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Bungee Jumping

Bungee Jumping Photo Courtesy of Lilly M, Wikimedia Commons.

Bungee Jumping is a thrill seekers adventure that also allows for an investigation of energy concepts including Kinetic Energy, Gravitational Potential Energy and Elastic Potential Energy. Gravitational Energy (determined by height above the ground) is converted into Kinetic Energy until the slackness in the bungee cord is taken up. When the jumper reaches the end of his rope, there is an interplay between the three types of energy until Kinetic Energy reaches zero .

In this simulation, a bungee jumper is dropped from a tower with a fixed length of bungee cord. The simulation operator can control the height of the tower, the stiffness of the bungee cord (determined by its spring constant k), the unstretched length of the bungee cord and the jumper's mass. The player buttons are the play/pause button, the rewind (to t=0) button and the reset button (resets all parameters to initial values). The operator may optionally display the forces acting on the jumper and a plot of the g-forces versus time. Note that the simulation measures the altitude in terms of the location of his feet, thus he hits the ground if his feet get within his 1.7m of height to the ground.

When trying for a minimum drop from a platform set for h = 10 m, the jumber will hit the ground. The impact is represented by a red cross symbol blocking our view of the "accident".

Start by setting the platform hieght to its minimum (h=10m), the spring constant of the bungee cord to its stiffest setting (k=200 N/m), the length of the bungee cord to its minimum (Lo=5m) and the jumper's mass to its minimum (m=40kg). Through trial and error determine the minimum platform height needed for a "safe" jump.

• Play the simulation with these safe jump settings and watch the interplay between the various types of energy. Does the total energy change?
• Are the g-forces experienced by the jumper reasonable, dangerous or even fatal?

With our "safe" jump settings above, consider the effect of the following on the saftey of the jump:

• increasing/decreasing the jumper's mass,
• increasing/decreasing the unstretched length of the cord,
• increasing/decreasing the stretchiness of the bungee cord (by decreasing/increasing k)
• What kind of changes do you think the jump operator should make in order to accomodate a heavier jumper after a succesful jump by a lighter jumper?

For a 40 kg jumper and a 30 m platform height and a "safe" jump,

• determine the longest (Lo) bungee cord that can be used for the stiffest bungee cord (k=200N/m)
• for the shortest bungee cord (Lo=5m) determine the least stiff springiness (smallest k)
• compare these two ride experiences from the jumper's perspective (look at g-force!)

 

Translations

Code	Language		Translator	Run

Credits

Michael R. Gallis; Fremont Teng; lookang

Briefing Document: Bungee Jump JavaScript Simulation Applet HTML5

1. Overview

This document analyzes a web resource from Open Educational Resources / Open Source Physics @ Singapore, specifically focusing on a Bungee Jump JavaScript Simulation Applet built using HTML5. The applet is designed as an interactive tool to explore the physics of bungee jumping, particularly the interplay of different forms of energy.

2. Main Themes & Key Ideas

• Energy Conservation and Transformation: The core concept revolves around the conversion between Gravitational Potential Energy, Kinetic Energy, and Elastic Potential Energy during a bungee jump. The resource emphasizes that Gravitational Energy is converted to Kinetic Energy until the bungee cord tightens. Then, there is an interplay between all three types of energy until Kinetic Energy reaches zero. The simulation allows users to observe these energy transformations visually. The document prompts the user to consider whether total energy changes during the simulation, testing the understanding of energy conservation.
• "Gravitational Energy (determined by height above the ground) is converted into Kinetic Energy until the slackness in the bungee cord is taken up. When the jumper reaches the end of his rope, there is an interplay between the three types of energy until Kinetic Energy reaches zero ."
• Interactive Simulation for Exploration: The applet provides a virtual environment to manipulate parameters such as tower height, bungee cord stiffness (spring constant 'k'), unstretched length of the cord, and the jumper's mass. This allows users to perform "what-if" scenarios and understand how these variables affect the safety and dynamics of the jump.
• "In this simulation, a bungee jumper is dropped from a tower with a fixed length of bungee cord. The simulation operator can control the height of the tower, the stiffness of the bungee cord (determined by its spring constant k), the unstretched length of the bungee cord and the jumper's mass."
• Safety Considerations: A significant aspect of the simulation is exploring the conditions for a safe jump. The resource explicitly prompts users to determine the minimum platform height for a safe jump and to investigate the impact of changing parameters on safety. It also introduces the concept of g-forces experienced by the jumper.
• "When trying for a minimum drop from a platform set for h = 10 m, the jumber will hit the ground. The impact is represented by a red cross symbol blocking our view of the "accident"."
• "Are the g-forces experienced by the jumper reasonable, dangerous or even fatal?"
• Experimentation and Inquiry-Based Learning: The simulation encourages users to conduct virtual experiments, analyze data, and draw conclusions. The questions posed within the resource promote inquiry-based learning by prompting users to predict outcomes, observe the effects of parameter changes, and explain the observed phenomena.
• "Through trial and error determine the minimum platform height needed for a "safe" jump."
• "What kind of changes do you think the jump operator should make in order to accomodate a heavier jumper after a succesful jump by a lighter jumper?"
• Applet Controls:
• Height h: Adjusts the height of the pole.
• Adjustable Rope: Dragging the box will extend the length of the rope.
• Mass of the Person: Adjusting mass by moving the box left will decrease the mass and moving it to the right will increase the mass.
• Play and Reset Buttons: Plays and Resets the simulation accordingly.

3. Suggested Activities

The resource suggests the following activities to do with the simulation:

• "Play the simulation with these safe jump settings and watch the interplay between the various types of energy. Does the total energy change?"
• "Are the g-forces experienced by the jumper reasonable, dangerous or even fatal?"
• Consider the effect of the following on the safety of the jump: increasing/decreasing the jumper's mass, increasing/decreasing the unstretched length of the cord, and increasing/decreasing the stretchiness of the bungee cord (by decreasing/increasing k)
• "What kind of changes do you think the jump operator should make in order to accomodate a heavier jumper after a succesful jump by a lighter jumper?"
• "For a 40 kg jumper and a 30 m platform height and a "safe" jump, determine the longest (Lo) bungee cord that can be used for the stiffest bungee cord (k=200N/m)"
• "For the shortest bungee cord (Lo=5m) determine the least stiff springiness (smallest k)"
• "Compare these two ride experiences from the jumper's perspective (look at g-force!)"

4. Target Audience

The simulation is suitable for students learning about energy, forces, and motion, particularly at the secondary or introductory college level. The interactive nature makes it engaging for visual learners and those who benefit from hands-on (virtual) experimentation. It is also useful for teachers looking for interactive tools to illustrate these physics concepts.

5. Technical Aspects

• The applet is built using JavaScript and HTML5, making it accessible through web browsers without requiring specific plugins.
• The resource provides embed code (iframe) for easy integration into other websites or learning platforms.

6. Credits & Licensing

• The simulation is credited to Michael R. Gallis, Fremont Teng, and lookang.
• The content is licensed under the Creative Commons Attribution-Share Alike 4.0 Singapore License.

Bungee Jumping Simulation Study Guide

I. Key Concepts

• Kinetic Energy: The energy an object possesses due to its motion. It depends on the object's mass and velocity.
• Gravitational Potential Energy: The energy an object possesses due to its position in a gravitational field. It depends on the object's mass, the gravitational acceleration, and its height relative to a reference point.
• Elastic Potential Energy: The energy stored in a deformable object, such as a spring or bungee cord, when it is stretched or compressed. It depends on the stiffness of the object (spring constant) and the amount of deformation.
• Spring Constant (k): A measure of a spring's stiffness. A higher spring constant means the spring is stiffer and requires more force to stretch or compress.
• Unstretched Length (L₀): The length of the bungee cord when it is not under tension or compression.
• G-Force: A measurement of acceleration, expressed in multiples of the Earth's gravitational acceleration (g ≈ 9.8 m/s²). It represents the force experienced by an object due to acceleration relative to freefall.
• Energy Conservation: The principle stating that the total energy of an isolated system remains constant over time. Energy can be transformed from one form to another (e.g., potential to kinetic) but cannot be created or destroyed.
• Trial and Error: A problem-solving method that involves experimenting with different approaches and learning from the results.
• Safety Parameters: Specific values of adjustable variables (platform height, spring constant, cord length, jumper's mass) that result in a "safe" bungee jump within the simulation.

II. Simulation Parameters and Controls

• Tower Height (h): The height of the platform from which the jumper is dropped. Adjustable via the "Height h" dragable box.
• Spring Constant (k): The stiffness of the bungee cord, measured in N/m. Adjustable via the tension slider, decreasing tension will increase stretchiness and lower the spring constant.
• Unstretched Length (L₀): The length of the bungee cord before it is stretched. Adjustable via the "Adjustable Rope" dragable box.
• Jumper's Mass (m): The mass of the bungee jumper, measured in kg. Adjustable via the "Mass of the Person" dragable box.
• Play/Pause Button: Starts and stops the simulation.
• Rewind Button: Resets the simulation to time t=0.
• Reset Button: Resets all simulation parameters to their initial values.
• Worldview Combo-box: Toggles between different views (World, Energy, Graph, World+Energy, World+Graph).
• Forces Display: Option to display the forces acting on the jumper.
• G-Forces vs. Time Plot: A graph showing the g-forces experienced by the jumper over time.

III. Simulation Experiments and Learning Goals

1. Energy Interplay: Observe the transformation of energy from gravitational potential energy to kinetic energy, and then to elastic potential energy as the bungee cord stretches. Does the total energy of the system remain constant?
2. Safety Parameter Determination: Use trial and error to find combinations of platform height, spring constant, cord length, and jumper mass that result in a safe jump (i.e., the jumper does not hit the ground).
3. Parameter Effects: Investigate the effects of changing individual parameters (jumper mass, cord length, spring constant) on the safety and g-forces experienced during the jump.
4. Accommodating Different Jumpers: Determine how to adjust the cord length and spring constant to accommodate jumpers of different masses while maintaining a safe jump.
5. Ride Experience Comparison: Compare the ride experience (in terms of g-forces) for different combinations of cord length and spring constant, while keeping the platform height and jumper mass constant.

IV. Quiz (Short Answer)

1. Describe the energy transformations that occur during a bungee jump, from the initial drop to the point where the jumper reaches their lowest position.
2. What is the significance of the spring constant (k) in determining the behavior of the bungee cord? How does a higher or lower value of k affect the jump?
3. Explain the concept of g-force and why it is an important consideration in bungee jumping.
4. How does increasing the mass of the jumper affect the forces on the bungee cord, and what adjustments might be necessary to ensure a safe jump?
5. In the simulation, what is the significance of the unstretched length (L₀) of the bungee cord in determining the minimum platform height needed for a safe jump?
6. Why does the simulation measure altitude in terms of the location of the jumper's feet? What practical concern does this address?
7. Describe the relationship between potential energy, kinetic energy, and elastic potential energy during the bungee jump. How are they related when the jumper reaches the lowest point of the jump?
8. What are the primary controls available in the simulation, and how do they allow the user to investigate the physics of bungee jumping?
9. In the context of the simulation, what constitutes a "safe" jump? What visual cue indicates an unsafe jump?
10. How can the Worldview Combo-box in the simulation enhance understanding of the physics of bungee jumping?

V. Quiz Answer Key

1. Initially, gravitational potential energy is converted into kinetic energy as the jumper falls. Once the cord stretches, kinetic energy is converted into elastic potential energy stored in the bungee cord.
2. The spring constant (k) quantifies the stiffness of the bungee cord. A higher k means a stiffer cord, resulting in a quicker deceleration and higher g-forces. A lower k indicates a stretchier cord and more gradual deceleration.
3. G-force is a measure of acceleration relative to gravity. High g-forces can be dangerous or even fatal, so it's important to keep them within reasonable limits during a bungee jump.
4. Increasing the jumper's mass increases the force on the bungee cord due to gravity, leading to a greater stretch. Adjustments such as a shorter cord or a stiffer spring (higher k) might be necessary to prevent the jumper from hitting the ground.
5. The unstretched length (L₀) contributes to the total distance the jumper falls before the cord begins to stretch. A longer L₀ means the jumper will fall farther before the cord engages, requiring a higher platform.
6. Measuring altitude based on the jumper's feet addresses the practical concern of the jumper's height. It ensures that even when the jumper reaches the lowest point, their entire body remains above the ground, preventing injury.
7. At the start, gravitational potential energy is high, while kinetic and elastic potential energy are low. As the jumper falls, gravitational potential energy decreases while kinetic energy increases. At the lowest point, kinetic energy is zero, and gravitational potential energy is at its minimum. Elastic potential energy is at its maximum as the cord is fully stretched.
8. The primary controls include tower height, spring constant (tension slider), unstretched cord length, and jumper mass. These controls allow users to manipulate the variables and observe their effects on the jump.
9. A "safe" jump is one where the jumper does not hit the ground during the entire oscillation. An unsafe jump is indicated by a red cross symbol blocking the view of the simulation.
10. The Worldview Combo-box provides different perspectives on the simulation. "World" shows the visual animation, "Energy" shows the energy bar graph, "Graph" displays the G-Force vs. Time plot, while the combo views present both in split screens.

VI. Essay Questions

1. Discuss the interplay between kinetic energy, gravitational potential energy, and elastic potential energy during a bungee jump. How do the relative magnitudes of these energies change throughout the jump, and how are they affected by different simulation parameters?
2. Analyze the factors that contribute to the g-forces experienced by a bungee jumper. How do the platform height, spring constant, cord length, and jumper mass influence the magnitude and duration of these forces, and what are the implications for safety?
3. Explain how the bungee jumping simulation demonstrates the principle of energy conservation. What are the different forms of energy involved, and how does the total energy of the system remain constant throughout the jump?
4. Using examples from the simulation, explain how trial and error can be used to optimize the bungee jumping experience for jumpers of different masses and skill levels. What are the key considerations in determining the appropriate values for the platform height, spring constant, and cord length?
5. Critically evaluate the strengths and limitations of the bungee jumping simulation as a tool for teaching physics concepts. How effectively does it convey the principles of energy, forces, and motion, and what improvements could be made to enhance its educational value?

VII. Glossary of Key Terms

• Altitude: The height of the jumper above the ground.
• Deformation: The change in shape or size of an object due to applied forces.
• Force: An interaction that, when unopposed, will change the motion of an object.
• Initial Values: The starting values of the simulation parameters when the simulation is reset.
• Oscillation: The repetitive back-and-forth motion of an object around an equilibrium position.
• Parameters: Adjustable variables in the simulation, such as platform height, spring constant, cord length, and jumper mass.
• Simulation: A computer-based model that mimics a real-world phenomenon, allowing users to explore and experiment with different conditions.
• Tension: The force exerted by a stretched object, such as a bungee cord.
• Thrill Seeker: Someone who enjoys engaging in activities that are exciting and potentially dangerous.

Sample Learning Goals

 

For Teachers: Instructions on how to use the Applet

Worldview Combo-box

Tension Slider

Drag-able Boxes

Play and Reset Buttons

Research

 

Video

 

 Version:

Other Resources

 

Bungee Jumping Simulation FAQ

Question 1: What physics concepts can be explored using the Bungee Jump simulation?

The Bungee Jump simulation allows users to investigate key energy concepts, specifically: Kinetic Energy, Gravitational Potential Energy, and Elastic Potential Energy. The simulation demonstrates the conversion of Gravitational Energy into Kinetic Energy as the jumper falls until the bungee cord becomes taut. After this point, an interplay between all three types of energy occurs until the jumper's Kinetic Energy reaches zero at the lowest point.

Question 2: What parameters can be controlled in the Bungee Jump simulation?

Users can control several parameters within the simulation, allowing for a varied exploration of the physics involved. These parameters include: the height of the tower, the stiffness of the bungee cord (represented by its spring constant 'k'), the unstretched length of the bungee cord (Lo), and the jumper's mass.

Question 3: How does the simulation indicate a "failed" jump?

If the simulation detects that the jumper's feet come within 1.7 meters of the ground (approximating the jumper's height), it indicates an impact or "accident" by displaying a red cross symbol, which obscures the view. This visual cue represents an unsafe jump.

Question 4: What is the purpose of the "safe jump" exercise in the simulation?

The "safe jump" exercise encourages users to find a combination of tower height, spring constant, cord length, and jumper mass that allows for a jump without hitting the ground. This reinforces the understanding of how these parameters interact to affect the jumper's motion and the transfer of energy.

Question 5: What questions are suggested for exploration in the Bungee Jump model?

The Bungee Jump Java simulation poses thought-provoking questions such as: Does total energy change during the jump? Are the g-forces experienced by the jumper reasonable, dangerous or even fatal? What happens when you increase or decrease the jumper's mass, the unstretched length of the cord, or the stretchiness of the bungee cord? What adjustments should a jump operator make to accommodate a heavier jumper? These questions are meant to promote experimentation and critical thinking.

Question 6: What tools does the applet provide to customize the experience?

The applet provides a Worldview Combo-box for toggling between graphs representing the world view, energy view, and a combined view. There is also a Tension Slider for adjusting the tension of the bungee string. The applet also allows you to drag boxes representing the Height of the Pole, Rope length, and Mass of the Person. Finally, the applet also provides Play and Reset Buttons.

Question 7: How does the simulation relate to real-world bungee jumping?

The simulation simplifies the complexities of real-world bungee jumping but accurately portrays the fundamental energy transformations. It models the interplay between gravitational, kinetic, and elastic potential energy, allowing users to visualize and understand these concepts in a dynamic setting. While not a perfect representation, it serves as a valuable tool for learning about the physics principles at play.

Question 8: How can the simulation be embedded in other webpages?

The simulation provides an embed code (iframe) that can be used to integrate the applet into other webpages. This enables educators and developers to easily incorporate the simulation into their own online resources, facilitating wider accessibility and use.