Teacher Notes

The Bungee-Jumping Egg

Student Laboratory Kit

Materials Included In Kit

Ceiling hooks, 2
Elastic bands with metal barb ends, 15
Plastic bags, 15
Plastic eggs, 15
String, one spool

Additional Materials Required

Water, 500 mL*
Balance, 0.1-g precision (one per classroom)
Beaker, 600-mL*
Marker, ink*
Mass with hook, 100-g (can be shared)
Meter stick*
Paper towels*
Scissors*
Clothes-pin clamp or paper clamp to secure string to the ceiling hook†
Stepstool or ladder†
Tape measure (to measure platform height)†
Trough or catch bucket (optional)†
*for each lab group
To make jumping platform

Prelab Preparation

  1. Set up a ceiling platform for a site to attach the bungee cord string. Ceiling hooks are provided to connect to ceiling tracks found in many schools (follow the instructions provided on the ceiling hook package). A clamping mechanism suitable for your school ceiling design will be needed if the ceiling hooks can not be used. A C-clamp connected to an I-beam, or clamping or tying the string to a ventilation duct screen may be one option. Do NOT use sprinkler nozzles that may be in the ceiling as an attachment point. It is best to consult the custodial staff if you are unsure about where to hang the bungee cords. Use caution when working on a ladder or step-stool to set up the ceiling platform.
  2. Once the jumping platform is set up, use a tape measure to measure the height of the jumping platform above the ground. This may take two people. Measure from the bottom of the platform (the bottom of the ceiling hook if that is used) where the “mark” on the string will be positioned (see Procedure step 23). Record the height of the platform to the nearest 0.1 cm and give this measurement to your students when they perform the experiment.

    Height of jumping platform (PH): _____________

  3. Cut fifteen (15) 150-cm long pieces of string from the string spool prior to class (or enough for each lab group).

Safety Precautions

If an egg cracks on the floor, clean up the spill immediately to reduce the risk of a slippery surface. Use caution when standing on a ladder, stepstool or chair when releasing the eggs. Only the teacher should climb on the ladder or stepstool to set up the bungee jump and release the eggs. Wear safety glasses. Please follow all laboratory safety guidelines.

Disposal

All the materials should be stored for future use.

Teacher Tips

  • Enough materials are provided in this kit for 30 students working in pairs or for 15 groups of students. This laboratory activity can reasonably be completed in one 50-minute class period. All materials are reusable.
  • The plastic eggs may have a hole in one or both ends. Cover the holes inside with tape or clay. Check for water leaks.
  • Have students double check all their calculations before bungee jumping.
  • The easiest method to attach the bungee cord string to the ceiling hook is to line up the “mark” on the string with the bottom of the hook, and then wrap the loose end of the string around the hook several times. Four or five wraps around the hook will be enough to secure the string and prevent it from slipping during the bungee jump. For additional security, a clothes-pin clamp or binder clip can be clamped over the wrapped string on the hook.
  • Make sure the bungee cord does not get tangled up or twisted together before the egg is released. Use one hand to hold the string apart and to the side before the drop. Let go of the string immediately when the egg is released.
  • Be careful not to drop the bungee cord and break the egg before it is time to bungee jump!
  • Slotted weights and weight hangers can be used in place of the 100-g hooked mass. Masses of 100 to 150 grams work well to stretch the elastic band and produce accurate spring constant calculations. Masses less than 100 grams may not stretch the elastic band enough and masses greater than 200 grams may overstretch and weaken the elastic band over time.
  • Measurement errors frequently occur when the length of string or stretched elastic band extends beyond the length of the meter stick. Students must use very precise techniques in order to accurately measure lengths that are longer than one meter. Inaccurate measuring may lead to a cracked egg or a very short “ride.”
  • The plastic egg may not crack open as easily as a real egg will. Connecting the egg pieces as “loosely” as possible will make a weak egg that should crack open from light contact with the floor. It may take some practice to determine just how “loose” they need to be. Tape can be added to one side of the egg pieces to act as a hinge. Then the pieces can be very loosely capped and placed into the sandwich bag.
  • It may save classroom time if the eggs are filled with water and placed into the sandwich bags prior to class.
  • If students want to really test the safety of their bungee jump, use raw or hard-boiled eggs in place of the plastic eggs. Do they trust their measurements and calculations?
  • The Background section assumes previous knowledge about the conservation of energy and Hooke’s law. Please refer to your physics or physical science textbooks for more information about these topics.
  • (Optional) Fill a trough or catch bucket with water to act as the pool or lake and place it below the bungee-jump platform. The splash from an over-exhilarated jump can be very dramatic.

Correlation to Next Generation Science Standards (NGSS)

Science & Engineering Practices

Planning and carrying out investigations
Analyzing and interpreting data
Developing and using models
Using mathematics and computational thinking
Constructing explanations and designing solutions
Engaging in argument from evidence

Disciplinary Core Ideas

MS-PS3.A: Definitions of Energy
HS-PS3.A: Definitions of Energy

Crosscutting Concepts

Cause and effect
Scale, proportion, and quantity
Energy and matter
Systems and system models

Performance Expectations

MS-ESS1-2: Develop and use a model to describe the role of gravity in the motions within galaxies and the solar system.
HS-PS2-4: Use mathematical representations of Newton’s Law of Gravitation and Coulomb’s Law to describe and predict the gravitational and electrostatic forces between objects.

Sample Data

{13877_Data_Table_1}
Calculations

Spring constant of elastic band:
k = (100 g) × (980 cm/s2)/19.1 = 5130.9 g•cm/s2•cm = 5130.9 g/s2

Calculated stretch distance of elastic band:
X = [2 x (66.5 g) × (980 cm/s2) x (263.1 cm)/(5130 g•cm/s2•cm)]½ = 81.8 cm

String length:
SL = 263.1 cm – 75.0 cm – 10.0 cm – 81.8 cm = 96.3 cm

Student Pages

The Bungee-Jumping Egg

Introduction

Bungee jumping would not be as “safe” as it appears without relying on some basic physics principles, such as the law of conservation of energy and Hooke’s law for springs. A safe bungee jump occurs when no one is injured. A safe and exhilarating bungee jump is one in which no one is injured, the free fall lasts as long as possible, and the bungee jumper comes as close to the ground as possible without touching it. In this activity, the law of conservation of energy and Hooke’s law will be used to build a safe and exhilarating model bungee jump of an egg!

Concepts

  • Hooke’s law
  • Conservation of energy
  • Acceleration of gravity

Background

The law of conservation of energy states that energy cannot be created or destroyed, only converted between one form and another. During a bungee jump, the stored, potential energy of the jumper on a tall platform (PE = mgh) is converted into kinetic energy during the fall (KE = ½mv2). This kinetic energy is converted back into potential energy as the bungee cord stretches. At the bottom of the “ride” when the jumper momentarily stops, all the kinetic energy has been converted into spring potential energy—the energy stored in the stretched bungee cord (PEspring = ½kx2). An instant later, the bungee-jumper is flung upwards as the bungee cord relaxes, thereby converting the spring potential energy back into kinetic energy. An egg will simulate a human bungee-jumper in this experiment.

In order to determine the length of string necessary to make the bungee cord long enough for a safe and exhilarating ride, five values are needed—(1) the total height of the jump that is desired, (2) the initial length of the unstretched elastic band, (3) the spring constant of the elastic band, (4) the mass of egg and basket, and (5) the length of the basket (see Figure 1).

{13877_Background_Figure_1}
The total height of the jump (h) is the height above the ground at which the jump begins (PH) minus the separation distance (d) between the egg and the ground at the bottom of the ride (Equation 1).
{13877_Background_Equation_1}

PH = Platform height above the floor
d = separation distance between the egg and the floor at the bottom of the ride
h = Total height of the jump
SL = String length
UL = Unstretched elastic band length
BL = Egg basket length
X = Stretch distance of the elastic band during the jump

The force produced by a stretched spring is directly proportional to the distance the spring is stretched compared to its unstretched state, according to Equation 2. This is better known as Hooke’s law. The negative sign in the equation signifies that the force produced by a spring is a restoring force; that is, the force wants to bring the spring back to its equilibrium, unstretched, state:
{13877_Background_Equation_2}

F = force produced by a spring
k = spring constant
x = stretch distance (the difference between the stretched and unstretched length of the spring)

The spring constant for the elastic band can be calculated by rearranging Equation 2:
{13877_Background_Equation_3}
By hanging a mass with a known value from the end of the elastic band, and measuring the total length of the stretched elastic band, its spring constant can be calculated (Equation 4).
{13877_Background_Equation_4}
Where mu is equal to the mass value, g is the acceleration of gravity constant (980 cm/s2), and xu is the stretch distance of the elastic band as a result of the hanging mass, mu. Remember that the stretch distance of the elastic band is the total stretched length, xT, minus the unstretched length.

To determine the total length of the bungee cord needed for a safe and exhilarating bungee jump, the stretched length of the elastic band at the bottom of the ride must be calculated. Since the initial potential energy of the “jumper” will be converted completely into spring potential energy at the bottom when the elastic band is fully stretched, the initial potential energy will equal the final spring potential energy in the elastic band according to Equation 5.
{13877_Background_Equation_5}
Rearranging Equation 5 to solve for x:
{13877_Background_Equation_6}
The calculated stretch distance of the elastic band at the bottom of the ride (X) is therefore equal to:
{13877_Background_Equation_7}

me = mass of the egg and basket
g = acceleration of gravity, 980 cm/s2
h = height of the ceiling platform above the floor minus the separation distance (d) at the bottom
k = spring constant of the elastic band

Once X is calculated, use the ceiling platform height, unstretched elastic band length and basket length to calculate the length of the string necessary to complete the bungee cord, following Equation 1.

Materials

Water
Balance, 0.1-g precision
Beaker, 600-mL
Ceiling hook or rod support platform
Egg, plastic
Elastic band with metal barb ends
Marker, ink
Mass with hook, 100-g
Meter stick
Paper towels
Plastic bag
Scissors
String, thin, 150 cm
Trough or catch bucket (optional)

Safety Precautions

If an egg cracks on the floor, clean up the spill immediately to reduce the risk of a slippery surface. Wear safety glasses. Please follow all laboratory safety guidelines.

Procedure

  1. Obtain the elastic band, 150 cm of string, scissors and a meter stick.
  2. Measure the unstretched length of the elastic band with a meter stick. Record the unstretched length, UL, to the nearest 0.1 centimeter in the data table on the Bungee-Jumping Egg Worksheet.
  3. With scissors, cut a 15-cm length of string from the 150-cm piece. Save the remaining 135-cm string for step 20.
  4. Securely tie one end of the 15-cm string to one end of the elastic band as close to the metal barb as possible. (The metal barb will prevent the knot from slipping off the elastic band.)
  5. Tie a loop knot at the other end of the string (see Figure 2).
    {13877_Procedure_Figure_2_Loop knot}
  6. Add a 100-g hooked mass (mu) to the loop at the end of the string.
  7. Hold the other end of the elastic band by the metal barb and allow the elastic band to hang vertically as the mass stretches it.
  8. With the meter stick, measure the length of the stretched elastic band (xT). Note: Measure between the metal barbs only. Record the stretched length to the nearest 0.1 centimeter in the data table.
  9. Calculate the spring constant, k, for the elastic band using Equation 4. Record the spring constant, k in the data table. What are the units for the spring constant?
  10. Fill a 600-mL beaker ¾-full with water.
  11. Fill a plastic egg with water by submerging the two pieces of the egg in the water in the beaker. Note: The egg may have small holes in each end. Cover the holes inside with tape or clay. Connect the two egg pieces together while they are submerged and full of water. To obtain a “weak” egg, it may be necessary to connect the two pieces loosely. It may take practice to determine the minimum tightness the two egg pieces need to be so that they stay together in the egg basket, but still crack open when the egg hits a rigid surface.
  12. Place the water-filled plastic egg into a plastic bag. Dry off the outside of the plastic bag if necessary.
  13. With a balance, weigh the water-filled plastic egg and bag. Record the mass of the egg and bag basket to the nearest 0.1 g in the data table.
  14. Attach the egg basket to the end of the string tied to the elastic band by using a “looping” knot (see Figure 3).
    {13877_Procedure_Figure_3_“Looping” knot}
  15. With a meter stick, measure the length of the egg basket from the elastic band’s metal barb to the bottom of the bag. It is best to do this when the basket is hanging. Record this length to the nearest 0.1 centimeter in the data table.
  16. Record the height of the ceiling “jumping platform” as measured by your instructor.
  17. Calculate and record the total height of the jump. Choose a separation distance (d) less than 5 cm, depending on how exhilarating the bungee jump will be.
  18. Calculate and record the stretch distance of the elastic band (X) according to Equation 7.
  19. Calculate and record the length of additional string that is necessary to successfully complete the jump (Equation 1).
  20. Obtain the long, 135-cm piece of string that was saved after step 3.
  21. Measure this string to the necessary string length (SL) with a meter stick. Use scissors to cut the string about 15 cm beyond the necessary length so that excess string can be used to tie and clamp the string to the elastic band and jumping platform.
  22. Tie one end of the string to the free end of the elastic band as close to the metal barb as possible.
  23. From the knot at the tied end, measure the string to the calculated string length (SL) again, and use a marker to mark the correct length on the string. This mark will be the connecting point of the string to the jumping platform. Your instructor will use a ceiling hook, C-clamp or other hooking mechanism to secure the free end of the string to the jumping platform. Make sure the ink mark on the string is clear so that your instructor can match this point up with the very bottom of the platform.
  24. Once the bungee cord is secured to the platform, double check the total length of the bungee cord and egg basket. Make sure to lift the egg basket slightly until the elastic band begins to slack in order to reestablish the unstretched length of the bungee cord.
  25. Raise the egg to the correct bungee-jump starting position.
  26. Release the egg!
  27. Did the egg survive the bungee jump? Was it the most exhilarating ride possible? Record observations on the Bungee-Jumping Egg Worksheet.

Student Worksheet PDF

13877_Student1.pdf

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