The Great Bungee Jump Concepts MODELS & DATA
Later in this unit, we are going to create a mathematical model of the
bungee jump. To see whether the model is correct, we need to compare the
model to real data from the scale model. Once we have confidence in our
mathematical model, we can apply the model to a real jump. Here is the
structure of our work:
Structure of Work
The parameters are values that apply to a particular jump, such as the
mass of the jumper and the stiffness of the elastic. When these values
are supplied, the mathematical model generates a prediction. We will compare
the prediction and data on a graph. Then we can change the parameters or
the model until the prediction and data agree. What form does the prediction
take? The model tells us where the jumper will be at any time. In mathematical
terms, it predicts pairs of numbers of the form (y,t) for all any
value of t, the time. Here, y is the height of the jumper
above the ground. To compare the prediction to reality, you need data in
the form (y,t) for several times. This means that you need to know
how high the jumper is above the ground for different values of t.
Taking measurements is central to science. Recording the measurements (data) can be done in the form of a table like this:
We will say that t=0 is when the jumper starts. In this example,
the jumper started 2.31 m above the ground.
Timing the Jump
We start a timer when the mass just starts dropping and stop it when it crosses a height you select. The time reported by the timer is one value of t, and the height of the mass when it stopped the timer is the corresponding value of y. We then move the bottom (off) switch lower on the tower to get different values for y and t.
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