Introduction
Hooke's Law is a law of mechanics and physics by Robert Hooke. The theory states that, if the load does not exceed the material’s elastic limit, the force needed to extend or compress an elastic object such as spring is directly proportional to the extension.
Hooke’s Law
equation:
F=kx
where,
F = force applied on
the elastic object (N)
k = spring constant
(N/m)
x = the length of
extension / compression of a spring (m)
*Hooke’s law applies, as long as the material
is within it’s elastic limit.
Experiment
Fig1
Fig1
1)
Set up the apparatus as shown in Fig 1.
2)
The spring to be
tested is fixed at one end of the clamp, hanging parallel with the ruler (meter
stick).
3)
A
known force is applied to the material, causing it to be displaced.
4) The displaced length is measured and recorded.
5)
Steps 3 to 4 are
repeated 9 times, each time applying a greater force.
6)
This
experiment is repeated 2 times with 2 other different materials. (total three
different materials)
Result
The results
of the experiment are shown below.
y1, y2 and
z is the extension of material 1, 2 and 3 respectively.
Deformation of y1:
The equation for deformation y1 is
given as : y1 = ax+b
Fig 2. Deformation of y1
By using
the result in Fig 2, a graph of Force Applied(N) versus Deformation of y1(mm)
is plotted.
Fig 3. Deformation of y1 against
force applied
From the
graph in Fig 3, we can obtain the value a and b from the equation .
Since y1 = 1.5583x+1.375
So a = 1.5583 and
b = 1.375
Deformation of y1 and
y2：
Fig 4. Deformation of y1 and y2
By using
the result in Fig 4, a graph of Force Applied(N) versus Deformation of y1 and
y2(mm) is plotted.
Fig 5. Deformation of y1 and y2 versus force applied
From the
graph above, line of deformation y2 has the equation : y2 = 2.0583x + 0.2
The line of
best fit was plotted, the lines indicate the relationship between the force
applied (N) and the deformation of y1 and y2, which is directly proportional to
each other. As the force applied increases, the deformation of y1 and y2
increases.
Line of deformation
y2 has a greater gradient compared to line of deformation y1 shows that
material y1 is stiffer compared to material y2.
Based on Fig 5 , the meeting point of y1 and y2
is estimated as (2.10, 4.90)
The actual meeting point is calculated by resolving the
simultaneous equations:
y1 = 1.5583x + 1.375 ---- ➀
y2 = 2.0583x + 0.2 ---- ➁
➀=➁
1.5583x + 1.375 = 2.0583x + 0.2
0.5x = 1.175
x = 2.35
When x = 2.35,
y = 2.0583 ( 2.35) + 0.2
y = 5.037
Therefore
the meeting point is ( 2.35, 5.037)
Deformation of z :
The
equation of deformation Z is given as : z =
x³+ b, where b = 1.375Fig 6. Deformation of z
By using
the result in Fig 6, a graph of Force Applied(N) versus Deformation of z(mm) is
plotted.
Fig 7. Deformation of z
By analysing
the graph above, the line of Z has the equation :
Conclusion
However
material z not show this result as it already into plastic region.
Thus it
shows that Hook’s Law is true, if the load does not exceed the elastic limit.
Since the
experiment is conducted, there are a few errors that can be improved :
1) Parallax error
- setting our eyes perpendicular to the metre ruler while taking reading
2) Inaccurate results obtained
- repeat the experiment at least twice
References
- Hooke’s law – Wikipedia, the free encyclopedia. 2016. Hooke’s law – Wikipedia, the
free encyclopedia. [ONLINE]
[Accessed on 16 November 2016]
