This will be a computer lab in which you will use Mathematica and Interactive Physics (IP) and Igor. You will investigate the difference between a drag force which depends on linearly on velocity as opposed ot quadratically on velocity.

Problem:

A ball of mass m falls from rest in the gravitational field of the Earth, i.e. g = 9.8 m/s².

Step 1:

Assume that the resistive force due to air resistance is -bv where b is a constant and v is velocity. Find v(t) - i.e., how v depends on time. We already did this in class

Step 2:

Repeat the above but now assume that the resistive force goes like -cv² where c is some other constant. Find v(t) again. You might want to use Mathematica to help with the integrals.

Step 3:

Now use these expressions in IGOR to make a plot of v(t) in both cases. Assume a 1 kg mass and pick the constants b and c so that that terminal velocity is the same: 30 m/s. Make a plot comparing the two curves on the same axis. Based on this - how difficult would it be to actually distinguish between the two possibilities. Feel free to choose a different mass and terminal velocity but once you choose these - use the same values in Step 4.

Step 4:

Now use Interactive Physics to simulate both situations - linear and quadratic resistive force using the mass and terminal velocity you chose in Step 3. Export the data for both cases to IGOR - see the Helpful Hints below. Superpose the "data" from IP on your theory curves. Display the "data" as markers (points, squares, etc...). Note that the data from IP give negative velocities - so you should plot the absolute values when comparing to theory.

Step 5:

Write up your results in a report - as a Word document. Include plots.

Helpful Hints:

Air resistance in IP - under the main menu World - you will find Air Resistance. Selecting this brings up a dialog box that allows you to select None, Standard or High. Standard and High refer to linear or quadratic in velocity. You can select the value of the contant or type it in.

Graphing velocity - you should open a graph window in IP to plot vertical velocity vs time. To do this select the object that will be falling - under Measure select Velocity then Y-graph. You can play with the masses and resistive constants to get the terminal velocity you want.

Exporting data from IP - in your IP window. Under File choose Export. This will bring up a dialog box. Under Type - select Meter Data (another option is QuickTime movie - which will be useful later). This saves the data associated with any graph you have open. Type in a file name and location to save it. In this case you will only have one graph - vertical velocity vs time.

Importing into IGOR - With IGOR open under Wave select Load Waves then Load General Text. This will bring up a dialog box. Select the file you saved in the step above and then Do It. Note that the time and velocity waves will be automatically named. Now you append these "data" to your theory plots.