Purpose:

We will be exploring how to characterize our surgical tube as a physics spring with an unknown spring constant(s). If you want a little history of bungee jumping start with this story from Vanity Fair magazine about the Oxford Dangerous Sports Club. Land diving in the Pacific Islands is a unique form of this form of crazy.

Equipment: COVID

To complete this lab independently you will need a rubber band of modest length (at least 10 cm (4 inches) long and 2 or 3 would be great!), a couple of paperclips, a small ziploc bag or envelope, and a good stack of small identical objects like quarters or 16d nails or large washers to use as weights. You will also need some form of linear measuring device that will depend on what you find for a rubber band. Since we are going to measure how the 'rubber band' stretches it would probably be ideal to have a ruler that measures mm. Many of the standard rulers have inches on one edge and cm and mm on the other edge. This rubber band will serve as your bungee cord for this lab.

Procedure:

For this lab you will need prepared surgical tubes, some lab weights, a meter stick, and your minds. The

  • 1) The spring constant describes the “stretchiness” of a spring. To determine the spring constant we need to know how much the spring stretches when subjected to a known force. Be sure you understand the relationship between these concepts before you dive into the lab.
  • 2) Because the bungee cord does not form an ideal physics spring we need to determine the spring force as a function of the `stretch'. How will you do this and how many data points do you need? A first question to consider is how many data points do you need to adequately characterized the spring? You will need to take some initial data and think about it before settling on an answer to this question. Plotting by hand as you go is an important skill to practice during this lab though if you have your JupyterLab notebook open you can do it there just as easily. This plot is a scatter plot. In the end you will be asked to generate this plot, and others, in a notebook now that you have those skills. For safety reasons we ask that you not stretch the bungee cord more than twice it's original unstretched length.

    • Commentary: When you make your measurements I'm looking for reasonable accuracy but not excessive accuracy. If we were in class together I could notice and talk to folks who are being overly concerned with accuracy. In the time of COVID all I can do is offer general guidance from a distance. If it takes you more than a minute or so to add the weights and measure the rubber band you may want to relax a little. There is a time and place for high precision but this is not it.As you make the measurements you will be adding weights in a consistent pattern and measuring the length of your bungee cord produced by each weight. Be careful to note the length of the bungee cord with no weight since we will be using that value in our calculations.

  • 3) We will be using this data to develop a thoughtful model for these "bungee" cords. For this reason I need you to duplicate some of your data enough times to be able to determine the standard deviation of your data points. You need to have data that supports your determination of the spread in your data points (standard deviation) at 3 points (begining, middle, and end) across the range of your data. When this is complete you should be able to articulate a rough estimate for the variability (standard deviation/mean) of your data.

    • Commentary: What you are trying to establish here is how reproducible you data is by making a number of measurements of the stretch of your bungee using the same weight. To do this you have to remove all the weights and add them back and remeasure the stretch. You need to do this 4-5 times for three points (begining, middle, and end). The rest of the data points that define the shape of your data only need a couple of data points to confirm the pattern.

  • 4) A physics model is an effort to describe the features or behavior of some observed data. In the event that your data does not seem to fit a Hooke's Law (linear) model what model might work better? Many complex behaviors can be modeled by two separate linear behaviors. Can you draw two or more straight lines that more effectively model the behavior of the bungee cord? What does this mean about the behavior of the bungee?

  • 5) (not during COVID!) Exchange data with another group whose bungee cord is at least 20% different in length. Plot their data on your plot so there are two sets of data. What are the similarities and differences between the plots?

Lab Deliverables:

Complete the Lab Deliverables embedded in the Jupyter notebook for this lab. Turn in a pdf of that notebook to the appropriate location on Bb.