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# Given a Batch of Factory Springs, Estimate the Average Spring Constant and Uncertainty of the Batch.

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Introduction

Given a Batch of Factory Springs, Estimate the Average Spring Constant and Uncertainty of the Batch.

## Outline plan

I have been given 3 springs to which I will add different weight. Using the value of extension (Δx) I will calculate the spring constant. Hooke's Law says that the stretch of a spring from its rest position is linearly proportional to the applied force (stress is proportional to strain). Symbolically,

F = kΔx

Where F stands for the applied force, x is the amount of stretch (found by new length minus original length), and k is a constant that depends on the "stiffness" of the spring, called the spring constant.

## Trial plan

Set up equipment as above. Measure original length of spring. Add weights 0.5N at a time until spring reaches elastic limit. Record extension (Δx). Plot these results on a graph and use this information to gain a sensible number and range of values to use in full experiment.

Safety Notes

Be sure to keep your feet out of the area in which the masses will fall if the spring breaks
Be sure to clamp the stand to the lab table, or weight it with several books so that the mass does not pull it off the table.
You need to hang enough mass to the end of the spring to get a measurable stretch, but
too much force will permanently damage the spring, as it will have exceeded its elastic limit.

Middle

0.033

0.034

0.032

0.032

0.033

0.033

3

0.067

0.067

0.068

0.067

0.067

0.067

4

0.100

0.101

0.102

0.100

0.100

0.101

5

0.134

0.135

0.135

0.134

0.134

0.133

6

0.169

0.168

0.172

0.171

0.170

0.170

7

0.203

0.203

0.208

0.207

0.204

0.205

8

0.239

0.239

0.241

0.241

0.240

0.240

 Force (N) Mean extension of spring(m-3dp) spring 1 spring 2 spring 3 Average 2 0.036 0.032 0.033 0.036 3 0.067 0.068 0.067 0.068 4 0.101 0.101 0.101 0.107 5 0.135 0.135 0.134 0.314 6 0.169 0.172 0.170 0.170 7 0.203 0.208 0.205 0.205 8 0.239 0.241 0.240 0.240

*5*

Conclusion

The values which were the smallest, and therefore the most significant, were the measure of extension of the spring. This was measured with a metre rule with 0.001m increments. This meant my answer could be given to 3 decimal places. However, as my results are conclusive to Hooke’s law, I believe them to be precise. I also checked my results with another member of my group. Her results were 28.169N/m  ±0.423. Her results were gathered using similar techniques to mine and with a spring from the same batch.

*8*

Improvements and further work

If this experiment was to be done again I would have used the experiment originally devised, but I would have to make something more appropriate to hold the spring so the parts would all work together. This feature was the main part that stopped me from using this method. It would have reduced the error due to gravity. The only problem would have been the possible stretching of the wire, but this is very unlikely, as it is the strongest link in a weak chain.

I could also do the experiment with a larger range (exceeding the elastic limit) and do more repeats.

Laura Yeomans 12s

*9*

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