I Static elastic properties of the bungee cord
Data
Make a “bungee cord” by tying two rubber bands together.
(Use the knot illustrated in Figure 1 when tying bands to
each other or to a hook.)
Suspend the rubber band from a ring stand (Figure 2).
Measure the rubber band's equilibrium length L, when a
mass m is suspended from it (and at rest) for a range of
masses from 0 to 900 g. (Don't let the heavier masses
hang from the rubber band for too long as this will
irreversibly (permanently) stretch the rubber.)
Fig 1
L
m
Calculations
Plot m versus L. Calculate the spring constant k near
m = 200 g.
2409 Bungee-Jump Accelerations - 1
Fig 2
Saved: 12/22/15, printed: 1/5/16
Part II “bungee-jump” accelerations
Data
a. Setting up the accelerometer
Measure the mass of the low-g accelerometer, and then tape it to a 200 g mass with the arrow
pointing up. Make sure that the data cord is as slack as possible during all parts of the mass’s
motion.
Start up LoggerPro® and open the file _Physics with Computers\07 Bungee Jump Acc.cmbl. A
graph of acceleration vs. time will appear on the screen with some default settings (feel free to
change as appropriate). The accelerometer is calibrated so that it reads zero acceleration
when at rest and −9.8 m/s2 when in free fall. The accelerometer can only measure the
component of the acceleration along the arrow painted on its housing.
“Zero” the accelerometer: Place the bungee mass stationary on the table, with the
accelerometer’s arrow pointing up. Click the “Zero” button to define this state as zero
acceleration.
To check the zero, click the “Collect” button to begin collecting data with the mass (“our model
jumper”) and accelerometer sitting stationary on the table. When data collection has finished,
select a region of the graph by dragging the mouse pointer across it. Determine the mean
(average) acceleration by clicking the “Statistics” button. It should be near zero.
To check the reliability of the displayed value, drop the mass (“jumper”) and let it free fall. Make
sure it is oriented with the accelerometer arrow pointed up. Catch the jumper before it hits the
floor and while the data cord is still slack. Use LoggerPro® to determine the average
acceleration during the fall. It should be close to 9.8 m/s2.
b. Measure “bungee” accelerations
Make a model bungee jumper by tying the rubber band to the hook of a 200g mass. (Use the
knot shown in Figure 1.) Fasten one end of the bungee cord to the edge of the table with a
C-clamp. Hold the mass upright when releasing the bungee jumper (some real bungee jumps
are head first, but let’s remove this extra complication of the rotation.)
Use LoggerPro® to record the acceleration a of the mass for 5 s, starting from just before the
release. Do this carefully a few times until you have a sensible data set.
Use the on-screen data of a versus t (called a “time series” of a) to:
1. Measure the time (duration) of free fall just after release using the mouse.
2. Measure the periods of any periodic components of the acceleration.
Also measure the following: the distance of the fall (with a meter stick); the period of the
up-down oscillation (with a stop watch). Assign appropriate uncertainties.
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Saved: 12/22/15, printed: 1/5/16
Ask the lab instructor to get you a printout of your time series. Indicate all times measured in
steps 1 and 2 on your printout.
Calculations/Conclusions
Describe the bungee-jump motion, identifying three components (free fall, “wobble”, and
“bounce”) of the motion qualitatively and quantitatively. Draw a picture to help explaining if
needed.
Calculate the expected value for the free-fall time from the free-fall distance and compare to
what you measured from the on-screen graph. Do they agree?
Calculate the expected value for the up-down oscillation period, using the spring constant you
obtained in Part I, and compare it to your direct measurement and to what you measured from
the on-screen graph. Do they agree?
Finish your lab report with a paragraph of discussion or comment about the experiment.
Part III (only if time permits)
Get a spring and some rope and experimentally check your answers to the Pre-Lab.
Measure the acceleration for a 500 g mass bungee-jumper (best to use only one rubber band
here).
Questions for you to think about (briefly discuss these in your report):
1. Does the lowest point in the jump correspond to the maximum acceleration and therefore
maximum force from the rubber band (therefore the maximum force on the jumper)?
2. Does the maximum acceleration depend on mass?
3. Can you find the maximum velocity of the jumper and when it happens? (Use LoggerPro®’s
integration function. Ask your instructor to show you.)
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Saved: 12/22/15, printed: 1/5/16