The Stiffness Of Springs

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The Stiffness Of Springs  

Task

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.  However, if I do not exceed the elastic limit the formula F = kx will be applicable.  

I predict that a system of springs in series will have a different spring constant to a system of springs in parallel.  I can use F = kx to show the different spring constants of spring systems in parallel and series.  Then I can examine these results to show a relationship between them.  To achieve this I must plan an experiment that shows the stiffness of different numbers of springs in series and I parallel.  

To find the spring constant of a spring I can place different masses onto a spring and measure the length of the extension of the spring.  This will show me the spring constant.  I can use Newton’s Second Law of Motion F = ma to find F – the force in Newtons.  The mass I can measure using scales in kilograms and the acceleration will be the acceleration due to gravity 9.81 ms –2.  However, 9.81 is an awkward number to use.  Instead I am going to use 10 ms –2. I now have all the information I need to plan a simple experiment to show the spring constant of a spring.

Equipment

Here is a list of equipment I will needs:

Springs (with a similar or identical stiffness)

Clamp stand + clamps

Ruler

6 masses of approximately 100g

Electric Scales

Pin

Piece of mechano

Method

  1. Set up the equipment for the experiment as shown in the diagram above.  
  2. Place one spring on to the clamp stand.
  3. Place one mass (approximately 100g) on to the spring slowly.
  4. Measure and record the extension of the spring in a table and a graph
  5. Repeat steps 3 and 4 each time increasing the force by one 100g mass.

I can repeat this experiment for different systems of springs.  I will firstly test each of the springs I am going to use to find their individual spring constants.  Then I will test 2 springs, 3 springs and then four springs in series.  After that I will do the same for springs in parallel i.e. putting 2 springs in parallel, 3 springs and then four springs.  

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The spring I am going to use in this experiment are quite cheap springs, therefore they probably wont have the same spring constant so I wont be able to use the same spring constant for each spring.  Hopefully the springs will have a similar spring constant so it will be easier to compare.  I can overcome this by numbering each spring and then testing each spring individually for its spring constant.  Then I can use these values for each spring.  

The masses I am going to use are said to be 100g.  However when I weighed these ...

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