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# The aim of this investigation is to examine the effect on the spring constant placing 2 identical springs in parallel and series combination has and how the resultant spring constants of the parallel and series spring sets compare.

Extracts from this document...

Introduction

Spring Constant of Springs in Series and Parallel

AS Physics Coursework

By Malcolm Davis

Planning

The aim of this investigation is to examine the effect on the spring constant placing 2 identical springs in parallel and series combination has and how the resultant spring constants of the parallel and series spring sets compare to that of a lone spring with identical spring constant.

## Hypothesis

Hooke’s Law states that “The magnitude of the spring constant (k) is equal to the stretching force applied (F) divided by the resultant extension (x)”, it should be possible to determine a spring constant for each spring set.

Due to existing knowledge of springs I propose that the series spring set will have a lower spring constant (and hence due to Hooke’s Law display a greater extension) than the parallel spring set. Also, as Hooke’s Law is a linear function, the spring constant of the series spring set should be exactly half that of a single spring, whereas the spring constant of the parallel set should be exactly double that of the single spring. This also means that if the resulting extension or spring length of the spring sets are graphed along a y axis with the increasing force mapped to the x axis (so that the results can be displayed in a traditional scientific graph fashion), the gradient will be the inverse of the spring constant.

This hypothesis is backed up by many sources, one such source is “Physics” by Ken Dobson, David Grace and David Lovettwhich in the 2000 edition states on page 90 that the spring constant of 2 springs in series is k = k/2 and for 2 springs in parallel k = 2k

This hypothesis will probably only hold true however while the spring extends at a directly proportional rate to the increase in force on the spring.

Middle

9

382

385.5

384

383.83

10

401

423

410

411.33

 Series Mass / 100g Length 1  /mm Length 2   /mm Length 3   /mm Average /mm 1 129.5 134.3 136.1 133.30 2 206 210.5 224 213.50 3 283 283 307.5 291.17 4 358.5 358 386 367.50 5 433 434 466 444.33 6 511 507 546 521.33 7 591 580.5 627.5 599.67 8 663 654 704 673.67 9 746 728 786 753.33 10 826 795 864 828.33
 Parallel Mass / 100g Length 1  /mm Length 2   /mm Length 3  /mm Average /mm 1 37.5 37 36 36.83 2 58 57 58 57.67 3 79 78 77.8 77.93 4 99 97.9 99.4 98.77 5 118.5 117 116.8 117.43 6 138 140 139 139.00 7 159 158 160.2 159.07 8 178 178 179 178.33 9 197.2 198 198.4 197.87 10 219 218 220.2 219.07

#### Analysis of Results

As mentioned in the plan, the results above do not show the actual extension of the springs (which is what is to be looked it during the analysis), however they show the total length of the spring(s), including the original spring length.

I have therefor completed tables below of the actual extension of the spring in each case. These extension values have been found by subtracting the original length of the spring (found before conducting each experiment) from the total length shown in the above tables. As the analysis only uses the average results of the 3 runs for each spring

Conclusion

These limitations all had possible negative effects on the results and in future experiments it would be advisable that modifications be made to minimise them. Some possible solutions to overcome the above mentioned problems could be respectively:

1. A distance measuring radar device could be placed underneath the spring set and masses so to judge more accurately the extension of the springs as so:

2. Stiffer springs (i.e. ones with a higher spring constant) could be used as the oscillations would decay far quicker, also if the springs are stretched to their estimated new position before being released, the vertical oscillation potential would be decreased. It is also beneficial that the experiments be carried out in an environment free from air movement (i.e. a vacuum) so that further oscillations can not occur.

3. As this limitation also came about due to using a ruler located a couple of centimetre’s away from the spring, the limitation would be solved if the same device used to eliminate limitation 1 was used.
1. This problem could be improved by using more symmetrical or specialised equipment by which it is better insured that the load is spread evenly over the 2 springs, such pieces of equipment could include something such as:

Summary

In conclusion, this investigation was able to prove experimentally what the effect placing springs in series and parallel combinations had on their overall spring constant. It showed conclusively that the spring constant of a spring halves when 2 springs of that type are placed in series and doubles when 2 springs of that type are placed parallel.

The experiments used in this investigation could be improved by using the modifications stated above however in general the experiments used proved satisfactory for obtaining results which were accurate enough to high light the described relationship.

This student written piece of work is one of many that can be found in our AS and A Level Waves & Cosmology section.

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