In the works of nature, the deepest discoveries show us the greatest excellencies.
— Robert Hooke.
What is Hooke’s Law?
Hooke’s law is a law of physics that states that the force needed to extend or compress a spring by some distance x scales linearly with respect to that distance. That is, where k is a constant factor characteristic of the spring: its stiffness, and x is small compared to the total possible deformation of the spring.
In the first part of our experiment, two materials in their elastic regions and their deformation in respect to the forces applied were observed. In this part of the experiment, the third material, z, and its deformation will be observed in comparison to the first two materials using the same forces.
The formula z = x^3 + 1.375 was first used to find its deformation compared to the rest and we graphed it to see the difference.
As shown above, the deformation values of z are various times higher than that of y1 and y2. This is due to the fact that y1 and y2 are still in their elastic regions whereas z is in the plastic region where it cannot go back to its original shape.
The result given was expected due to z’s polynomial formula that shows its exponential tendency.
Conclusion
In conclusion, the results obtained satisfied proof of Hooke’s Law. Hooke’s law states that the force added to the spring will be directly proportional to the extension and this is indicated through the various graphs.
In our experiment, we were given several forces applied (x) and 3 types of materials (y1,y2, and z) and their deformations in co ordinance with the forces applied.
The first two materials, y1 and y2, are still in their linear elastic regions whereas, the third material, z, has gone past its elastic region and now is in its plastic region.
How does this happen?
The experiment began by making tables for each value of x, y1, y2, and z and graphing them with Force (x) VS the respective material’s deformation.
The values of y2 and z’s deformation were found by following their respective equations y2 = (a+0.5)x + c and z = x^3 + b. The values a and b were found to be the slope of y1 and its intercept.
As indicated in the graph above, two materials are forming a linear graph. This happens because the materials are in their elastic region and their deformation is directly proportional to the force applied on the object.
Two lines can also be seen intersecting at point (2.35,5.04). This was calculated using simultaneous equations, indicating that the two objects have the same deformation of 5.04mm at a specific force x of 2.35N.
Hooke's Law Experiment