Phys 131, Fall 2012
TA GUIDE—Lab 2 (Part 2)
Lab 2 (Part 2)—Error Propagation and Analysis of Directed Motion
& Resistive Forces
Overview:
This is the second week of a two-week lab sequence designed to introduce the students to
video capture, error propagation, and analysis of directed motion and resistive forces. In the first
week, students collected video data using ImageJ for two separate investigations. In the first
investigation, students gathered data investigating how resistive forces and terminal velocity scale
with the mass of the falling object. In the second investigation, students gathered data investigating
how resistive forces and terminal velocity scale with the viscosity of the fluid. This week students
will analyze their data and try to determine how the terminal velocities scale with respect to the
varied quantities. The lab handout will give explicit instructions on error propagation, but no
guidance in the performance of the physics skill goals. Your tasks are: 1) to demonstrate and explain
error propagation concepts when asked, 2) to help with Excel when asked, and 3) to act as a guide
for the physics skills (see the document on helping student groups learn). In the past week, the
students have gained (through recitation, readings, and lecture) the necessary theoretical background
to analyze their data regarding the scaling of resistive force. (It is often a good idea to put the
approximate timing on the board, as well as a short list of the objectives/skill goals—see the next
page.)
On the blackboard, you should write information about the viscosities of the percent
solutions that students worked with last week. Other possibly helpful information is listed below—
if there is information (physical data) that students think they will need, they should ask you—but
students have to know what they are asking for!
Viscosities:
Percent Glycerol (by Volume)
Dynamic Viscosity (Ns/m^2)
0%
0.009
30%
0.0026
40%
50%
0.0041 0.0070
60%
0.0132
70%
0.0278
80%
0.4346
Other possibly helpful information:
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Diameter of the Spheres: ¾” = 1.905 cm
Mass of 500 Coffee Filters = 836 g
Mass of 25 ‘Black X’ Plastic Spheres = 108 g
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Mass of 25 ‘Red X’ Plastic Spheres = 110 g
Mass of 10 Steel Spheres = 283 g
Mass of 10 Brass Spheres = 308 g
Phys 131, Fall 2012
TA GUIDE—Lab 2 (Part 2), cont.
Materials:
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Excel data files for investigations 1 and 2, as collected last week
1 per person—Error Propagation instructions/lab guide
Introduction:
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Groups of three or four students—performing in the Community Lab roles
Mention that resistive forces, like drag resistance and viscous resistance, are proportional
to some power of velocity (v1 (viscous, laminar, non-turbulent flow) or v2 (drag,
turbulent flow))—by taking careful data, we can see which of these is more appropriate.
(Although turbulent and laminar flow are both possible options for either air or fluids,
depending on the Reynolds number—they’ve heard about this in lecture.)
Briefly review the Physics Skill Goals on the next page
Inform students that a lab report will be due at the end of the lab today!
Intermission:
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Between the analysis of investigations 1 and 2, have students share their results with
other groups studying the same investigation 1. Then have the groups share their results
with the class. Does terminal velocity scale with mass in the same way for a falling
coffee filter and for a sphere falling through viscous fluid?
Settle on a relationship for the ball-through-fluid. (It should be viscous resistance,
proportional to v1.) This is necessary to set the stage for the analysis of the 2nd
investigation.
Summation/Submission:
o Have the groups share their results concerning the way that terminal velocity scales with
viscosity.
o Recap the Skill Goals, clarifying any remaining confusion about physics concepts
o Discuss the challenges and considerations with the class, if any have not yet been
addressed. Ask the students what they found most difficult/challenging about the
analysis.
Phys 131, Fall 2012
TA GUIDE—Lab 2 (Part 2), cont.
Physics Skill Goals:
Analyze 1-D motion from a
video/image sequence
Tabulate the position-at-time for an
object’s motion
Calculate average speed
Understand the concept of terminal
velocity
Understand the scaling of terminal
velocity with mass
Understand the scaling of terminal
velocity with dynamic viscosity
Understand the types of resistive force
in ‘fluids’—Drag vs. Viscous resistance
Analyze motion graphs (y vs. t, v vs. t,
(a vs. t))
Determine uncertainty in video
measurements
Challenges/Considerations:
What is 1-D? How do you separate out a second
dimension? (Does the perpendicular-direction motion
matter? Why?/Why not?)
Where is the object? (What part do we track?) How do
you match the pixel locations and time slices to the given
scales?
What is the difference between average and instantaneous?
What should the units be?
What does it mean? What does it look like on a y vs. t or
v vs. t graph?
How is vt proportional to m? Is it linear with vt1? Is it
linear with vt2? What are the implications of each of these
options?
How is vt1 proportional to viscosity (μ or η)? Is it linear?
Is it polynomial? Is it exponential? What are the
implications of each of these options?
Which is proportional to vt1? Which proportional to vt2?
What is a ‘fluid’ in physics?
How are the graphs connected? What do
positive/negative values imply? What do
positive/negative slopes imply?
How do you determine uncertainty? Is it the same for all
videos? How can the uncertainty in position be
propagated into the average speed? Is there uncertainty in
time?
Approximate Timing: (~2 hours)
o
o
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o
o
Introduction:
Data Analysis (1st investigation):
Data Analysis (2nd investigation):
Class Discussion/Summation:
Finalize Report:
10 minutes
30 minutes
30 minutes
10 minutes
30 minutes