Lab 2, Part B: Drag forces and terminal velocity

Materials and Process
  1. Use the same setup as in previous part of the lab to record the terminal velocity of beads under several different conditions:
    1. Randomly choose two beads (either steel, aluminum or nylon, either 1/2, 1/8 or 1/16 inch diameter) to be measured in water.
    2. Randomly choose one bead (steel or aluminum, either 1/2, 1/8 or 1/16 inch diameter) to be measured in glycerin.
  2. Enter your terminal velocity measurements in the class google spreadsheet by the end of lab.
  3. Use the entire class’s data to assess the agreement (or lack thereof) between the effective weight of the bead and the drag force, at terminal velocity.
Questions to be answered in the lab report (due after week 2 of the lab):
  1. Why didn’t we ask you to measure the terminal velocity of a nylon bead in glycerin?
  2. Using data from a small (1/8 or 1/16 inch) steel beed in water, convince us that the quantity that you measured is in fact the terminal velocity. There are several ways to do this.
    • One plausible way is to plot speed vs time and show that it is constant (since this is the definition of terminal velocity).
  3. Using the collective data from the entire class, calculate the effective weight of the bead (its weight minus the buoyant force), the Stokes drag force and the aerodynamic drag force. Which of the two possible drag forces seems most accurately to be balancing the bead’s weight at equilibrium (at terminal velocity)? Convince us with a plot of some kind.
  4. Drag force is normally divided into two classes: “large, fast objects” have Reynolds numbers much larger than 1; “small, slow objects” have Reynolds numbers much smaller than 1. Using the class’s data, can you determine which drag force is appropriate for which range of Reynolds number?
    • In questions 3 and 4, you are basically trying to show whether Faerodynamic = Weffective or, alternatively, Fviscous = Weffective, and whether the answer depends on the Reynolds number. (See the bead physics document for definitions of these concepts). In general, an elegant way to test whether A=B is to examine either
      • A/B (which should be one if A=B, and is unitless) or
      • A-B (which should be zero) or
      • (A-B) / B (which should be zero and unitless).
    • In this case, since you have to determine whether the Reynolds number matters, you can plot one of those quantities as a function of Re. For instance, plot the quantities (Faerodynamic = Weffective) / Weffective and (Fviscous = Weffective) / Weffective vs Re, and see which (if either) is consistent with zero.

Your group will submit one collective lab report. Grab this this blank word file (basically just a cover sheet) as a starting point for your lab writeup.