Hooke's Law Experiment

Boran Beyit Kolcu

University Of Southampton ID: 28834887

Experiment Of Hooke's Law

Hooke's law is a principle of physics which states that the force (F ) required to extend a material (for example a spring) by some length (X) is directly proportional to the extension.  compared to the total possible deformation of the spring. The law is named after 17th-century British physicist Robert Hooke. He first stated the law in 1660 as a Latin anagram.

As we can see from the diagram above, the extension on the coil is directly proportional to the load attached (force applied) to it. Which means that if we double the amount of the the first force (F) the coil or string is likely to extend more than the first time with a force twice the first (2F). As a result, the rate of extension (X) is twice the other (2X).

Equation of Hooke's Law

Where k is the spring constant which can be found by an experiment (its stiffness), and delta L is so small compared to the total length of the spring (the extension of the spring which can be found by subtracting final length from the original length). 

Experimental Values and Graphs

x	1,00	2,00	3,00	4,00	5,00	6,00	7,00	8,00	9,00
y1	3,00	4,50	6,00	7,50	9,00	10,50	13,00	14,00	15,00

Values of a and b :
a	1,5583
b	1,375

• Where y1=ax+b and y2=(a+0.5)x+c and "c" is constant that is c=0.2

y2	2,2583	4,3166	6,3749	8,4332	10,4915	12,5498	14,6081	16,6664	18,7247
z	2,375	9,375	28,375	65,375	126,375	217,375	344,375	513,375	730,375

• In this case, z=x^3+b

Estimated value :				Equations :			Checking estimated values:
x	2,35			y1 = 1,5583.x + 1,375			y1	5,037005
y	5,04			y2 = 2,0583.x + 0,2			y2	5,037005

x	1,00	2,00	3,00	4,00	5,00	6,00	7,00	8,00	9,00
z	2,375	9,375	28,375	65,375	126,375	217,375	344,375	513,375	730,375

Lines Of Y1 And Y2 On The Same Graph

   

Slope Of Z versus X

Information Observed From The Graphs Of the Experiment

It can be clearly observed from the graphs that the extensions of the two materials in mm (y1 and y2) is directly proportional to the force applied (x) to the materials since the graphs are two straight lines. This means that both of the materials are elastic and they are going to stay in their elastic regions unless the force applied (x) to them does not pass the elastic region into plastic region. Gradients of the graphs ( spring constant of the strings) are close to each other but as it can be seen from the graph, the spring constant of y2 is slightly higher than that of y1. 

On the other hand, if we look at the second graph which is slope, we can see that the Hooke's Law does not fit into this situation because the materials are in their plastic region rather than elastic region. Also, graph being a slope is another reason for not obeying the Hooke's law. 

Physical Observation Of The Hooke's Law Experiment

Since the materials in the graphs of y1 and y2 obey the Hooke's Law, the extension of the materials is directly proportional to the force applied to them and the springs would return to their original dimensions when applied forced (or the attached load) was removed. If the force applied passed the limit of proportionality, the two materials would not be able to turn back to their original shape and size when the force was removed. From this statement, we understand that y1 and y2 would pass their elastic region. 

In the Z versus X graph, their is an uneven extension and returning to the original dimensions can not be considered.

Differences Between Two Graphs

In this experiment, we had both plastic and elastic materials. It can be understood from the graphs that both of the different type of the materials are going through different rates of extension, they deform differently. When we compare the lines of y1 and y2, we can obviously see that y1 reaches the limit of proportionality of its own while y2 does not even when the maximum force is applied.

Errors Happened During The Experiment

Just like in any other experiment some errors happened and these errors can be caused by systematic faults or can be simply explained by human error. When taking the values of y1 and y2 it can be said that a human error happened in this stage because of not reading the values properly or not placing the load or applying the force in the way that it should be, resulting in a higher rate of extension on the material.

How Can The Experiment Be Improved?

The experiment can be improved by repeating the steps when taking the values a couple of times. When more values are obtained (like 5 values), the average of the output can be calculated to end with a more accurate result.

Conclusion

To sum up, different materials extend or deform in a different way as a result of different and unique values of spring constant (k) when a force is applied. Y1 and y2 obey the Hooke's law and they are elastic materials whereas material "z" does not obey since it is plastic material, it extends and does not turn back to its original dimensions.

References For The Law Explanation And The Images

Henry Petroski, 1996. Invention by Design; How Engineers Get from Thought to Thing. Reprint. Edition. Harvard University Press.

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Universe Today. 2016. What is Hooke's Law? - Universe Today. [ONLINE] Available at: http://www.universetoday.com/55027/hookes-law/. [Accessed 16 November 2016].

Hooke’s Law – density, elastic limit. 2016. Hooke’s Law – density, elastic limit. [ONLINE] Available at: http://physicsnet.co.uk/a-level-physics-as-a2/materials/hookes-law/. [Accessed 16 November 2016].