calculating the gravitational acceleration

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