Download Sample semiformal report

Sam Poole
Ava Ridge, partner
Friction Lab
Physics 101 30 February 1980
For this lab, the coefficient of static friction was determined by two methods and the
results compared to determine if there was a statistically significant difference between
them. This is a limited test of whether or not the friction relation f = μn is correct for
varying normal force n. In the second part, pulling horizontally with varying mass, we
also check one experimenter’s results against another to see what kind of variation exists
between different investigators with the same technique.
Method A : Inclined plane method
For this method, an inclined plane is tilted until the block starts to move and the angle is
recorded. The force balance is then used to determine the coefficient from the data.
The force diagram is:
The resolution of the weight vector gives:
Balancing forces normal to the ramp gives
n – w cos() = 0 (no acceleration)
so
n = w cos()
Just before the block moves on the tilted ramp, the static friction has reached its
maximum value, s n, and the block is not yet accelerating.
Balancing the forces along the ramp gives
w sin() – fs = 0 (not yet accelerating)
which gives
w sin() = fs = s n
substituting for n from the vertical force balance,
w sin() = s w cos()
sin() = s cos()
s = sin()/cos()
s = tan()
Method A data and results:
angle

30.0
0.577
31.0
0.601
30.4
0.587
29.7
0.570
30.2
0.582
avg
0.583
std dev.
0.011
Method B : Friction and Normal Force.
In method B, each lab partner measured the force needed to just begin moving the block
with various added masses on the horizontal ramp. A best fit line to each series of data
was then used to determine the coefficient of friction from the data.
The force diagram is:
Balancing forces gives:
Vertical :
n–w=0
n=w
Horizontal
pull – f = 0
pull = f
Using the formula for maximum static friction
f = s n
and substituting gives
pull = s n
Substituting for n from the vertical force balance gives
pull = s w
This means that plotting the pull needed to just move the block versus the weight of the
block gives a line with slope s .
Method B data and results:
weight of
block (N)
1.23
11
20.82
30.61
40.41
Pull ( partner1)
(N)
0.71
6.2
11.78
17.3
22.9
Pull ( partner2)
(N)
0.81
7.03
13.41
19.58
25.95
Graphing the friction force (= pull) versus the weight (= normal force) gives:
static friction
30
friction (N)
25
20
15
10
y = 0.5663x - 0.0089
Pull 1
y = 0.6413x + 0.0076
Pull 2
5
0
0
10
20
30
normal force (N)
40
50
The slopes give values of 0.57 and 0.64 for the coefficient of static friction. Only 2 digits
are kept due to the force measurements being steady in the second digit, the third digit
varying throughout the pull.
Comparison of results:
The results for the different methods are summarized in the table below:
method
A
B avg
B partner1
B partner2

std
0.583
0.605
0.57
0.64
0.01144
0.049497
Results from methods A and B seem quite different. Trying to get a reproducible force
for part B was difficult and may contribute to such a difference. This is also consistent
with the fact that the results in method B for the two partners bracket the result for part A.
The percent difference between the results for methods A and B is calculated below.
Since neither is a theoretical or accepted value, the difference is compared to the average
of the two experimental values.
0.605 – 0.583
x 100% = 0.93%
½ (0.605 + 0.583)
The small percent difference indicates that the apparent difference between the results of
the two methods is obvious because of precision in the results, not large differences in the
values.
Comparing the results from methods A and B using a t test gives the following
information, calculated from the website http://www.bio.miami.edu/rob/Students_t.html
T score = 1.0548
Method A P value = 0.170
Method B P value = 0.34
The T score indicates that the two values are different by a bit more than 1 standard
deviation. This means that there is only a 65% chance of them being different, not
enough to say that the difference is significant.
The results for partners 1 and 2 in method B differ by about 1.5 standard deviations. This
is likely to be statistically significant. If so, this would indicate that the two
experimenters were not consistent with each other.
Other questions:
To measure the coefficient of kinetic friction, method B could be used, but now pulling to
keep the block moving at a constant velocity. The same data analysis using a linear fit
will give the coefficient of kinetic friction.