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# Finding the Spring Constant (k) and Gravity (g) using Hooke&amp;#146;s Law and the Laws of Simple Harmonic Motion

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Introduction

Finding the Spring Constant (k) and Gravity (g) using Hooke's Law and the Laws of Simple Harmonic Motion Aim: In this investigation I will calculate an estimate for the spring constant of a certain spring. To do this I will use Hooke's Law - F = k e I will then use the laws of simple harmonic motion to get a better estimate and compare the two results. The equation that I will use is below: T = 2? Plan: To use Hooke's Law to calculate k I will need to find the extension of the spring when a certain force is hanging from it. To use the simple harmonic motion formula I will need to time the period (T) of the oscillations of the spring when a certain mass is hanging from it. To calculate gravity (g) I will need the square of the period (T2) and the extension of the spring for each mass as I will be using the following formula: T2 = 4 ?2 e g which is derived as follows: T2 = 4 ?2 m k F = m g F = k e k e = m g k = m g e T2 = 4 ?2 m e m g T2 = 4 ?2 e g Equipment List 1. ...read more.

Middle

k 15. The final graph will use the formula; T2 = 4?2 e g to calculate an estimate for gravity. Examples of all three of the graphs are shown on the following pages along with the results of my investigation. Investigation First Set of Results: Mass (kg) Extension (m) Period (s) 0.101 0.035 0.375 0.203 0.070 0.566 0.302 0.105 0.624 0.404 0.140 0.734 0.503 0.175 0.839 0.605 0.210 0.922 0.101 0.035 0.324 0.201 0.070 0.546 0.302 0.105 0.627 0.401 0.140 0.724 0.504 0.175 0.820 0.606 0.210 0.919 0.101 0.035 0.354 0.200 0.070 0.545 0.300 0.105 0.655 0.399 0.140 0.699 0.498 0.175 0.836 0.601 0.210 0.921 The results now need to be averaged so that I can start to produce the graphs that I need: Mass (kg) Force (N) Extension (m) Period (s) 0.102 1.001 0.035 0.351 0.202 1.978 0.070 0.552 0.302 2.963 0.105 0.635 0.401 3.937 0.140 0.719 0.501 4.915 0.175 0.831 0.604 5.925 0.210 0.921 Graph 1 I will use this graph to calculate an estimate for the spring constant. It can be found on page 7. on the y-axis I will plot Force (N) ...read more.

Conclusion

I could use more accurate scales. The ruler that I used was accurate to 0.5mm. * Human error when recording or measuring * The eye can only measure to 1mm therefor a more accurate ruler would not make any difference. A digital measurement device could be used. * Human error often occurs when recording or transferring data. There is no way to correct this other than checking all data as it is entered. * Spring is damaged due to exceeding elastic limit * If a spring exceeds its elastic limit it is permanently damaged and results will be affected by this. To overcome this problem too much weight must not be added to the spring. I don't think that any of the possible sources of error mentioned above will have had much effect on the outcome of the investigation. The investigation went very well. I calculated two values for the spring constant of the spring which were very close. I also calculated an approximation for gravity which is very close to the real value. If I were to redo the experiment I would take more data and use more accurate equipment so that I could get a more accurate estimation for the spring constant. Finding The Spring Constant and Gravity Page 1/12 Andrew Howlett ...read more.

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