Friction Lab
PH 101/201
Name ________________________
informal
Course _________________________
______________________
Partner’s Name (s) _________________
Equipment
Inclined plane with protractor, friction block, meter stick, force probe, rubber
band, 1kg masses
Purpose
To find the coefficients of friction for a block on a board using three different
situations, to gain proficiency with force vectors, and to learn about cross
checking results using different methods.
Suggestion: In this activity it seems to work best for students if they do all
measurements for all Methods very carefully and then, after all measurements are
completed, do the derivations and then calculations for each method.
Method A:
Inclined Plane Method
Place the friction block on the inclined plane with the surface horizontal. Tilt the plane
upward slowly until the block just begins to slip. Carefully read the protractor and
record the result. Repeat five times.
Trial #
1
2
3
4
5
average
Stnd. Dev.
θ (deg)
Sample Data and Calculations Table(since this is an informal lab you will have to make your own Table on
engineering paper or computer print-out to turn in.)
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Friction Lab
PH 101/201
1.
Calculations:
2.
Combine the formulas,
informal
(The calculations for this method and the other methods are easiest to do after all data has
been collected as you can then concentrate on the part. Appendix C on using Excel for calculating averages and
standard deviatiosn may also be helpful)
fk = k n
w = mg
and the trigonometry for obtaining vector components to derive an equation for the
launch coefficient of static friction, k, in terms of the angle . Show all steps for this
derivation on your calculation sheet, including an appropriate force diagram. Use your
equation to calculate the coefficient of friction for each of the five trials and record in a
table on your data and calculations sheet (see table above as an example).
From these five values find the average coefficient or friction for this method (method
A). Note the bar over the  is a standard shorthand notation for average.
5
A 
1   2   3   4   5
5


i 1
i
5
Find the standard deviation for your velocity measurements. The standard deviation
( 1  
SA 
5

 (
i 1
i

A
A
) 2  ( 2  
A
) 2  ( 3  
4
A
) 2  ( 4  
A
) 2  ( 5  
A
)2
)2
4
gives a measure of the scatter in your data points. Record both the average and standard
deviation clearly on your data and calculations page for Method A.
Method B: Fiction force with various normal forces.
1. Return the inclined plane to horizontal.
2. Hang the friction block from the force probe and record the reading _______ N.
3. Remove the block, still holding the force probe vertical, and record the reading
with no weight hanging on the probe.
“zero reading” =
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____________ N
Friction Lab
PH 101/201
informal
4. Calculate the weight of the friction block and record it in the table on your
calculation sheet, similar to that below.
5. Set the force probe down on the table, oriented horizontally (writing on top face).
Zero the probe by clicking on experiment, set up probes, labpro. You
should now see a picture of the Labpro interface with a force probe in a square
next to it. click on the force probe and select zero.
6. Place the friction block on the inclined plane and tie the rubber band on the hook.
Hook the force probe to the other end of the rubber band and pull gently. Increase
the strength of your pull slowly until the block begins to move. Record the force
necessary to just get the block to move.
7. Repeat step 6 four more times, adding a 1 kg mass on top of the block each time.
The results should be recorded in a table like that below.
8. Repeat each trial again with the second lab partner doing the pulling. record these
values in the last row of a data table.
Trial #
block
block + 1kg
block + 2kg
block + 3kg
block + 4kg
Weight
(N)
Pull (N) 1
Pull (N) 2
Sample Data and Calculations sheet(since this is an informal lab you will have to
make your own Table on engineering paper or computer print-out to turn in.)
Calculations:
(The calculations for this method and the other methods are easiest to do after all data has been
collected as you can then concentrate on the part. Appendix C on using Excel for calculating averages and standard
deviation may also be helpful)
For each partner’s data, plot the friction force against the normal force and determine
the coefficient of static friction from a linear fit to the data. Your calculation sheet
should show how the friction and normal forces are related to the pull and weight
data, including an appropriate force diagram. Call the results for partner 1’s data B1
and those for partner 2’s data B2.
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Friction Lab
PH 101/201
informal
Analysis of your results
1. Is the average coefficient of friction calculated from method A different from that
calculated by method B? Explain
2. Is the average coefficient calculated by method B1 different from that calculated
by method B2?
A bit of Statistics (homework).
3. Use the Student t-test to compare your average coefficient from Method A with
the average value from method B. Show your results in a table.
4. Are the averages from methods B1 and B2 different. That is, were the two
members in your group statistically different?
Other questions:
How could you modify this experiment to determine the coefficient of kinetic friction for
the block and plane?
The links below are easy to use Web-based t-test calculators which you may use to
simplify the calculations.
http://www.bio.miami.edu/rob/Students_t.html This link allows you to enter data and
calculate the average, standard deviation, and t-score.
http://nimitz.mcs.kent.edu/~blewis/stat/tTest.html
To answer the above questions quantitatively (statistically) you can use the Student ttest. Student by the way was the last name of the man that developed this statistical test.
The Student t-test tests the hypothesis that two averages are same with some level of
confidence. To perform the t-test you must first calculate the t statistic
t
v1  v 2
1
n1  1s12  n2  1s22 

n1  n 2  2
n1

1 

n 2 
Don't panic it gets a little easier. When comparing two averages from our measurements,
n1=n2=5 (the number of measurements), v1, s1 are the average and standard deviation of
one method and v2, s2 are the average and standard deviation of another method. The
number of degrees of freedom is n1+n2-2=8 and is needed to use the statistical table
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PH 101/201
Friction Lab
informal
(Appendix B) related to this method. For these values of n1 and n2 the t statistic is much
simpler,
t
v1  v2
s12  s22
5
Here's an example to show you how the method works.
Example 1
Two measurements have averages of 12.5 and 12.2 respectively and corresponding
standard deviations of 0.9 and 0.7. Are these two averages statistically different at the
95% confidence level? If t is larger than 1.86 (from row 8 of Appendix B) then there is
only a 5% chance that the two means are the same; a 95% probability that they are
different.
t
12.5  12.2 0.3

.588
2
2
0.51
.9 .7
5
No, they are not statistically different.
Example 2.
If the values of s1 and s2 in example 1 were instead s1=0.2 and s2=0.1 then
t
12.5  12.2 0.3

3
2
2
0.1
.2 .1
5
We can say that the two values are statistically different at the 99% confidence level (see
eighth row of Table in Appendix B). The smaller standard deviations in the second
example, indicating greater measurement precision, suggests that the averages 12.5 and
12.2 are indeed statistically different.
Clark College Physics Dept
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Friction Lab
PH 101/201
Appendix B.
informal
t statistic for the Student t-test.
Confidence>>>>
95%
97.5%
99%
Degrees of freedom
t (0.05)
t(0.025)
t(0.010)
1
6.314
12.706
31.821
2
2.92
4.303
6.965
3
2.353
3.182
4.541
4
2.132
2.776
3.747
5
2.015
2.571
3.365
6
1.943
2.447
3.143
7
1.895
2.365
2.998
8
1.860
2.306
2.896
9
1.833
2.262
2.821
10
1.812
2.228
2.764
11
1.796
2.201
2.718
12
1.782
2.179
2.681
13
1.777
2.160
2.650
14
1.761
2.145
2.624
15
1.753
2.131
2.602
16
1.746
2.12
2.583
Degrees of freedom n1+n2-2
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