HPP Activity A27v2
Bending, Stretching, and Jumping
Exploration - Examining How Bending Your Knees Helps You Jump
Each group will be given a jumping toy apparatus to be studied.
Experiment with the function of this apparatus.
1. Once you have the toy working properly, write a
description of the workings and the resulting motion of
this toy. Make a list of as many related physics
principles as you can identify.
2.
What aspects of this toy seem to change the height to which it jumps? Make a list of the
properties of the jumping toy system. Describe how each property influences the height
to which the toy jumps.
3.
Can you jump keeping your legs completely straight? Does the amount of bending of
your legs have any relation to how far up you can jump? Try this out and describe your
results and compare to the jumping toy.
Modeling your legs with springs
Invention Discussion
During the Invention, your laboratory instructor will lead a discussion of your results and help you
to formalize important ideas.
From your discussion, record definitions for the following quantities:
(a) Work (W),
(b) Spring potential energy (PESp),
(c) Gravitational potential energy (PEGr),
(d) Kinetic energy (KE), and
Activity Guide
 2010 The Humanized Physics Project
Supported in part by NSF-CCLI Program under grants DUE #00-88712 and DUE #00-88780
HPP Activity A27v2
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(e) Total energy (E).
Task #1 - Using a new sensor for measuring force

Check that there is a Pasco force sensor connected to your interface. Open
the file MBL Force Sensor. You will now be able to use the computer to
collect and display force data as a function of time.
There are two very important things that you need to keep in mind when
using the Pasco force sensor.
•
The Pasco force sensor must be "zeroed" before using it. To do this, complete
the following steps.
a) hold the sensor in the position that you will be using it (horizontal
or vertical).
b) make certain nothing is touching the end of the sensor
c) keeping the sensor still, press the Tare button.
Repeat this process any time you change the sensor's orientation (i.e.,
vertical or horizontal).
•
Never apply too much force to the sensor. It can handle a maximum push or
pull of 50 Newtons. Please be careful not to damage these expensive sensors!
Using the force sensor

Remove the force sensor from the bracket affixed to the track by loosening the two
screws on top of the force sensor. (Be sure not to lose these screws!) Gently remove the
flat disk attachment and replace it with the hook attachment. Screw in this hook so that it
is snug, but do not over tighten.

Design and perform a mini-experiment to allow you to compare the readout of the force
sensor to a spring scale. For example, you could weigh a block of wood or a hooked
mass and compare the weight as measured by the spring scale to the weight as measured
by the force sensor. Collect data for at least 5 seconds for each measurement device.
Include a description of your mini-experiment and sketch the setup when appropriate.

Remember! you should make sure the force sensor and the spring scale are both zeroed
before you begin to take your measurements. You can test this by taking a measurement
of no force and verifying that the scale reads 0 N. If it does not read 0 N for zero force,
then ask your instructor for assistance before continuing!

During this course, all the force values quoted in your lab logbook should be the average
(mean) value over an appropriate range of time. For example, weigh the block for five
seconds and then take the average force reading during that time to get the final value for
your mini-experiment.
Activity Guide
 2010 The Humanized Physics Project
HPP Activity A27v2
4.

3
Compare and contrast your results between the spring scale and the force sensor. Hint!
You should calculate a percent difference for the values!
Once you have finished this page, reattach the force sensor to the bracket using the two
screws.
Task #2 - Work done to compress the toy’s spring (bend its knees)
Data Collection - Toy Parameters
Using your toy and a measuring device, record the following parameters. Please do not
take the toy apart!
5.
(a)
(b)
(c)
(d)
What is the length of the spring (with no compression)?
What is the compression distance when the toy is uncompressed?
What is the compression distance when the toy is fully compressed?
What is the compression distance when the toy is just about to jump?
Data Collection - Compressing the Spring
Using the force sensor, flat disk attachment, and fixed bracket, devise an experiment that will
allow you to measure the average force it takes to compress the toy’s spring to each of four
different distances. Note, compression distance is not the same as the length of the spring!
Record your average forces and compression distances in a data table in your logbook. Include a
brief description of your experimental techniques. Do not include positions where you are pushing
on the toy's suction cup.
Data Analysis - Numerical model
After you have collected your data, quit the DataStudio software. Open up the Spring
Data Analysis file in Excel. Enter your data into the spreadsheet. Be sure to label the columns.
Save this file and record the file name in your logbook.
Data Analysis - Graphical model
Use Excel to create a graphical model of your force vs. compression distance data.
Activity Guide
 2010 The Humanized Physics Project
HPP Activity A27v2
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Data Analysis - Mathematical function model
Examine your graphed data and discuss with your partners what kind of functional
model will best describe this data. Use the "Add Trendline…" feature of Excel to fit this data
and to display the best-fit mathematical functional model.
Print a copy of your graphical and functional model for each member of your group. Do not forget
to rewrite the functional model using meaningful variables and units.
Data Analysis - Verbal model
6.
In words, describe the relationship between applied force and compression distance for
the toy's spring.
Now that you have fully described the behavior of the toy's spring, you have the information
necessary to determine how much work is done to compress the spring to its pre-launch position.
The work done in compressing a spring can be found by determining the area under the curve of a
force vs. compression distance graph.
Work done compressing spring (J)
= area under curve = area of triangle
= (1/2) base  height
= (1/2) (xFinal - xInitial) (FFinal - FInitial)
7.
Find the work done to compress the toy's spring from its initial position (question 5b) into its prelaunch position (question 5d). Show and explain your work.
Save your file one last time and then quit the Excel software.
Task #3 - Resulting energy during the jump
Data Collection
Open the file Overhead Motion Sensor. You should be looking at two graphs: Position Above the
Table (m) vs Time (s) and Velocity (m/s) vs Time (s).
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 2010 The Humanized Physics Project
HPP Activity A27v2
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Place the jumping toy on the table directly underneath the motion sensor. Have one lab partner
compress the toy’s launching mechanism and then start recording data. Collect motion data for the
toy including before its launch, during its flight, and when it returns to the table.
Your data does not need to be "perfect," but it should be a reasonable representation of the toy's
motion. Do not continue with the lab if you have "bad" data. For example, if the toy jumped such
that the motion sensor missed most of its trajectory, then that would be "bad" data. If you collect a
set of bad data, then simply adjust your technique and repeat the experiment until you get a good
set of data. Feel free to have your instructor inspect your data before continuing. If any data run is
really bad, then choose "Delete Last Data Run" under the "Experiment" menu to delete it. By
deleting bad runs, you will use less of the computer memory.
Data Analysis
Print a copy of the graph of the toy’s motion and tape it in your logbook. Using your pencil, draw
a graphical model (smooth curve on the graph) that best represents the toy's motion during the
jump. Use this smooth curve when answering the following questions.
8.
Label the following five events on each graph:
(a) just leaving the table,
(b) half of the way up,
(c) maximum height,
(d) half the way back down, and
(e) just returning to the table.
Record the numerical values for the toy's height and vertical velocity for each event in a table.
9.
(a)
(b)
(c)
Assume that the toy has a gravitational potential energy of 0 J when it is sitting on
the table. For each of the five events identified in the previous question, calculate
the toy's gravitational potential energy, kinetic energy, and total energy.
What can you say about each of these quantities as functions of time throughout the
toy's flight?
Assume that time = 0 at the instant the toy leaves the table. Sketch a graphical
model for PEGr vs. t, KE vs. t, and E vs. t based on your data.
Summary Questions
10.
(a)
(b)
Compare the work done to compress the toy's spring to the maximum potential energy obtained
by the toy when it reaches its highest height. Calculate a percent difference.
Was some energy "lost" during the jumping process? If so, where might it have gone?
Activity Guide
 2010 The Humanized Physics Project
HPP Activity A27v2
11.
(a)
Suppose you work for a toy company. If you wanted to redesign this toy so that it would jump
higher, what might you try? Give at least three specific examples, describing why you would do
each change in terms of physics.
Suppose you are an athlete who needs to be able to jump high as possible. What kind of training
or fitness changes might you try to improve your jumps? Give three specific examples and
describe the physics behind them.
(b)
12.
In what ways is the jumping toy a good model of a human jumper? In what ways is the
model limited? Consider the model on page 1 in your answer.
End of Lab Procedures

Return the toy to the box at the side of the room.

Verify that the hook attachment for the force sensor is stored in the provided box.

Restart the computer at your station if another lab section is about to start. If you
are the last lab of the day, then shut the computer down.
Want More Information?
a)
b)
c)
d)

6
Using a triple beam balance (see Reference F)
Springs (see Walker, Section 6-2)
Work and kinetic energy (see Walker, Chapter 7)
Potential energy (see Walker, Chapter 8)
Modeling human running and jumping (see The Human Machine, R.M. Alexander,
Columbia University Press, 1992)
Activity Guide
 2010 The Humanized Physics Project