Calculating the Gravitational
Constant
JASEUNG KOOKANGSAN KIMKYUNGJU LEE
JAEYOUNG HWANG
Purpose of experiment
• Calculating the value of the gravitational constant (experiment 1)
• => Accuracy is the prime importance• Validating the period formula for a simple
pendulum– Experiment 2: the independency of the formula to
the mass of the pendulum– Experiment 3: the validation of the length factor in
the abovementioned formula
Experimental setup #1
5o
1.26
1m
the initial oscillation angle was taken at a conservative 5 degreeswith 1.261m string
Added guidance bars to eliminate irrelevant oscillation
formula
𝐠=(𝟐𝝅𝑻 )𝟐
× 𝒍
Data from experiment 1Time (s)
time per 3 periods (s)
time per period (s)
Gravitational constant (m/s2)
6.32 6.32 2.106666667 11.2171713.48 7.16 2.386666667 8.73959520.02 6.54 2.18 10.4751926.79 6.77 2.256666667 9.77552333.5 6.71 2.236666667 9.95112840.31 6.81 2.27 9.66102347.05 6.74 2.246666667 9.86273953.81 6.76 2.253333333 9.80446660.61 6.8 2.266666667 9.68945967.38 6.77 2.256666667 9.77552374.13 6.75 2.25 9.83353880.86 6.73 2.243333333 9.89207187.64 6.78 2.26 9.746708
Graph for experiment 1
1 2 3 4 5 6 7 8 9 10 11 12 132.1
2.15
2.2
2.25
2.3
2.35
2.4
Tim
e in
terv
al p
er p
erio
d
Calculation for experiment 1
Experimental setup #2
Hung a bigger, hence a heavier ball for the pendulum
Data from experiment 2Time (s) time per 3 periods (s) time per period (s) Gravitational constant (m/s2)6.3 6.3 2.1 11.288513.09 6.79 2.263333333 9.7180219.85 6.76 2.253333333 9.80446626.64 6.79 2.263333333 9.7180233.36 6.72 2.24 9.92153340.08 6.72 2.24 9.92153346.73 6.65 2.216666667 10.1315153.57 6.84 2.28 9.57646360.49 6.92 2.306666667 9.35632267.04 6.55 2.183333333 10.4432373.95 6.91 2.303333333 9.38342280.56 6.61 2.203333333 10.254587.41 6.85 2.283333333 9.54852394.18 6.77 2.256666667 9.775523100.81 6.63 2.21 10.19272107.32 6.51 2.17 10.57196114.48 7.16 2.386666667 8.739595121.28 6.8 2.266666667 9.689459127.9 6.62 2.206666667 10.22354134.56 6.66 2.22 10.1011
Graph for experiment 2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 202.1
2.15
2.2
2.25
2.3
2.35
2.4
time
inet
rval
per
per
iod
Calculation for experiment 2
Formula is independent of pendulum mass
Experimental setup #31.
291m
Increased the length of the stringfrom 1.261 mto 1.291 m
Data from experiment 3Time (s) time per 3 periods (s) time per period (s) Gravitational constant (m/s2)
6.69 6.69 2.23 10.2488813.61 6.92 2.306666667 9.578915
20.3 6.69 2.23 10.2488827.21 6.91 2.303333333 9.60665934.08 6.87 2.29 9.71885340.87 6.79 2.263333333 9.949218
47.8 6.93 2.31 9.5512954.5 6.7 2.233333333 10.21831
61.39 6.89 2.296666667 9.66251268.18 6.79 2.263333333 9.949218
75 6.82 2.273333333 9.86188181.91 6.91 2.303333333 9.60665988.56 6.65 2.216666667 10.3725495.49 6.93 2.31 9.55129
102.26 6.77 2.256666667 10.00809109.12 6.86 2.286666667 9.747209116.07 6.95 2.316666667 9.496397122.73 6.66 2.22 10.34142129.72 6.99 2.33 9.388023136.47 6.75 2.25 10.06748
Graph for experiment 3
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 202.1
2.15
2.2
2.25
2.3
2.35
2.4
time
inet
rval
per
per
iod
No elimination required
Calculation for experiment 3
Formula’s length factor is justified
Discussion Questions
Q1: Does the period formula for a pendulum given and its algebraic modification give the correct value for the gravitational constant?A1: Yes. The formula proved to be sound in all three experiments
Discussion Questions
Q2: Is the formula and its modification given independent of the mass of the pendulum?A2: Yes. Comparing the results from experiment 1 and experiment 2 shows that difference in mass of the pendulum is minimal to the value of the gravitational constant
Discussion Questions
Q3: Does the length difference in the pendulum get the correct modification to the results to acquire a result coherent with the literature value?A3: Yes. Comparing the results from experiment 1 and experiment 3 shows that the length factor in the formulas given in (1) and (2) gives the correct modification to suit a result consistent within experimental error
END OF PRESENTATION
References1. Douglas C. Giancoli. Physics Principles with Applications, 6th edition;
Pearson Education, 2005, p.2972. 3rd General Conference on Weights and Measures (CGPM) “standard
acceleration of gravity”, 1901
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