Lab 2, Part A: Drag forces and terminal velocity


All of micro-, cellular and molecular biology takes place in water, a viscous medium that produces drag force on objects moving through it. You may not think of water as particularly viscous (compared to molasses, say), but it certainly is compared to air (the other important medium in biology). In addition, small slow objects are proportionally more strongly affected by viscous forces than large fast objects, so your intuitions about the properties of water are probably not appropriate for a cellular- or sub-cellular-sized object.

In this lab, you will measure the drag force on a falling bead. Since the force is small and the bead is moving (and therefore hard to measure directly), you will infer the form of the drag force formula by looking at the terminal velocity of falling beads of different sizes and densities.

Materials and Process
  1. Set up a camera (probably your cellphone) to get a clear, stable image of your 2L graduated cylinder. Please (1) bring your phone, (2) delete some cat videos from it to make room for lab recordings, (3) bring your phone cable; this will upload video to computer much more quickly than WiFi or cell data plan service. A white background generally improves the video contrast. Include some kind of a distance scale in your video.
  2. We will provide a nylon, aluminum or steel bead, with a diameter between 1/8″ and 1/2″. Drop the bead in the center of the cylinder (try to avoid the sides) and record the falling bead. Transfer your video to a computer; load into Fiji / ImageJ and measure the terminal velocity of the bead.
  3. Repeat this a half dozen times (that is, measure the terminal velocity of several identical beads).
  4. Condense all your measurements into a single number and an uncertainty (aka error) on that numbers.

Next week you will repeat this with different sized beads, made with different materials, and compare your results to predictions from two possible formulas for the drag force. However, you can already answer questions 1 and 2 below:

Questions to be answered in the lab report (due after week 2 of the lab):

(1) Convince us that the quantity that you measured is in fact the terminal velocity. This isn’t a totally trivial issue: the first time I tried this lab I just grabbed a large steel marble from my son’s room – the speed I measured using this setup was not its terminal velocity.

(2) Explain clearly how you combined all your measurements into a single number (plus error).

(I acknowledge that these “questions” are not actually phrased as questions. Sue me, Alex Trebek.)

After next week’s lab, your group will submit one collective lab report. This will be graded by the TA according to our lab rubric. Good attention to detail now will save you time later! Remember, your TA is here to help you with equipment and ImageJ, but the physics is up to you and your group.

Grab this this blank word file (basically just a cover sheet) as a starting point for your lab writeup.