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Last Modified: 2:01pm 10 Aug 11

The dependence of air resistance on velocity

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: 


                                      2
          drag force D  =  (const) * v

However, some other sources suggest that at low speeds, the air resistance grows linearly with velocity: 


                                       
          drag force D  =  (const) * v

Your job today is to figure out which of these formulae more accurately fits the data from a simple experiment.

The experiment

  1. Create a set of objects with the same size and shape, but different mass, by nesting increasing numbers (1 to 5) of coffee filters.
  2. Give the objects what we HOPE will be terminal velocity by having one team member stand on the third floor of the atrium and drop them, one at a time. After a short acceleration, they will (we hope) reach a constant speed for the majority of their fall.
  3. Have a second team member stand at the bottom of the atrium and measure the time it takes for the ball to fall from the carpet of the second floor to the bottom of the atrium.
  4. Calculate the speed of each object during this final portion of its flight; the distance from atrium floor to second-floor carpet is 9 meters.

The model

Write down two equations showing the forces on an object when it has reached terminal velocity: one for the first form of drag force (proportional to speed squared), and one for the second form (proportional to speed).

Then re-write the equations so that they look like this: 



                 n
       (velocity)     =   (const) * (mass)

where n is either 1 or 2, depending on the form of the air resistance formula.

You must decide which of these two formulae better matches your experimental results. I suggest that you make a graph, but exactly what to put on that graph is up to you. Feel free to ask one of the instructors for suggestions.

Extra

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 like this: 


                 n
       (velocity)     =   (const) * (mass)

they take the logarithm of both sides, and then make a graph based on that new equation.

  1. Take the logarithm of both sides of the equation above, and write down the result
  2. How can you use this new equation to determine the value of the power n?
  3. Make a new graph and use it to estimate n. Which of the models -- air resistance going like velocity or velocity-squared -- does this method support?


Sorry, we could not find this page | RIT CIS - Center for Imaging Science

Sorry, we could not find this page

We apologize, but the page you were looking for is not available. Most of our material is available from the menus above.

Last Modified: 2:01pm 10 Aug 11