Name – James Wainwright Date – 06/11/18 Student ID – 29871573
CONTENTS
- Introduction
- Abstract
- Method
- Results
- Conclusion
INTRODUCTION
In this blog post, I shall be reporting upon an experiment I have recently carried out regarding Hooke’s Law.
Hooke’s Law is a theory within physics discovered by the scientist Robert Hooke in 1660. Hooke stated that the strain felt by a solid is directly proportional to the stress within the elastic limit of that solid. This means that as a solid has force applied to it, its atoms will undergo displacement proportional to the force.
The equation used in physics states the force applied (F) is equal to the product of the materials elastic constant (k) and the change in length (x). F = kx
ABSTRACT
The behaviour of three materials was measured when stretched with a series of different forces. The first two materials remained within their elastic regions while the last reached its elastic limit. The results were transferred into an Excel file and analysed. The results showed a directly proportional relationship between force and deformation and a clear sign when a material had reached its elastic limit.
METHOD
All three materials, Y1, Y2 and Z, had equal forces applied to them. For each change of force, the extension of the material was measured. The forces applied began at 1N and rose incrementally by one Newton increases until reaching 9N for each material. The deformation was measured in millimetres for each change in force.
RESULTS
For the first material, Y1, the results were taken and tabulated below in Excel.
Once all the results for Y1 were input into the table, it can be seen that a rise in force evokes a rise in deformation. As with linear graphs, it is known that the equation for a straight line is given as y = mx + c where m is the gradient and c is the intercept.. Using this, deformation was assigned as the y value while force was used as the x, resulting in the graph seen below.
When the values for x and y for material Y1 were plotted into the graph, a gradient of 1.5583 was rendered with an intercept of 1.375. The equation for this graph is given as y = ax + b where a = 1.5583 and b = 1.375. From the graph it can be seen that one of the values did not follow the trend outputted. This can be treated as a anomaly.
With material Y2, the same method was repeated and the results were placed into a table.
From the results it can be said that as force applied increases, as does deformation linearly, much like with Y1. However, it can be seen that material Y2 has a larger deformation due to force. This implies Y2 has a higher elasticity than Y1. The values for force and deformation were also then plotted onto a graph.
The equation of the graph was given by y = (a + 0.5)x + c. the intercept was shown to be 0.2 and the value of a had previously been calculated to be 1.5583. This meant the gradient of force vs deformation had increased by 0.5 in Y1 compared to Y2.
Once all the values had been found for materials Y1 and Y2, the two materials elastic regions could be compared.
Where the two lines meet on the graph above, when the right force was applied the materials had the same deformation. Judging by the graph, I estimated the point where the two lines crossed to be at 2.4N and 5.2mm. The correct values were then checked through the use of simultaneous equations.
Y1 => y = 1.5583x + 1.375 Y2 => y = (1.5583 + 0.5)x + 0.2 = 2.0583x + 0.2
The two equations taken from the graphs above can be taken away from one another to leave one variable.
Y1 – Y2 => 2.0583x – 1.5583x = 1.375 – 0.2 = 0.5x = 1.175 Therefore x = 2.35N
This means the deformation for both materials was the same when force equalled 2.35N. As can be seen, my estimation was not far off. To obtain deformation, the force can be substituted into equation Y1.
Y1 => y = (1.5583 x 2.35) + 1.375 = 3.662005 + 1.375 Therefore y =5.037005mm
It can be deduced that the materials had the same characteristics when force applied equalled 2.35N and deformation equalled 5.037005mm.
For the final material, Z, the material was tested under the same conditions as Y1 and Y2, only material Z had reached its elastic limit. The equation for Z was given to be y = x^3 + b. The intercept variable b had previously been found to be 1.375, the same intercept as Y1. Using the equation, a table was created along with a graph fro material Z.
It can be seen with material Z that after the elastic limit has been reached, deformation increases rapidly with force applied. If force would be continuously applied, the material would eventually no longer stretch or inevitably break.
CONCLUSION
From my findings during this experiment concerning Hooke’s Law, it has been beneficial in proving Hooke’s theory. While a given material is still within its elastic region, deformation and force applied are directly proportional. My findings also show that after the elastic limit is reached, a material can only stretch so much due to the force. Once said limit has been passed, the integrity of the material has been compromised.
Sources –
2- https://www.britannica.com/science/Hookes-law (Encyclopaedia Britannica)
Hooke’s Law Experiment 