Bungee Jump Intro

## Bungee Jumping

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!)
Bungee Jump

### Software Requirements

SoftwareRequirements

 Android iOS Windows MacOS with best with Chrome Chrome Chrome Chrome support fullscreen? Yes. Chrome/Opera No. Firefox/ Sumsung Internet Not yet Yes Yes cannot work on some mobile browser that don't understand JavaScript such as..... cannot work on Internet Explorer 9 and below

### Credits

Michael R. Gallis; Fremont Teng; lookang

### For Teachers: Instructions on how to use the Applet

#### Worldview Combo-box

Toggling between the world-view Combo box will show the respective graphs.
(World)

(Energy)

(Graph)

The first three options will select them in fullscreen.
The last two options will combine the two views into one screen.

#### Tension Slider

Moving the slider will adjust the tension of the string in the Bungee Jump.
Adjusting the slider to the left increases the tension,
While adjusting it to the right decreases the tension.

#### Drag-able Boxes

1) Height h

Adjusts the height of the pole.

Dragging the box will extend the length of the rope.

3) Mass of the Person
(Default)

Moving left will decrease the man's mass
Extending it will make him fatter

#### Play and Reset Buttons

Plays and Resets the simulation accordingly.

Research