## Hands On Physics

### The Great Bungee Jump Messing Around Investigation 1: A First Model

#### Remember: Your job in this unit is see whether you could save lives with a bungee cord escape system. In this activity, you see what you can learn by carefully observing a scale model.

• How a bungee escape might work.
• What might go wrong.
• What you need to know before you would try the bungee escape.

2. Make a scale model. Securely attach about 1 meter of elastic to a mass. The mass should be large enough stretch the elastic to about 1.8 m.

3. Observe the drop. Simulate a bungee escape. Hold the elastic in one hand and drop the mass. Try different lengths of eleastic and different masses. Does this help you answer any of your questions?

Figure M1
Model Bungee

4. Simplify the problem. The art of modeling is to make good simplifying assumptions. To understand the bungee jump, we need to simplify it. But we always have to be careful that our assumptions don't invalidate our results.

• Ignore one dimension. The real jump takes place in two dimensions: the up-and-down motion is one and the back-and-forth motion is the other. It will be much easier to understand if we can focus on the up-and-down dimension and ignore the other. From your observations, explain why is this reasonable.
• Ignore air friction. Air rushing by will slow down the bungee jumper a bit. This is called air friction. But perhaps air friction will be so small compared to the other forces that we can ignore it. Can you justify ignoring air friction?

5. Diagram the forces in each part of the jump. To really understand what is going on, you have to understand the force acting on the jumper. Draw four diagrams that show the size and direction of all the forces on the jumper in different parts of the jump.:

• In free-fall when the elastic is limp. During this time the bungee cord can be ignored; it might as well not be there. Only one diagram is needed during this part of the jump.
• In downward motion while the elastic is taut. This is the part when the elastic is slowing down the jumper. Make diagrams of three different times during this part.

Of course, there continue to be additional parts to the motion of the mass, but we are not really interested in them. We hope the jumper gets off at the bottom of the first drop!

6. Predict the motion. Imagine that a camera could get a single photograph of the position of the jumper at regular intervals. This is like what you see when there is a blinking strobe light on a dance floor. If you recorded a rolling ball you might see the following:

Figure M2
Rolling Ball

Make a drawing like this for the bungee jump. Show where the bungee cord is limp and taut. As in the drawing above, show where the jumper is going fast and slow as well as where it is accelerating. Explain your predictions.

7. Summarize. What have you learned so far? Can you answer any of the main questions? What else do you need to know?