LabQuest
7 Bungee Jump Accelerations In this experiment, you will investigate the accelerations that occur during a bungee jump. The graph below records the acceleration vs. time vs. time for an actual bungee jump, where the jumper jumped jumped straight upward, then fell fell vertical vertically ly downward. The positive direction direction on the graph is upward. For about the first 2 seconds, the jumper stands stands on the platform in preparation preparation for the jump. At this point the acceleration is m!s2. In the next short period of time, the jumper dips dips downward then pushes upward, both accelerations showing showing up on the graph. "etween about 2.# 2 .# seconds and 2 $.# seconds, the jumper is freely falling and the acceleration is near % &.' m!s . (hen all of the slac) is out of the bungee cord, the acceleration begins to change. As the bungee cord stretches, it exerts an upward force on the jumper. *ventually *ventually the acceleration acceleration is upward although the jumper is still falling. A maximum positive acceleration corresponds to the bungee cord being extended to its maximum. +ne should be sufficient since, unli)e an actual bungee jump, you you will be able to control the rotation of your jumper. A c tu a l B u n g e e J u m p D a ta
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Figure 1 In your experiment, a bloc) of wood or a toy doll will substitute for the jumper, and a rubber band will will substitute substitute for the bungee cord. An Accelerometer Accelerometer connected to the jumper- will will be used to monitor the accelerations. accelerations.
OBJECTIE! •
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se an Accelerometer to analy/e the motion of a bungee jumper from just prior to the jump through a few oscillations after the jump. 0etermine where in the motion the acceleration is at a maximum and at a minimum. 1ompare the laboratory jump with an actual bungee jump.
"ATE#IAL! LabQuest LabQuest App Vernier Low-g Accelerometer
Physics with Vernier
bungee jumper (wooden block or small doll) bungee cord (long, flexible rubber band) ring stand
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LabQuest 7
$#ELI"I%A#& Q'E!TIO%! . 1onsider the forces acting on the bungee jumper at the lowest point of the jump. 0raw a free3 body diagram indicating the forces acting on the jumper. 4onger arrows should represent the force vectors with greater magnitude. 4abel the force vectors. 2. 5tudy the graph of the acceleration during an actual bungee jump 6Figure 7. +n the graph, label the time corresponding to the lowest position during the jump. 8. (hat was the acceleration at that point9 (as the direction of the acceleration up or down9 $. 4abel the time where the jumper reached the highest position during the first bounce. #. (hat was the magnitude of the acceleration at that time9 (as the direction of the acceleration up or down9 :. ;ow long was the bungee cord used in the real bungee jump9 ;int< 1onsider the time the jumper fell before the cord started to apply a force.
$#OCE('#E
$art I T)e Jump*!tep b+ !tep
. 1onnect the 4ow3g Accelerometer to 4ab=uest and choose >ew from the File menu. If you have an older sensor that does not auto3I0, manually set up the sensor. 2. Attach a bloc) of wood or small doll 6your jumper7 to the Accelerometer. The arrow on the Accelerometer should be pointing upward 6toward the ho o) if using a bloc), or toward the feet of the doll7. 8. Tie the rubber band to the hoo) on the wooden bloc) or to the feet of the doll. Tie the other end of the rubber band to a rigid support, such as a large ring stand. Adjust the length of the cord so that the bloc) or doll does not hit the floor when dropped. $. The Accelerometer must be /eroed so that it reads, only for the vertical direction, /ero acceleration when at rest and % &.' m!s2 when in free fall. ?ou will verify this in 5tep @. a. est the bungee jumper stationary on the table, with the Accelerometer arrow pointing directly upward.
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Physics with Vernier
Bungee Jump Accelerations
b. (hen the readings stabili/e, choose Bero from the 5ensors menu. The readings should be close to /ero. #. Ca)e sure your jumper is oriented properly 6arrow pointed up7. 5tart data collection. ;old the jumper motionless for one second, and then release it. 1atch the jumper while the cord is still slac). :. (hen data collection has finished, your graph will be displayed. To examine the displayed graph, tap any data point. As you tap each data point, acceleration and time values will be displayed to the right of the graph. For the first second or so, the acceleration should be near /ero, since you /eroed the sensor in 5tep $. This value represents the acceleration of the jumper prior to jumping. @. Tap the points and read the acceleration during the fall. It should be close to %&.' m!s2. Ignore any data collected after you caught the jumper. '. >ow collect some data corresponding to the bounces after the free fall portion of the jump. a. b. c. d.
4et the jumper hang from the bungee cord. Dull the jumper down # cm and hold it stationary. 5tart data collection. (ait about one second, and then release the jumper, creating an up3and3down oscillation similar to a mass suspended from a spring. e. After data collection has finished, your graph is displayed. 0etermine the point in the motion where acceleration is both positive in direction and has a maximum magnitude. 0oes this occur when the jumper is at the bottom, middle, or top of the oscillation9 $art II A Complete Jump
&. 4ift the bungee jumper to the height of the ring stand, as shown in Figure 2. The bungee cord should be hanging to the side and the Accelerometer cable should be clear of the jump path. Ca)e sure that the Accelerometer arrow is pointing upward. The connection point between the bungee cord and the jumper should also be pointing upward, so that the jumper does not turn over during the jump. a. 5tart data collection. b. (ait second and release the bungee jumper so that it falls straight down with a minimum of rotation. 4et the jumper bounce a few times. "e sure that the Accelerometer cable still has some slac) when the jumper reaches the lowest point. . epeat the measurement until you have a satisfactory set of data. A successful run should include a minimum of rotation, a section of free fall before the cord starts to pull on the jumper, and a few bounces, with at least the first bounce high enough to cause the cord to again go slac). The acceleration vs. time graph for the laboratory jump should show features similar to the graph of the real bungee jump. Drint or s)etch your final graph.
(ATA TABLE Time (s)
Physics with Vernier
Acceleration (ms2)
Direction of motion (up! "o#n! or rest)
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LabQuest 7
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Physics with Vernier
Bungee Jump Accelerations
A%AL&!I! . *xamine the graph. 0etermine the acceleration at eight different points on the graph, choosing points during the initial rest, free fall, when the cord is taut, and several bounces. ecord the values in your data table. Indicate the direction of the motion using up, down, or at rest . 2. Derform the same analysis on your bungee jump as was done on the real bungee jump in the Dreliminary =uestions section. 8. ;ow well does the laboratory jump compare with the real jump9 0iscuss the similarities and differences. $. ;ow could you improve the correlation between the lab jump and the real jump9
E,TE%!IO%! . Dlace a Cotion 0etector on the floor during a jump. *xamine the Cotion 0etector data 6position vs. time and velocity vs. time graphs7 of the jump. ;ow do these data compare to the Accelerometer data9 (hich sensor do you thin) is a better tool for the analysis of the jump9 *xplain. 2. If a video camera is available, videotape the laboratory bungee jump or a real bungee jump. Eiew the videotape and match the Accelerometer graph with the video of the jump. 8. epeat the experiment with a jumper of different mass. (hat are the similarities and differences between the two sets of data9 0iscuss some methods that might be used by operators of commercial bungee jumps to assure the safety of jumpers of different weights. $. 1onnect the bungee cord to a Force 5ensor to examine the cord tension during the jump. #. se reference boo)s or the Internet to learn the accelerations experienced by the 5huttle astronauts during ta)eoff and re3entry. ;ow do the accelerations experienced by the astronauts compare to the maximum acceleration experienced by a bungee jumper9
Physics with Vernier
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