Lab Report 5_PHYS1100
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Mechanical Engineering
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Feb 20, 2024
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Lab Report 5
Circular Motion
October 3, 2023
Objectives
The goal of this three-part virtual lab was to help us understand concepts relating to circular motion and to use different formulas to find the necessary values. In the first exercise, we had to calculate the period (T) of a revolution (total time divided by number of revolutions) and the frequency (1/T) at different speeds. The second exercise focused on the relationship of the centripetal force to the mass of a rotating object, the radius of the circular path and the speed. First, six different random speeds were applied to a rotating object, and this speed was later calculated using the centripetal force, radius, and mass. A linear Fc vs. v^2 graph was constructed from the results. Next, we observed how the centripetal force changed as the mass of
the rotating object was increased, and their relationship was shown on a graph (Fc vs. m). Similarly, the radius was also increased to see its effect on the centripetal force, and a third graph
(Fc vs. 1/r) was made. For the last part of the lab, a video was watched where the radius of the rotating object and the number of cycles was kept constant, but the mass of the object was changed. The information from the video helped determine the period for each revolution, calculate the centripetal force and create a Fc vs. 1/T graph.
Tabulated Results/Data Sheets
B: Circular Force Lab
Part 1: Dependence of the centripetal force (
F
c
) on the speed of rotation (
v
) at a constant radius
m = 1.5 kg
r = 1.5 m
Table 1
Random speed #
Time for 5
cycles (
s
)
Period,
T
(
s
)
ω
(
rad
/
s
)
random speed
v
(
m
/
s
)
F
C
(
N
)
1
5.66
1.13
5.55
8.3
68.59
2
11.24
2.248
2.795
4.2
17.48
3
9.38
1.88
3.35
5.0
24.73
4
13.08
2.616
2.402
3.6
12.86
5
6.78
1.36
4.63
6.9
47.55
6
6.52
1.30
4.82
7.2
51.76
Slope of
F
C
versus v
2
(and give units!): 1.0 kg/m
Expected slope (in algebraic form): mass / radius or m/r
Numerical, expected value of slope: 1.0 kg/m
Percentage difference between expected and measured slope values: 0%
Part 2: Dependence of the centripetal force (
F
c
) on the mass of rotating object (
m
) at a constant radius
Random speed # 6 and radius, r
=
1.5
m
.
Table 2
Mass (kg)
Time for 5 cycles (
s
)
Period, T (s)
⍵
(rad/s)
v (m/s)
Fc (N)
1.5
6.48
1.30
4.85
7.2
51.74
1.6
6.48
1.30
4.85
7.2
55.32
1.7
6.50
1.30
4.83
7.2
58.75
1.8
6.60
1.32
4.76
7.2
62.23
1.9
6.58
1.32
4.77
7.2
65.57
2.0
6.46
1.29
4.86
7.2
69.20
Slope of F
C
versus m
(and give units!): 34.34 m/s
2
Expected slope (in algebraic form): (velocity)
2
/ radius or v
2
/r
Numerical, expected value of slope: 35 m/s
2
Percentage difference between expected and measured slope values: 0.96 %
Did the period, T
change? Explain: The period, T, did not vary significantly over the 6 trials. The radius remained constant over the trials, which means that the object needed to travel the same amount of distance to complete one revolution. Additionally, as the mass increased, the Fc also increased, so the change in mass did not affect T.
Part 3: Dependence of the centripetal force, F
c
on radius, r
for a constant rotating mass, m
m
=
1.5
kg
, and random speed, v
# 6
Table 3
r
(
m
)
Time for 5 cycles (
s
)
Period, T (s)
⍵
(rad/s)
v (m/s)
Fc (N)
0.5
2.16
0.432
14.5
7.2
155.44
1.0
4.34
0.860
7.31
7.2
77.79
1.5
6.46
1.29
4.86
7.2
51.81
2.0
8.74
1.75
3.59
7.2
38.95
Does the period, T
change? Explain: The period, T, in this experiment did change significantly over the 4 trials depending on the radius. T is the amount of time it takes for the object to complete one revolution, therefore, it would be expected that with a smaller radius, it would take less time to complete a revolution (because the object is traveling less distance), thereby decreasing T. Slope of graph of F
C
versus 1/
r
(and give units!): 77.683
kg * m
2
/ s
2
Expected slope (in algebraic form): mass*(velocity)
2
or mv
2
Numerical, expected value of slope: 78 kg * m
2
/ s
2
Percentage difference between expected and measured slope values: 0.055%
C: Online video
Table 4
r
(
m
)
Number of cycles
Time measured (s)
Period, T
(
s
)
Hanging mass (kg)
Fc (N)
0.63
20
10.54
0.527
0.200
1.96
0.63
20
12.09
0.6045
0.150
1.47
0.63
20
14.43
0.722
0.100
0.95
Slope of graph of F
C
versus 1
/
T
2
(and give units!): 0.601 kg*m
Expected slope (in algebraic form): (mass * 4π
2
* radius) or m4π
2
r Mass of rotating object, obtained using slope of graph (show calculation): 24 g (calculation shown in calculation section below under Table 4)
Calculations
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