Jessica Philllips – 30426987 – jp11g18

Hooke’s by Definition

Hooke’s law states that, within the elastic limit of a solid material, the strain is directly proportional to the applied stress of that solid. F = kx (where, F= spring constant, k = spring constant, x = spring compression or extension).

Through no surprise, Hooke’s law of elasticity was defined by an English scientist named Robert Hooke. He discovered that deformation in a spring is directly proportional to the force/load that is being applied to it. The force the solid spring experiences, can be applied by either, stretching, squeezing, bending, compressing or twisting. No matter how it is applied, the length increase will always be directly proportional to the force. Essentially, if you was to double the load on a spring, the extension would therefore be doubled. The elasticity of an object is shown, when this load would then be released and the object return to its original state, although there is usually a limit to a solids elasticity (its elastic limit). Once a solid has exceeded its elastic limit, it will no longer return to its original position.

Hooke’s Experiment

Hooke’s can be easily proven through a simple demonstration, using a spring and a known force (N). this is done by recording the length of the spring originally and comparing this to the length of the spring once the load is added. You can then use the difference to compare to the elasticity of the material.

In an attempt to demonstrate how Hooke’s law works, I decided to complete an experiment of my own. In this experiment I used 3 different materials: y1, y2 and z (where y1 and y2 are elastic materials and z is a plastic material). With a known mass I then continued the simple experiment I described previously and that left me with some interesting results which began to instantly prove the theory.

From looking at these results we can clearly see Hooke’s law at work. It is clearly displayed in the results that the more force (x) applied on to the materials (y1, y2 and z) the more the length deforms, so these materials clearly follow within the rules of the law. Results like these can then be used to discover a materials elastic potential.

On the graph with both y1 and y2 plotted, I made an estimate that the point at which both the trend lines cross on the x axis I believe to be 2.4N. I then used simultaneous equations to try and find the actual value of the point where they cross. So using the results i was able to work out that the point x = 2.35N, which is very close to my estimation and only 0.05 off.

The results displayed by the materials y1 and y2 both show a positive correlation between the force applied (N) and the deformation (mm). This proves the theory of Hooke’s law of elasticity, and that the deformation in the material, is directly proportional to the force displayed on the spring. In addition to this, the results for z also display a positive rise, correlating with the theory. Although, these results show a curve when displayed on the graph, this suggests that the plastic material grows weaker and deforms more with every added weight. Even through the trend line does not follow through every single point, it still displays a constant positive, this still proves Hooke’s law is at work in this material. It may not be directly proportional for the plastic material, as it is for the elastic, but it is still proportionally consistent.

Citations:

https://en.wikipedia.org/wiki/Hooke’s_law 12/11/2019

https://www.britannica.com/science/Hookes-law 12/11/2019

Fig 1: https://www.britannica.com/science/Hookes-law/images-videos 13/11/2019

Fig 2, 3, 4, 5, 6 : Excel spreadsheets

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