Hooke’s Law Experiment

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Hooke’s Law is a principle of physics which was discovered and named after English physicist, Robert Hooke. Hooke’s Law states that the size of the deformation of an object is directly proportional to the force being applied the object. For the small forces applied here, the object should go back to its original shape once the force has been removed. This force can be applied to the object by either stretching, compressing, bending or twisting the material. For example, if we had a small metal wire and a force of 2 Newtons was applied to it and the material deformed by 1 millimetre, then a force of 4 Newtons should deform the material by 2 millimetres.

The aim of the experiment performed below was to compare real world results to Hooke’s Law and interpret the difference between both if there is any.

To start with the results obtained from this experiment were tabulated so they could be turned into a graph more easily. This has been shown below.

Force (N)	Deformation (mm)
1.00	3.00
2.00	4.50
3.00	6.00
4.00	7.50
5.00	9.00
6.00	10.50
7.00	13.00
8.00	14.00
9.00	15.00

Using the equation from the trend line we were able to determine what a and b would be out of the original equation: y1 = ax + b. a = 1.5583 and b = 1.375

Using those same results obtained from a and b we obtained an equation which can be plotted using this original equation: y2 = (a + 0.5)x + c (where c = 0.2 in this scenario). This gave us y2 = 2.0583x + 0.2 which has been plotted in the same graph as y1 as it’s shown below.

Using both trend lines we can get an estimate of what the value of x is by looking at where both lines intercept with each other. Looking carefully I estimated this number to be 2.3. Following this, using simultaneous equation, an accurate value for x was calculated.

Equation (1) y = 2.0538x + 0.2

Equation (2) = 1.5585x + 1.375

Equation (1) – (2) -1.175 = 0.4998x

x = -2.351

The reason that the ‘x’ turned out to be negative is normal as it usually a negative sign is added to show the restoring force of the spring which is in the opposite direction of the force pulling it.

As seen in the graph above we can see there is one point of the y1 set of results which doesn’t match with the Trend line. In experiments it is actually quite common to have one or two results which are not 100% accurate. A lot of times, these results can simply be ignored as they are either a mistake or there might’ve been a problem with the material being tested. Whilst the material does tend to follow Hooke’s Law, there might be a case where it quickly reacted with outside factors and caused it to perform differently. Another reason this result could be off is human error or faulty equipment. This is because there would be a person reading the equipment and noting down the results. For example, these could have either been misread or read at the wrong time. There can also be issues if the equipment being used hasn’t been calibrated properly which results in slightly wrong readings .

Furthermore, we can also see that both materials being tested follow Hooke’s Law. This is true because the material’s deformation is proportional to the force being applied to it. This also means that we can easily calculate the material’s deformation at any given force using their respective equations and force using deformation. In these cases the material will always go back to its original shape once the force is no longer being applied to it.

Generally, this is all true for all elastic materials, however it will eventually get to a certain force that is simply too much and will result in the material never being able to go back to its original shape. After this point, the material’s deformation will no longer be linear. This is called Plastic Deformation and the graph below shows the deformation of a material that has reached Plastic Deformation.

As a quick recap, an elastic material’s deformation is proportional to the force until the force is to much and it reaches plastic deformation, also resulting in the material never being able to go back to its original shape.

In the picture below, we can see the whole journey of an elastic material as more and more force keeps getting applied to it. After the Plastic Deformation point, there is also the Fracture Point. This generally requires a large amount of force as it causes the material to snap which will eliminate any possibility of getting any accurate results to perform an experiment with said material.

In conclusion, the experiment performed here, supports the claims under Hooke’s Law as both materials tested in the experiment had a deformation proportional to the force. Even if there was one result which didn’t quite match with the trend line, as it was explained above this could be possibly simply be ignored.

References:

https://phys.org/news/2015-02-law.html