Hooke's Law Experiment

Ssamihan Sukllikar

27139573

ss23g14@soton.ac.uk 

“I am aware of the requirements of good academic practice and the potential penalties for any breaches”

                                                                                                                                                    

Hooke's Law Experiment

To validate Hooke’s law and its relationship with materials, an experiment was carried out to understand the behaviour of three materials (spring). Two of the materials remained within their elastic region whereas one was in plastic region, past elastic region.

 These materials were tested with force applied in Newton.

In the experiment I carried out, I will be proving that Hooke’s law is valid by analysing my results in relation with the equation.

Hooke's law states that “the extension of an elastic object is directly proportional to the force applied to it” [1]. This means that when force is applied to spring, it will cause the spring to extend. As long as the spring returns back to its original length, Hooke’s law applies and it is considered as an ideal spring. If the spring doesn't return back to its original length, it is considered to have entered the plastic region.

Fig.1 Visual aid to relationship between force applied and material (spring extension).[2]

As seen from Fig.1 above, the original length is x=0 but when force is applied, the spring extends to x=L. The force increases when the mass is doubled, thus the length also increases proportionally at x=2L.

The Hooke’s law is determined by the following equation:

                               

F = - kx [3]

F represents the force in Newton (N)

K represents the material constant (N/m)

X represents the length of extension (m) 

The minus sign is to represent the force acting in the opposite direction of the material extension or compression.

Method of experiment

This experiment is suggested to be carried out in pairs.

Once the apparatus is set up as shown in fig.2 below, we can begin with the process of carrying out the experiment.

Fig.2 Apparatus for experiment

As seen from Fig.2, the spring, our material is set up on the clamp. Record the original length. And then slowly add mass and record the new length of the spring. As seen on the meter stick placed next to it. A new mass would be added nine times, thus having to record nine different lengths and repeated for each of the three materials. 

Results

To calculate the value of y2, the following equation was used

   Where c= 0.2

To calculate the value of z, the following equation was used

As seen from Fig.3 below, I calculated the values of y2 and z from the equation mentioned above.

Fig.3 Table to calculate values of y2 and z

The MSE formula used to calculate the values y2 and z is shown below in Fig.4. I have made use of different sheets and linked them together, thus the formula is long.

Fig.4 Table showing formula used to calculate y2 and z

For all the results obtained and calculated, I put them in a table together.

Fig.5 Results table

From the data obtained and calculated, I have created graphs to give better understanding of the results and the trend present.

Fig.6 Graph showing y1 and y2 plotted against x

Analysing Fig.6 graph, I’m estimating that both y1 and y2 intersect each other at these coordinates (2.5, 5.0).

I have calculated the actual coordinates by using simultaneous equation.

When y1=ax+b and  where a=1.5583 b=1.375 c=0.2

Therefore

Y1 = 1.5583x + 1.375

Y2 = (1.5583 + 0.5)*x + 0.2

Y2=Y1

2.0583x + 0.2 = 1.5583x + 1.375

0.5x=1.175

X= 2.35

When x=2.35, therefore y= 2.0583(2.35) + 0.2

Y= 5.037

Thus actual coordinates are (2.35, 5.04)

Fig.7 Graph showing z plotted against x

Conclusion

Hooke’s law has been confirmed to be true as seen from the results obtained and plotted on graphs. The materials y1 and y2, as seen on graph (Fig.6) are showing that the extension is directly proportional to the force applied and therefore showing a linear relationship. Y2 has shown the ability to extend more than y1 at the same force of 9N with a difference of 3.20mm between them. Although to begin with at force of 1N, y2 has displaced less than y1 by 1.20mm between them. This suggests that y1 is more elastic with less force and y2 is more elastic at greater force.

The value I estimated for the coordinates of intersection were (2.50, 5.00) for graph in Fig.6 but when I calculated using simultaneous equation, the values I got were (2.35, 5.04). The estimated for x value was a 0.15 off whereas the value of y was 0.04 off, therefore I think that my estimate was pretty decent.

Material z entered the plastic region as seen from the graph (Fig.7), i.e. it is not able to return to its original length. The exponential trend on the graph suggests that the material is not obeying Hooke’s law where there is a linear relationship between the force applied and extension of material. Material z in comparison to y1 and y2 requires a lot more force for any extension to occur but at the same time z isn’t very elastic either.

Since this experiment was carried out by humans in lab, errors are a possibility. As seen from graph (Fig.7) we can see that there is an anomaly is present on y1 at force 7N where the extension is at 13mm. The reasons for this to occur could be that

- The ruler wasn’t read from at a correct angle also known as parallax error.

- The spring should be stationery before measuring

- The springs could be used and lost their elasticity overtime

- The values of calculations were always kept to 2 decimal places, thus a rounding error in calculations is possible.

If I were to do this experiment again, I would make sure that the errors mentioned above are reduced or eliminated completely. Especially to read the ruler, I would perhaps keep sensors to notice the amount of extension occurred in the material. Use of such technology will certainly improve the accuracy of my results in the experiment. Also whilst calculating, make sure that the values are not rounded up until the end. Although overall, I believe this experiment was a success to prove Hooke’s law.

Bibliography

[1] Bbc.co.uk, (2014). BBC - GCSE Bitesize: Hooke's Law. [online] Available at: http://www.bbc.co.uk/schools/gcsebitesize/science/add_aqa/forces/forceselasticityrev2.shtml [Accessed 13 Nov. 2014].

[2] Dev.physicslab.org, (2014). [online] Available at: http://dev.physicslab.org/img/815b2975-ff7d-4c93-a45a-00db5bce9496.gif [Accessed 16 Nov. 2014].

[3] Steven Holzner, (2014)  Physics I For Dummies 2^nd edition, John Wiley and sons

[4] : Batesville.k12.in.us, (2014). [online] Available at: http://www.batesville.k12.in.us/physics/phynet/mechanics/newton3/Labs/Images/Hooke1.GIF [Accessed 16 Nov. 2014].