Calculating Stiffness Constant k of a Bungee Rope: An Experiment

[deeman1]

2. The equation you will be using is given by T = kx. Please refer to chapter 17 in the book for a reminder. I require you to design an experiment to calculate the stiffness constant k for the bungee rope I have given you. In the report you should consider the following points

a. What type of equipment will you require?
b. What type of measurements will you be making?
c. Are you making any assumptions and do you think they are valid?

3. Write up the experiment as if you have actually done. Obviously you will not have actual results, but you should write an aim, a method, the graphs you would be expecting to find and your conclusions. Your conclusion should involve a way of calculating the stiffness k from the graphs you have drawn.

4. You should then research a suitable value of k for your situation.

5. Calculate how high up you would have the bungee platform placed. Remember how you described your idea of an exciting bungee jump in question 2.

6. Finally calculate what your maximum speed would be during the jump.

a. Remember that the total energy of the jump is the sum of potential energy, kinetic energy and elastic energy. You will need to research what elastic energy is and how you calculate it.
b. To find the maximum velocity you will need to use techniques from calculus, i.e. find the velocity in terms of the extension x, differentiate and find when V has a maximum point

how can i calculate this
i have started but just want to be sure

 

[jbsteele]

i am on the right trackExperiment to calculate the Stiffness Constant k for a Bungee RopeAim: The aim of this experiment is to calculate the stiffness constant k for a bungee rope.Equipment: The equipment required for this experiment includes the bungee rope, a tension measuring device, a stopwatch, and a ruler. Method: First, the bungee rope is attached to the tension measuring device and an object of a known mass is attached to the other end of the bungee rope. The object is released from a platform of known height and the time taken for it to fall to the ground is recorded using the stopwatch. The distance between the object and the tension measuring device is also measured using the ruler. This process is repeated multiple times with different platform heights, and the results are plotted on a graph.Graphs: The graph that would be expected to be produced by this experiment is a plot of the extension of the bungee rope against the time taken for the object to fall. It should show a linear relationship between the two variables, with the slope of the line representing the stiffness constant k.Assumptions: The assumptions made in this experiment are that the platform is at a constant height, the mass of the object is constant, the rope is at a constant temperature, and that the rope is not subject to any external forces. These assumptions are valid as long as the experiment is conducted under controlled conditions.Calculating k: The stiffness constant k can be calculated from the graph by finding the slope of the line. The equation for calculating k is k = (Change in Extension)/(Change in Time). Therefore, by measuring the change in extension and the change in time, k can be calculated.Result: The result of the experiment is the stiffness constant k for the bungee rope. Conclusion: The experiment was successful in calculating the stiffness constant k for the bungee rope. The value of k will depend on the type of rope being used, but it can be calculated by measuring the change in extension and the change in time for a given platform height.Researching a Suitable Value of k: The suitable value of k for a bungee rope can be found by researching the type of rope being used and its properties. For