Physics 1 Lab 1 PDF

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Physics 1 Lab 1 ...

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Graphical Analysis: Simple Pendulum Conor Gugliotta Collaborator: Stephanie Cardenas & Daniela Osorio

February 3, 2017 Physics 2091 Kean University

Purpose: The purpose of this experiment is to determine through graphical analysis the value of the coefficient, represented by (k), and the exponent, represented by (a) in the equation.

Theory: A simple pendulum when pulled then released, will swing freely due to the action of gravity. One complete round trip, or one cycle, is called the period of motion. Most of the time when running this experiment, the initial displacement of the pendulum from equilibrium should be 10° or less. -

T = kLa

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T = period of motion

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L = length of the pendulum

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If T = kLa , then logT = alogL = logk

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a is equal to the slope of the line, which is: (Y2 - Y1)/(X2 - X1)

Equipment Sketch/List: -

Timer (to calculate the period of motion)

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Meter Stick (used to change the length of the pendulum)

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Pendulum w/ metal ball attached (weight unknown)

Data:

L (m)

t (s)

t (s)

t (s)

t (s)

t (s)

t (s)

0.40

12.80

12.75

12.70

12.80

12.80

12.77

0.60

15.40

15.50

15.40

15.50

15.40

15.44

0.80

17.90

18.10

18.00

18.10

18.00

18.02

1.00

20.20

20.10

20.10

20.00

20.40

20.16

1.20

22.40

22.00

22.20

22.10

22.40

22.22

1.40

24.00

24.30

24.20

24.30

24.10

24.18

1.60

25.60

25.50

25.70

25.60

25.80

25.64

1.80

27.30

27.10

27.00

27.20

27.10

27.14

2.00

28.60

28.50

28.40

28.60

28.50

28.52

1

2

3

4

5

Data Analysis: T (s)

L (m)

lnT

lnL

La (a=

1.277

0.40

0.245

-0.916

0.652

1.544

0.60

0.434

-0.511

0.788

1.802

0.80

0.589

-0.223

0.894

2.016

1.00

0.701

0

1.00

2.222

1.20

0.798

0.182

1.106

2.418

1.40

0.883

0.336

1.204

2.564

1.60

0.942

0.470

1.250

2.714

1.80

0.998

0.588

1.322

2.852

2.00

1.048

0.693

1.391

avg

Summary of Results: In conclusion, it was found that by increasing the length of the pendulum (string), the time of the period of motion would increase as well. The calculations were made by gravity pulling the pendulum in two directions and it was calculated that time increased over the period of added length.

Conclusion & Discussion: During this experiment we determined the value of ‘a’ & ‘k’ by using graphical analysis. The percent error of ‘a’ was 0.500% & ‘k’ was 9.50%. This error was calculated by true value – expected value / expected value. To decrease the percent error one could have pre cut strings at the exact length given & multiple people timing the pendulum to get a better average.

References: - Physics 2091 Lab Manual...