Lab: Determining the Coefficient of Friction between Two Surfaces using Video Analysis
By Christopher Lyke, Denver School of the Arts, 10/22/14. Contact [email protected] with questions.
Purpose:
To determine the coefficient of friction between two surfaces using video analysis.
Materials:
Pulley (mounted to edge of), test bench, cord, dropping mass, friction sled, various test masses, scale, meter
stick, video camera, tripod (optional), video analysis software. (See picture below for examples of some of the
above).
In our lab we used a bag of sand for the
dropping mass, a wooden box for the
friction sled, string for the inelastic cord
(possible source of systematic error?), and
bars of modeling clay for the test masses.
The pulley was a screen door roller clamped
to the edge of a classroom table with a
clamp (both available at hardware stores)
(Meter stick, video camera and scale not
shown). We used Tracker video analysis
software.
Procedure:
1) Weigh friction sled on scale. 2) Attach dropping mass to friction sled with string. 3) Place meter stick (for
scaling video image) on table extending away from pulley toward friction sled. 4) (Use optional tripod to)
record video from above, at an angle orthogonal to the table surface, while releasing dropping mass and
causing friction sled to accelerate alongside meter stick. 5) Weigh clay bars (or other objects) and place in
friction sled, repeating step 4 for an evenly distributed set of test masses.
Data:
video files from smartphones (emailed by students to themselves) are the raw data. Dropping Mass = X kg.
Friction sled = Y kg, Test masses = A, B, C kg.
Analysis:
Using Tracker video analysis software, we imported our data files and created P/T graphs reflecting the friction
sled (relative) position over time. We used Tracker to fit a quadratic equation to this P/T graph and multiplied
the 2nd order coefficient of the quadratic model by 2 to find the acceleration, since acceleration is the second
derivative of distance (or because you can tell through inspection of the distance formula that the rate of
acceleration must be twice the coefficient of t^2 as in the relationship d=0.5at^2). We then calculated the
friction force using Ff = m2g - (m1+m2)a where ‘m1’ is the mass of the friction sled plus test mass and ‘m2’ is
the mass of the dropping weight and ‘a’ is the acceleration of the dropping weight-friction sled system (as
determined through video analysis). We then created scatter plots of F f vs Fn for our data points and found an
equation and coefficient of correlation for a line of best fit. The coefficient of friction between our materials
of interest is the slope of this line, as it represents
Results:
Combined Sled/Test
Mass M1 (kg)
Acceleration (from
Tracker) a (m/s)
.
Normal Force (N) = m1g
Friction Force (N) (see
above)
SCATTER PLOT WITH LINE OF BEST FIT, EQUATION, AND CORRELATION COEFFICIENT goes here.
Conclusion:
Our analysis depended on many assumptions, including 1) frictionless pulleys 2) massless and inelastic strings
3) constant coefficient of friction over length of test surface (for constant acceleration) 4) no air resistance.
Despite the unrealistic nature of these assumptions, and the initially frustratingly results which emerged from
our attempts at video analysis, several groups managed to determine realistic (0.2 – 0.7) coefficients of
friction between the tabletop and wooden boxes. This is in line with friction coefficients for wood on a variety
of surfaces ranging between 0.2 and 0.55 as determined from a brief internet survey. Systematic errors were
clearly present as the y-intercepts of our lines of best fit were not zero, and we would expect zero friction
force with zero normal force. A positive y-intercept seems indicative of frictive pulleys and/or non-massless
strings. Negative y-intercepts are more difficult to explain as systematic error and may be a result of the
overall uncertainty of the results as related to the coefficient of correlation for the line of best fit. Not holding
the video-recording device parallel to the tabletop might also account for systematic error as foreshortening
of video image could give unrealistic acceleration values. Also in the category of systematic errors would be
any movement of the camera during filming of a test run though this “systematic” effect would be limited to a
single data point resulting in unrealistic relationship between multiple data points. This would be an example
of a systematic error in collecting data for a single event resulting in a random error when considered across
related events.
Sources of random error included uncertainty in weight measurements of test masses, friction sled, and
dropping weights. Random errors of marking position of test sled in consecutive video frames for video
analysis would also be included in this category.
This experiment could be improved by improving lighting and taking video at a higher rate of frames/sec to
get clearer images to analyze in video tracking software. I would standardize video-recording practices and
take more care in positioning camera above test bench (table) and use a tripod to hold it still. I would try to
find pulleys with less friction and I would use fishing line instead of cotton string to attach dropping weight
and friction sled for(presumably) less stretch and/or mass. I would make a very visible high-contrast sharpdefinition mark on the test sled to aid in determining position in tracking videos. And I would clean test bench
surface and friction sled bottoms uniformly or use alternative surfaces (such as boards without wear or
contamination, and upgraded friction sleds with a single material at bottom (our friction boxes had a
combination of plywood veneer and end-cut grain in contact with table). Alternative materials could be
attached to bottom of friction sled and/or test surface such as sand-paper, regular paper, rubber, plastic, etc…
if comparisons of different materials were desired.