Hooke’s law experiment
Name: Matt
Byford Username: mb4g13
What is Hooke’s law?
Hooke’s law is a law in which states that the strain in a
solid object is proportional to a stress applied to the object with its elastic
limit. 1
Hooke’s law is also referred to as the law elasticity in
which determines how elastic a material is. This is why experiments are needed
as different materials are made in different ways so have different properties
therefore it makes different materials have different elasticity, for example a
polymer such as polyethylene would be more elastic than a metal like iron as
the properties of the material and the way the monomers make up the material
are different. However although a polymer would be more elastic than a metal
material, it is also more likely to fail due to brittle facture because of its
structure.
[1.1]
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
|
y
|
3
|
4.5
|
6
|
7.5
|
9
|
10.5
|
13
|
14
|
15
|
[1.2]
To create a graph as like the one shown above [1.2] I used
Microsoft Excel. I first started by creating a table with the data for the
equation y=ax+b as shown in [1.1]. I then inserted a scatter graph, from this I
can; title the graph, label the axis, insert a trendline and insert the
equation of the trendline.
From the graph above showing the results of a Hooke’s law
experiment. I can calculate the values for ‘a’ and ‘b’ to do this I will create
two equations using two points on the graph from the equation y=ax+b {1}. I
then solved them simultaneously and found that both ‘a’ and ‘b’ are 1.5. Tis is
shown in [1.3]. However when I inserted the equation of the graph, it shows
that a=1.5583 and b=1.375. Therefore there must be anomalies within the data, I
then looked at the graph and inputted values for all the values and found that
there are two anomalies when x=7 and when x=8.
[1.3]
A common experiment for Hooke’s law is one which uses; a
spring, ruler, weights and something to attach the spring. As shown in [picture
1] below. So the cause of the errors in the data could have been when taking
the readings. Or an alternative error could be the time constant in which you
take readings as it should remain the same between each reading but this could
have been different for the two anomalies.
[2.1]
x
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
y
|
3
|
4.5
|
6
|
7.5
|
9
|
10.5
|
13
|
14
|
15
|
y2
|
2.2
|
4.2
|
6.2
|
8.2
|
10.2
|
12.2
|
14.2
|
16.2
|
18.2
|
[2.2]
I then repeated the process to create the graph, as shown
above [2.1], but with the formula y=(a+05)x+c {2}, where c=02, as well as the
first equation y=ax+b {1}. From this data another graph is created as shown
above [2.2]. From this an estimation of the intersection of the two lines was
made. This estimation was x=2.7 and y=5.6. Then using the method of
simultaneous equations, the equations where solved to find the x and y values. As
shown below in [2.3]
[2.3]
[3.1]
x
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
z
|
2.5
|
9.5
|
28.5
|
65.5
|
126.5
|
217.5
|
344.5
|
513.5
|
730.5
|
The last graph that’s was created was that for the equation
z=x3+b. this then gave a curved graph rather than the straight line
of the linear equations graphs. As shown in the graph [3.2].
From the three graphs [1.2], [2.2] and [3.2] I can see that
when the force applied to the object increases the change in length or
extension of the object also increase. This shows that stress and strain are
proportional so if one was to increase then so would the other. However
although the graphs show this they also show it a different rate, as the graph
[3.2] shows this happing very quickly compared to the other two graphs.
However upon reviewing I thought that the first graph may
not have anomalies in and that the material has started to deform. Therefore I
created a line graph so all the point were joined by the line as shown in
[4.1]. I then researched this and realised that the graph is showing the
material at the elastic region. It will then enter the plastic region as in
graph [3.2] in which the material will become permanently deformed because of
t5he forced applied. This is all represented by the graph [4.2].
[4.1]
[4.2]
"I am aware of the
requirements of good academic practice and the potential penalties for any
breaches".2
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