Lab 6 Atwood's machine
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Lab #6
Lab partner-2: Alexia Reyes
ID: 6313144
Lab partner-3: Anna Schieferdecker
ID: 6304351
Title: Atwood’s Machine
Preliminary Question Answers:
1) If two objects of equal mass are suspended from either end of a string
passing over an alight pulley, there would be no motion because there be a
force of gravity strong enough on one weight to overcome the friction in
order to move.
T
T
2)
3) The two masses have the same magnitude acceleration because in an
Atwood’s machine, the two masses are connected via string which passes
over the pulley. The tension from the string exhibits equal and opposite
forces that act on each mass. This is supported by Newton’s Second law,
which states that when all forces and masses are equal, the acceleration will
also be equal. This is represented as F=ma.
4)
Analysis:
1) Look at table for part 1
2) Look at table for part 2
3) The graph shows a positive slope, as mass difference increases the
acceleration also increases.
4) The graph has a positive slope with the x-axis as 1/m
T
, so as total mass
decreases the acceleration increases and vice versa.
5) Our results are consistent with the theoretical expression given. The
theoretical expression is a=(
)g. With mass
(𝑚1 − 𝑚2)/(𝑚1 + 𝑚2)
difference in the numerator there is a directly proportional relationship with
acceleration which means as mass difference increases the acceleration
increases and vice versa. With total mass in the denominator there is an
inversely proportional relationship with acceleration which means that as
total mass increases the acceleration decreases and vice versa.
6) The slope of the Part 1 graph is 0.0232. Using the equation “gravity = slope
(total mass),” gravity can be calculated to be 9.28 m/s^2 according to the
Part 1 data. This value has a 5.40% difference from the actual value of
around 9.81 m/s^2. Using the data from Part 2, gravity can be calculated
using “gravity = slope / change in mass,” resulting in a value of 8.36 m/s^2.
This value has a 14.8% difference from the actual value. While the value
from Part 1 is very similar to the actual value with an under 10% difference,
the value from Part 2 is less similar. In both cases, the discrepancy can be
attributed to similar factors. The small amount of data points result in less
accuracy, since small outliers can have a large impact on the slope of the
graph. Additionally, factors like friction, air resistance, and the gravitational
variances dependent on location can make the data different from the ideal
or standard values. The pulley could have also been slightly uneven,
throwing off the data because the weights weren’t equally balanced.
Data Tables:
1.
Part I Constant Total Mass
Trial
M1 (g)
M2 (g)
Mt,
m1+m2
(g)
Acceleration
(m/s^2)
mdiff ,
m1-m2 (g)
1
200
200
400
0
0
2
210
190
400
0.4196
20
3
220
180
400
0.8969
40
4
230
170
400
1.368
60
5
240
160
400
1.850
80
Part II Constant Mass Difference
Trial
M1 (g)
M2 (g)
MT,
m1-m2
(g)
Acceleration
(m/s^2)
MT,
m1+m2
(g)
1/mT
(g^-1)
1
160
150
10
0.2525
310
3.23x10^-3
2
170
160
10
0.2264
330
3.03x10^-3
3
180
170
10
0.2170
350
2.86x10^-3
4
190
180
10
0.2053
370
2.70x10^-3
5
200
190
10
0.1938
390
2.56x10^-3
Graphs:
Part I Constant Total Mass
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