An Investigation into Hooke's Law

Categories: Law Spring

Essay, Pages 7 (1629 words)

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The aim of this experiment is to find out if the amount of weight applied to an elastic or stretchable object is proportional to the amount the object's length increases by when the weight is applied.

Since Hooke's law is famous, and is used a lot, I have many resources and researchable information available to use. I took this from a website; http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/hooke.cfm

"Robert Hooke, who in 1676 stated,

The power (Sic.) of any springy body is in the same proportion with the extension.

He announced the birth of elasticity. Hooke's statement expressed mathematically is,

where F is the applied force (and not the power, as Hooke mistakenly suggested), u is the deformation of the elastic body subjected to the force F, and k is the spring constant (i.e. the ratio of previous two parameters)."

The equation will be very useful in calculating the change in size, and for preparing my hypothesis.

I took this from http://www.tiscali.co.uk/reference/encyclopaedia/hutchinson/m0021767.html.

Elasticity (physics)

In physics, the ability of a solid to recover its shape once deforming forces (stresses modifying its dimensions or shape) are removed. An elastic material obeys Hooke's law, which states that its deformation is proportional to the applied stress up to a certain point, called the elastic limit, beyond which additional stress will deform it permanently. Elastic materials include metals and rubber. However, all materials have some degree of elasticity.

This was taken from the text book issued to me from my school:

" The extension is directly proportional to the load.

This is called Hooke's Law. This law also applies to the stretching of metal wires and bars.

From your results, plot a graph of extension against load.

A straight line through the origin of the graph confirms that the extension is directly proportional to the stretching force.

What happens with very heavy loads?

Hooke's Law only applies to the straight part of the graph (up to the limit of proportionality)."

The point P is called the elastic limit. If a spring is taken beyond this limit, it will not return to its old shape. It is permanently deformed.

Hooke's Law also applies to your bed-springs, to car springs, and to the steel girders used to bridges and buildings.

Graphs of extension; load are important to construction engineers."

I plan to take a wide range of results for this experiment, to ensure I get accurate readings and a good sense that Hooke's law works in a wide range of examples. Certain Results may have to be repeated due to the spring breaking, or if the spring is used too much, it may be permanently stretched out of shape, this will produce anomalous results.

Apparatus:

These are the equipment pieces id need to use:

* 30cm Ruler

* Spring with hooks at each end.

* Retort stand and clamp

* Varied Selection of weights

* Weight holder with hook at the end.

Method:

* Collect and set up apparatus as shown in diagram.

* Measure the spring's original length.

* Place required amount of weight on weight holder

* Measure the spring's new length.

* Record results in suitable table

* Remove weights and start experiment again with different amount of weights.

As a safety precaution I will ensure the spring is not stretched so much it could fly off and injure someone's eye.

Hypothesis:

I predict that I will find that the more weight that is added, the greater the extension of the spring will be. The change in weight will be proportional to the change in the length of the spring. I think this will happen because the greater the mass (measured in Kilograms, or Kg for short) an object has the greater the weight (measured in Newton's, or N for short) it will have. The force of gravity pulls the object toward the ground with greater force and speed the greater the mass it has. If an object is attached to an elastic or stretchable object, and left to hang freely, it will be pulled toward the Earth's centre of gravity. If the elastic object is attached firmly to something it will stretch toward the ground, more if a great weight is added, or less if less weight is added.

To aid me with this prediction I looked up this experiment in a different school text book:

Figure 1 shows a simple experiment to investigate the behaviour of a spring. The spring stretches when a load is hung on the end of it. The increase in length of the spring is called its extension. You can enter values in a spreadsheet and then plot a graph of load against extension on a computer.

You will find that it produces a straight line such as AB in figure 2. This shows that the extension is proportional to the load. A material that behaves in this way is said to obey Hooke's Law:

Extension is proportional to the load

At point B the spring ahs reached its elastic limit. Hooke's law is no longer obeyed. Over the region AB of the graph the spring shows elastic behaviour. This means that when the load is removed from the spring, it returns to its original length and shape.

However, if a load of more than 7N (beyond point B) is applied to this spring, it changes its shape permanently. When the load is removed it does not return to its original shape. This is called plastic deformation. When you bounce a hard rubber ball it deforms elastically. How do you think Plasticine deforms?

Only some materials obey Hooke's Law. You can see from figure 2 that a rubber band certainly does not.

Figure 3 shows what happens when a load is put onto two springs. When you put 2 springs in series each one is pulled by the force of 1N. Each spring is extended by 1cm, and the total extension is now 2 cm (Figure 3a). When springs are put in parallel (side by side) each one supports half of the load. Each spring only extends by 0.5 cm.

Fair Test

It will be a fair test because:

* I will make sure the spring has stopped oscillating (vibrating or moving) before I take the measurement.

* I will use the same ruler for each attempt, and make sure that that ruler is not damaged in a way that it may impair my results.

* I will use the same spring for each attempt, as different springs may have different lengths and elastic properties.

* I will check the spring before each reading to ensure that it has not been permanently deformed, and if it has, I will restart the experiment with a new spring and make sure I don't use the same amount of weight as I had previously.

* I will measure the spring's length from the same angle each time, to attempt to rule out parallax errors.

Observation

The starting length of the spring was 23mm. These were the results we collected after applying different numbers of 50 gram weights to the spring:

AnalysisI chose to display the results graphically as it gives a good representation of the results being proportional, and it is easy to pinpoint anomalous results. You can easily see that the results are roughly proportional. They are not perfectly proportional as my experiment could have been flawed by many factors, which I will explain in my evaluation section. It provides a good answer to what I set out to prove.

Conclusion

I have learnt that Hooke's law is true (The extension of an elastic body is directly proportional to the force applied to it). I know this because I can draw a line of best fit straight through the origin, co-ordinates (0,0). The results fit my prediction well as I predicted that the results would be proportional, and the results are roughly proportional. These results support my original theory well.

Evaluation

I think that my plan went well, and I have proved what I set out to prove. I was able to show that Hooke's law is true, that the force applied to an elastic body is proportional to how much it extends by. My measurements were reasonably accurate, but the experiment may have been flawed by several factors:

* The spring may have been deformed beyond visual detection so that results wouldn't have been proportional.

* Parallax errors caused by viewing the spring from different angles each time could affect the results, the results would have been off by a millimeter or two.

* Human error would lead to inaccurate readings.

* If the measuring device was damaged, bent, or not calibrated correctly this would lead to inaccurate results.

* If the spring was oscillating, or vibrating this would lead to the measurements continuously changing.

I could make the experiment more reliable by making sure the spring was not moving or vibrating in any way during measuring. I could make sure I measured from the same angle (as close as I can get to the same angle each time) to rule out parallax errors. I would make sure that the measuring device was intact, calibrated correctly and/or straight before use. I would also ensure that my spring was not damaged in any way, with the use of a magnifying glass or other enhanced viewing apparatus. I did not encounter any anomalous results in this experiment.

I believe that this method was the most appropriate as there aren't any ways of measuring a spring's extension that differs greatly from this experiment. I have gained enough evidence from this experiment to support my conclusion.

To gain further knowledge and evidence for Hooke's law, an experiment where multiple springs are used, and elastic bodies made from different materials than metal, for example, an elastic band are used to see if Hooke's law works in differing circumstances.