Hooke's Law Experiment.

Hooke's Law Experiment


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Introduction to Hooke's Law

"When an elastic object - such as a spring - is stretched, the increased length is called its extension. The extension of an elastic object is directly proportional to the force applied to it:

Force equals k multiplied by extension, where k is the 'spring constant'

Picture 1: An example of an increasing force being applied to a spring.

This equation works as long as the elastic limit (the limit of proportionality) is not exceeded. If a spring is stretched too much, for example, it will not return to its original length when the load is removed"

Picture 2: An over-stretched spring that exceeded its elastic limit.

"The spring constant k is different for different objects and materials. It is found by carrying out an experiment. For example, the unloaded length of a spring is measured. Different numbers of slotted masses are added to the spring and its new length measured each time. The extension is the new length minus the unloaded length.

Assuming the elastic limit is not exceeded, a graph of force against extension produces a straight line that passes through the origin. The gradient of the line is the spring constant, k. The greater the value of k, the stiffer the spring."

More about Hooke's law can be found here: https://www.britannica.com/science/Hookes-law



The Experiment

This experiment was carried out to investigate the behaviour of three materials: y1, y2 and z.
A force, x, was applied to each material, and it's deformation was recorded. This was repeated for a number of different sized forces.

Picture 3. A typical Hooke's law experimental set-up

Table of Results

Table 1

Graph and Calculations for y1 and y2

Graph 1

From the above graph it can be seen that the two lines intersect at about a force of 2.3 newtons. This can be found out more accurately by resolving the simultaneous equations that are on the graph:

1.5583x  +  1.375  = 2.0583x +0.2

so 1.375 = 0.5x +0.2

and x = 2.35

Graph for z

Graph 2

Conclusions

From graph 1 it can be seen that both plots for y1 and y2 are straight lines, therefore the elastic limit has not been exceeded and the gradient of those lines is the spring constant, k, for each of those materials.

So for y1 the spring constant is 1.5583 and for y2 it is 2.0583.

From graph 2 it can be seen that the elastic limit has been exceeded as the graph is not a straight line. 
This material will not return to its original shape when the force is removed.


Errors

Errors may occur when reading of the extensions resulting from different forces. 

The forces, which are most likely to be weights, may not be exactly what it says on them.

The springs may not be new which may alter their elasticity.

The above suggestions may account for one of the results from  y1 being some distance away from the line of best fit.



References


Hooke's law description: http://www.bbc.co.uk/schools/gcsebitesize/science/add_aqa/forces/forceselasticityrev2.shtml
(Accessed 25 October 2015)

Picture 1: http://schoolphysics.org/age11-14/matter/text/Stretching_things/images/2.gif
(Accessed 25 October 2015)

Picture 2: http://www.1800trampoline.com/ProductImages/stretchedspring.jpg
(Accessed 25 October 2015)

Picture 3: http://www.carolina.com/images/product/large/751950_phy.jpg
(Accessed 25 October 2015)