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Investigation based on Hooke's law.

Extracts from this document...

Introduction

Background Information.

This investigation will be based on Hooke’s law. Robert Hooke was born in 1635, he was well known for his studies of elasticity. Hooke’s most important discovery is the correct formulation of the theory of elasticity. An object is said to behave elastically when equal increases in the force applied to it produce equal changes in length. If a graph is drawn to show the average extension plotted against the load in Newtons a positive straight-line gradient should be seen, as extension is directly proportional to the load. The ratio between the load and the extension gives us a constant, this constant is called the spring or force constant.  

Hooke’s law states:  F = kx

k = the constant of proportionality (the spring constant).

x =  the spring extension (e.g. x metres)

Or:

The deformation of a material is proportional to the force applied to it provided the elastic limit is not exceeded.

The elastic limit is when the spring is permanently stretched on deformed, so it doesn’t return to its original shape, as the molecules in the metal of the spring cannot return to the original shape; as the following graph demonstrates.

Elasticity can also be shown in this simple diagram:

The Molecular Level Description.

Before.

After.

Combinations of springs.

Hypothesis.

1) I think that the stretch of the two springs in series will be double the stretch of a single spring.

2)

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Middle

image03.png        The load should increase steadily by 100 grams each time.

image03.png        The extension should be measured in the same way each time, preferably centimetres.

image03.png        The extension or stretch should be measured with a ruler each time.

Pilot Study.

I began by setting the apparatus up correctly. I proceeded to do the single spring first. I measured the length of the spring, to work out the extension when I added weight to it. Then I added 1 Newton to the spring and recorded the extension, and proceeded to do this until I reached 6 Newtons. Then I removed 1 Newton one-by-one and recorded the reduction. This made my results more accurate. The experiment had no obvious problems.

I then proceeded to do the experiment with the springs in series. I connected the springs together and started to add the weight, as before. I discovered that I needed to hang the springs off the table, as they would touch the tabletop with the full weight on them. So I have decided to hang the springs off the table when I do my actual experiment.

Lastly I did the experiment with the springs in parallel. I did the same as the single spring, but I used a pencil to balance the mass hanger between the two. This was very complicated as the mass hanger was difficult to balance. So I have decided to try and cut a groove for the mass hanger in my actual experiment.

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Conclusion

image01.png         The clamp stand was slipping due to the weight of the mass hanger.

image01.png         The extension of the springs was not always read at eye level, due to human error.

image01.png         The ruler cannot be completely accurate; the ruler is only accurate to +/- 0.1 centimetres.  

These points can be improved by:

image02.png        Design a new pointer, for example a fixed piece of metal to the spring and use a spirit level to make sure it is at 90o.

image02.png        Design and make a piece of plastic with measured and cut grooves for the mass hanger and the springs to be securely placed on.

image02.png        Fix the clamp stand to the work area.

image02.png        Use a spirit level to make sure that the extension is always read at 90o.

Further experiments could be done to follow on from this experiment. Two experiments, which could be carried out, are firstly using three or four springs in series and parallel formations to see whether a relationship can be found. Secondly, springs of different materials could be used (for example copper, aluminium and plastic) to test how different materials affect the extension of springs.

Test one.

Test two.

Hooke’s Law states that:

Due to the molecular make-up of different metals it may be possible that r (the distance between the molecules in the metal) maybe different. In a further experiment we could investigate the elasticity point in different metals. This could give us indication to their usefulness in building materials, i.e. in suspension bridges. In a suspension bridge the cable needs to be strong, yet, elastic. This enables the bridge to move in the wind without snapping.  

...read more.

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