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
To calculate the value of z, the
following equation was used
Fig.3 Table to
calculate values of y2 and z
Fig.4 Table showing
formula used to calculate y2 and z
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 2nd 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].
