Hooke’s Law
The elasticity of different materials can be calculated using
a formula called Hooke’s Law, the formula was discovered by a scientist named
Robert Hooke in the 1600s. The basic definition of his Law is “it takes about
twice as much force to stretch a spring twice as far”. This image
shows the basic concept of Hooke’s Law in action.
(Quote & Image from
Hyper Physics,http://hyperphysics.phy-astr.gsu.edu/hbase/permot2.html#c3
)
Hooke’s basic equation is simply F=kx, F is the force acting
down on the spring, in the case of my experiment this was represented by
varying weights. K is the spring constant which is simply a number representing
the elasticity of the spring itself, the elasticity of a material is determined
by is actual material and the thickness of it. X just represents the distance
that the spring has stretched when the force was applied.
The experiment that I performed was very easy but
demonstrated Hooke’s Law perfectly. The experiment is conducted by hanging
masses of different sizes on a spring hanging next to a ruler and just
measuring how far the spring stretched. The masses used went from 1N up to 9N
in increments of 1. This table shows the results of the experiment, y1 is the
distance that the spring stretched and x is the masses.
|
x
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
|
Y1
|
3
|
4.5
|
6
|
7.5
|
9
|
10.5
|
13
|
14
|
15
|
This is the graph (fig.1) that was given from the data which
I plotted into excel, I used excel because it can give a much more accurate line
of best fit than I can and that is important for the next calculation. The line
with the red squares on it the relationship between x and y1, the line with
blue diamonds is found using the equation y2=(a+0.5)x+c the values for a and c are taken from the
original y1 line.
The trend that is being depicted in the graph is that as the
mass increases so does the extension which is good as that is what Hooke’s Law
says should happen. The line of best fit is linear which shows that the changes
are proportional to each other, I have displayed the equations of both the
lines so you can see how I got the line y2 and to use in the next section.
The intersection of the two lines in the bottom corner of
the graph using the scale on the graph I guessed the value of x to be slightly
under 2.5. This shows the point where the two springs will be extended the same
distance by the same weight. Using simultaneous equations I was able to get a
much more accurate value.
Y2 =2.06583x+0.2
Y1=1.5593x=1.375
By putting the two equations
equal to each other I could then solve to find x
2.06583x+0.2=1.5593x=1.375
0.5x=1.175
X=2.35
As you can see my value for x is pretty close to what I estimated
to it be which means that the graphs are accurate.
I’m sure that you know
that there is a point at which you stretch a spring so much that it will no
longer return to its original form but stays in its extended form. When this happened
we say that the spring has undergone plastic deformation, this means that you
have deformed it so much that the molecular structure has undergone significant
changes. When this occurs the force and the extension stop being linearly proportional
and become exponential.
This is a graph demonstrating the relationship between force
and extension, as you can see the blue diamond’s go up in a curve instead of a straight
line, this is an exponential curve.
My conclusion for this experiment is that the findings have
proven Hooke’s law to be true and showed the results to be true. As far as
improvements go there are not many as excel was used to make sure the graph and
equations were as accurate as they could be from the data. There was one data
pint which you can see was slightly off the trend, the only thing I can attribute
this to is either human error from me reading the ruler wrong or that the mass I
used was not entirely accurate for some reason. The only other thing I would
change to make this experiment more accurate would be to use a piece of
equipment such as a laser distance measuring device to get even more accurate data
to begin with. This is not needed particularly as my results were within an acceptable
boundary.
I am aware of the requirements of good academic
practice and the potential penalties for any breaches
Student No. SW29G14
