The force of air resistance clearly depends on the velocity of an object moving through the air: the larger the speed, the larger the drag force. But what is the exact form of this relationship?
Your textbook suggests that under some circumstances, air resistance depends on the square of the velocity:
However, some other sources suggest that at low speeds, the air resistance grows linearly with velocity:
Your job today is to figure out which of these formulae more accurately fits the data from a simple experiment.
Each team will make measurements of the same event: I'll drop one set of filters, and the entire class will share all the resulting measurements.
You'll need to know the masses of the objects involved:
When an object has reached terminal velocity, the downward pull of gravity exactly balances the upward push of air resistance:
That means that you can calculate the force of air resistance easily, if you know the mass of the falling filters.
Now, your job is to determine which of these relationships between the force of air resistance and velocity is a better fit to your measurements.
A good way to see if measurements match a theory is to make a graph on which the theory predicts there should be a straight line:
If the data lie in a line on the graph, then they agree with the theory. The slope of that line must correspond to the symbol m in the equation, and the y-intercept of the graph must correspond to the symbol b.
Suppose that a coffee filter had a very tiny mass; for example, 0.001 grams. What would the force of air resistance be on that filter when it reached terminal velocity?
Make a prediction: if we were to place 8 clips into a filter, and drop it, what terminal velocity would it reach? How long would it take to fall from the first-floor railing to the floor of the atrium?
If you have time, consider ...
We have only considered two very simple possibilities, in which the the force of air resistance depends on velocity to the first power, or the second power. It's quite possible that real life may be more complicated: maybe air resistance depends on some fractional power of the velocity, like
When physicists think that one quantity depends on some other quantity raised to a power, they often turn to log-log graphs. Starting with a formula in which velocity goes like some power n of the mass, they take the logarithm of both sides, and then make a graph based on that new equation.