• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3
4. 4
4
5. 5
5
6. 6
6
7. 7
7
8. 8
8
9. 9
9
10. 10
10
11. 11
11
12. 12
12
13. 13
13
14. 14
14
15. 15
15

# The Stiffness Of Springs

Extracts from this document...

Introduction

The Stiffness Of Springs

The spring constant is a measure of the stiffness of an elastic system.

How is the stiffness of a single spring related to the stiffness of springs in series and parallel?

Plan an experiment that will enable you to make a comparison of the stiffness for identical springs in series and parallel from your results.

Plan

The task of this experiment is to determine the relationship between the stiffness of springs in series an in parallel.

The stiffness of a spring can be shown as:

## F = kx

Where F is the force on a spring, x is the extension of the spring and k is the spring constant or the spring’s stiffness.  This means that the force on a spring is proportional to the extension with k being the constant.  Therefore as more force is put onto a spring the more it will extend.  By using this simple formula we can find the spring constant.

## k = F/x

By dividing the force by the spring extension we can find k.  Both the force and the spring extension are easily measurable.  We can show the relationship between the force and the extension in a graph.

x

.                                  F

The graph shows that as the force gets bigger the extension does.  The gradient of the line is the spring constant.  It is a straight line, as the spring constant does not change up to a certain point.  There is a point when a certain force will create a very large extension.  This point is called the elastic limit.  Once a spring reaches this point it becomes permanently deformed.  This means it does not return to its original shape or that its spring constant becomes altered.

The point at which the gradient of the line changes in the elastic limit.

Middle

321

6

355

Springs in Series

 Mass No. Spring I + II (mm) 1 239 2 307 3 376 4 445 5 513 6 580
 Mass No. Spring III + IV (mm) 1 249 2 330 3 395 4 462 5 520 6 601
 Mass No. Spring I + III (mm) 1 249 2 315 3 382 4 448 5 514 6 582
 Mass No. Spring I + II + III (mm) 1 317 2 420 3 523 4 622 5 724 6 824
 Mass No. Spring II + III + IV (mm) 1 329 2 433 3 535 4 637 5 737 6 840
 Mass No. Spring I + II + III + IV (mm) 1 404 2 539 3 674 4 811 5 946 6 1080

Springs in Parallel

 Mass No. Spring I + II (mm) 1 158 2 173 3 192 4 209 5 226 6 243
 Mass No. Spring II + III (mm) 1 162 2 177 3 196 4 213 5 229 6 246
 Mass No. Spring III + IV (mm) 1 167 2 184 3 200 4 218 5 235 6 252
 Mass No. Spring I + II + III (mm) 1 175 2 183 3 193 4 204 5 215 6 226
 Mass No. Spring II +III + IV (mm) 1 176 2 186 3 198 4 209 5 220 6 231
 Mass No. Spring I + II + III + IV (mm) 1 158 2 163 3 170 4 177 5 186 6 195

On the following pages are graphical interpretations of these results.

Analysis

These are the spring constants.  These have been worked out by first drawing the force/extension on a graph.  Then by drawing a line of best fit through these points.  Then the inverse of the gradient of the line gives you the spring constant.  This is because the gradient of a line is y/x.  This would mean that the gradient showed that spring constant was extension/force when it should be force/extension.  To solve this I have to use the inverse function of the gradient as my spring constant.

The lines on these graphs do not pass trough the origin.  This is due to the fact that I have not taken away the original length of the springs from the totals.  This gives every result an offset which will vary from spring systems.  However I found that this is irrelevant, as this would not affect the gradient from which I will obtain the spring constant.

Spring constant should be measured in Nm however as I have measured all my extensions in millimetres I will have to change everything into metres, as it is a standard unit of measurement.

Conclusion

If I had used identical springs instead of similar springs then I would have had more conclusive results.   Also if the springs became slightly deformed during the experiment then my results could be affected.

Where I took the results there might have been a breeze which might have fractionally affected my results which could lead to more errors.  If I did this experiment in an environment where air pressure was normal and there was no breeze then I could achieve more accurate results.

There are several anomalous results in my experiment.  These have either been marked with ** or with a circle.  These results do not fit the pattern which the other results do.  This could be due to many different errors.  If I had repeated these results I might have a got a results that did fit the pattern.

On my graphs I have quantified some of the errors by drawing error boxes around the points I have plotted.  This is because the masses were ± 3 of 100g.  Also I left some space for error for the extension.  This was ± 1mm.  This accounted for if I had incorrectly read any results or if there was a breeze or friction.

To improve my results I also could have repeated the experiment and taken averages for each value or taken more readings.  However I did not have sufficient time for this.

The formulas that I had found out might not be correct as none of the results actually correlated with the formula exactly.  However this is probably due to the many errors that could affect my results.  I based my formulas on rough patterns which seemed to fit with my results.

Another avenue to explore in this experiment would be mixed systems with both series and parallel systems within it.

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

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related AS and A Level Waves & Cosmology essays

1. ## Black Holes Research and Report

4 star(s)

Circumference of a circle = 2?r = velocity x time Therefore... A simple acceleration equation can be used to measure the gravitational field strength, as they are essentially the same thing... The gravitational inverse square law can now be rearranged and used to find the mass of the black hole.

2. ## The aim of this investigation is to examine the effect on the spring constant ...

During this time, the spring obeys Hooke's Law, meaning that the extensions is equal to the stretch force applied divided by the spring's 'Spring Constant' (which will be discussed later). a - b: After point a there is a small section of the graph where the spring is still within

1. ## Finding the Spring Constant (k) and Gravity (g) using Hooke&amp;amp;#146;s Law and the Laws ...

The value that I got was 9.998N/m2. The true value for gravity is 9.81N/m2 so we can say that this is a good estimate and the data collected was accurate. Evaluation Possible sources of error: * Horizontal oscillations of spring when timing for SHM * When the spring is pulled

2. ## Determine the value of 'g', where 'g' is the acceleration due to gravity.

The value of gradient is used to determine the value of the spring constant (k). By putting the value of 'k' into the intercept formula shown below will give us the value of the effective mass. The value of the gravity can be obtained by using the gradient ()

1. ## In this experiment, I am going to find out the relationship between Force and ...

Cello tape and Plastacine 8. A weighing balance 9. 10grams X 10 of metals I will set up my apparatus as shown in the diagram and then record the initial length of the stretchy sweet. Using a cork with a pin attached to it, I will suspend the following objects of mass 20.2g, 25.0g, 30.0g, 40.0g and 45.0g.

2. ## Calculating the value of &amp;quot;g&amp;quot; (Gravitational field strength) using a mass on a spring

Average length of spring (mm) Average unloaded length of spring (mm) Average length of spring -unloaded length (extension) (mm) 50 37 21 16 100 58 21 37 150 80 21 59 200 103 21 82 250 124 21 103 300 147 21 126 350 167 21 146 400 190 21 169 450 201 21 180 Mass (g)

1. ## The experiment involves the determination, of the effective mass of a spring (ms) and ...

18 0.093 0.127 0.135 0.158 0.170 0.196 0.194 0.208 23.62 25.86 25.01 23.35 22.01 28.25 24.67 26.89 22.61 26.33 25.09 23.37 22.01 28.32 24.61 26.88 23.80 25.75 25.06 23.26 22.09 28.34 24.66

2. ## An investigation into the behaviour of springs inparallel when a mass is applied.

� Attach a pre-determined mass (from preliminary experiment) and measure length of the spring using the set square and the metre rule, measure to the nearest mm. � To calculate the extension use the following equation: Extension = Final length - Initial length Note: That the mass of the rod

• Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to