Introduction
Bungee jumping looks pretty exciting. Today we will let you decide how
long to make the bungee cord for a fragile jumper -- a raw egg. The goal
is to make it exciting but not fatal for your jumper. A small prize
will be given to the group that gets closest to the ground without harming
their egg.
The Experimental Stage Gather your data as follows:
Make 3 jumps each with 2, 3, 4, and 5 rubber bands from a height of 1
meter. You may wish to use a pen, and hold it perpendicular to the top of
the stick, so that you drop the egg sufficiently far away from the meter
stick.
Record how far the egg travels from the top of the
meter stick to the point closest to the ground (12 data points).
Be very careful with your egg - protect it from hitting anything
and make sure that it doesn't swing back and hit the meter stick.
Accuracy is important, so
the same person should drop the
egg each time, and the same person should be watching the meter
stick each trial.
Number of rubber bands
Distance dropped in centimeters
2
2
2
3
3
3
4
4
4
5
5
5
Excel and Data Analysis
Enter your data into excel, in columns, and highlight the number of
rubber bands columns by clicking on the grey A box, then hold down the
shift key and click on the B box to highlight both columns.
Use Insert and release on Chart. Now choose XY(Scatter) to
create a scatterplot chart. Next click on the chart,
click on Options (on the top right), and then click on the bottom two options (Display equation on chart, Display r-squared value on chart)
and add a trendline
and r^{2} value. Write down your
results here
EQUATION OF THE LINE OF BEST FIT:
R^{2} VALUE:
For Discussion
Even with the variability in rubber bands and possible measurement
inconsistencies,
using the r^{2} value,
your number of rubber bands should be a very strong predictor of
the distance traveled (r^{2} measures how good the best fit line
fits the data and a strong correlation occurres between 65% and 100%).
Explain how common sense alone applied to the stretch ability and
similarity of the
rubber bands and the problem setup can be used to explain why
the relationship is linear (with a constant slope)
and why this predictor is so strong.
EXACTLY what prediction of the distance traveled does the
regression line give for
10 rubber bands (plug in 10 for the x-value)?
EXACTLY what prediction of the number of rubber bands required
for 2.0 meters does the equation of the regression line give
(plug in for the y-value)?
For Discussion
Why won't everyone in the class have the same answer for this question?
Relate your response to the placement of the paperclip, the weight of the egg,
the egg dropper, etc.
Using the predicted number of rubber bands, the R^{2}
value, and anything else you want to factor into your decision,
decide how many rubber bands you will use for the
2.0 meter bungee jump. You may be creative and
fold a rubber band in half. How many will you use?
The Contest - Directions
Build, but DO NOT TEST
the bungee machine, adding the rubber bands until you reach
the number of rubber bands that you previously decided on,
and then leave it alone
in a safe place until we come back together as a class.
While waiting for the contest, read p. 15-21 in New Connections:
1) Write down one policy that surprised you, that you
found interesting, or that you disagreed with.
2) Write down one item that relates to something in your own life.
During the contest, the team closest to the ground without egg
damage wins.