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An Experiment to Evaluate the Acceleration due to Gravity using a Spiral Spring

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Introduction

An Experiment to Evaluate the Acceleration due to Gravity using a Spiral Spring

TEP062N

Introduction

Gravity affects all things that have mass and therefore must affect how much a mass placed on a spring will extend. Measuring the time period and extension of a mass on a spiral spring for oscillations allows for the calculation of g.

The experiment was carried out as described in the worksheet using masses of 0.2 – 1.2kg

Results and Plot

Figure 1

Load On Spring

(kg)

Initial Length Of Spring l0 (m)

Final Length Of Spring l (m)

Extension Of Spring b (m)

0.2

0.037

0.040

0.003

0.4

0.037

0.0495

0.0125

0.6

0.037

0.061

0.025

0.8

0.037

0.071

0.034

1.0

0.037

0.082

0.045

1.2

0.037

0.092

0.055

Figure 2

Load On Spring

(kg)

...read more.

Middle

5.92

0.21649

6.272

0.098

0.6

7.32

7.43

7.38

7.53

7.82

0.1968

7.496

0.141

0.8

8.22

8.28

8.33

8.53

8.32

0.11675

8.336

0.174

1.0

9.25

9.26

9.19

9.12

9.28

0.06519

9.22

0.213

1.2

9.95

10.19

9.88

10.03

10.29

0.16947

10.068

0.253

Figure 3

Figure 4

Load On Spring

(kg)

g

 (ms-2)

0.2

2.73

0.4

5.69

0.6

7.58

0.8

7.73

1.0

8.18

1.2

8.34

The mean value for g is calculated as 6.71 ms-2 with the standard deviation calculated as 2.17

Calculations

Calculating the extension of the spring or b

b=(l-l0)

b is the extension on the spring when a mass is loaded, l is the total length of the spring with the mass attached and l0is the length of the spring without

...read more.

Conclusion

compared to the accepted value of 9.81ms-²

This is an extremely high percentage of error and this can be attributed to the factors discussed previously.

If the investigation was to be repeated there are a number of improvements which would add to the accuracy of the results and give a value closer to that of 9.81ms-². Firstly, a stiffer spring with a known spring constant would be used to eliminate any errors in measurements or calculations of this. The point of release of the spring for each load would be the same each time and the spring would be held in a rigid tube to prevent any horizontal oscillation.  A more accurate stopwatch and ruler would also be used to increase the accuracy of the measurements.

The standard deviation value for g was calculated at 2.17. This means the values of g show  a large deviation from the mean value of 6.71ms-².  which supports the inaccuracy of the data gathered.

Conclusion

The mean value of g is calculated at 6.71ms-2 +/-2.17ms-2

...read more.

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