(learncbse.in, 2016)
ABSTRACT:
To show how
different types of elastic material influences the behaviour of respective elasticity,
three materials with different elasticity were used in this experiment. The value
of a and b was calculated from the formula of y = ax + b based on the graphs. As
expected from the theory of Hooke’s Law, the force applied to the elastic
materials is proportional to the extension from the graph of y1 and y2
against x. The results of measurements were logical, where the trend lines for
the graph of y1 and y2 against x are linear lines, which both are still in
their linear regions (within elastic limit). On the other hand, the graph of z
against x shows a polynomial trend line which describes the behaviour of the
material which has gone past its elastic region (in the plastic region). There
is a slight difference between the experimental graph to the theoretical graph,
which is the best fit line in this experiment does not pass through the origin.
This is due to the values of force applied is too small, which influences the
experiment as the range of extensions of the springs is considered narrow. Besides, parallax error when taking the values of extensions is also one of the factors contributing to this error.
INTRODUCTION:
Elasticity is
the ability of an elastic material to return back to its original shape or size
after the load applied is removed. When the elastic materials
are within their linear regions, the force applied is directly proportional to
its extension. This phenomenon is described by Hooke's Law. Elasticity of a spring depends on its elastic region. In order
to show this, three materials with different elasticity, representing the
elastic and plastic region, were used to show the relationship between the
force applied on the materials and their respective extensions. In this
laboratory report, the results of this experiment was presented and compared
between the materials with different elasticity to clearly show how the elastic
region is related to the elasticity behaviour.
Hooke’s Law, law of elasticity discovered by the English scientist Robert Hooke in 1660. According to Hooke’s Law, the extension of the spring is directly proportional to the force exerted by the spring on the weight hanging on it. This can be defined using the formula of
𝑭=−𝒌𝒙 ,
note that the force mention here is restoring force.
Spring constant, k can be obtained by taking force versus extension: 𝒌= 𝑭𝒙
(msstud2014.wordpress.com, 2014)
Hooke’s Law is only applicable within a specific limit of an elastic object, known as the
elastic limit. Once the force applied on an elastic object exceeds the elastic limit,
permanent deformation will happen such that the object is no longer able to return back to
its original length and size. In this case, the elastic object loses its elasticity permanently.
METHODS:
The following apparatus was used to measure the elasticity trend lines of the elastic materials: a stand, three types of elastic materials, a metre rule and a mass hanger with extra slotted weights (1N each).
The apparatus was set up by first setting the elastic materials on a stand and the initial lengths of the materials were measured and recorded. Once the apparatus was set up, a 1.00N weight was hooked onto each of it, and the new lengths of each material and the slotted weights were measured and recorded. The extensions of the elastic materials were calculated and recorded when different weights (1.00N, 2.00N, 3.00N, 4.00N, 5.00N, 6.00N, 7.00N, 8.00N, 9.00N) were hooked onto each of it.
The measurements were tabulated to a table, and the trend line of the each elastic material was observed from the slope by plotting a graph restoring force applied (x) versus extension (y1, y2, z).
RESULT/ DISCUSSIONS:
Annexe 2 shows different trend lines of three materials with different elasticity. As shown from the graph of y1 against x and that of y1 and y2 against x, the force is in proportional to the extension so that as the force applied increases, the extension increases. Therefore, the Hooke’s Law is confirmed. The slope for the graph of y2 against x is steeper than the slope for graph y1 against x due to the difference in elastic constant of different material. Since it is an extension against force graph, the spring constant,k can be calculated by taking 1 over gradient and hence, k1 > k2 which means material y1 is stiffer than material y2. Besides, there is an intersection point in the graph of y1 and y2 against x, where both elastic materials have the same extension of 5.037005mm when 2.35N of force is applied. As for the graph of z against x, the trend line is not in a linear form due to its behaviour of undergoing plastic deformation whereas the material is unable to fully return back to its original shape and size after being stretched in the plastic region. Hence,the graph no longer obeys to the theory of Hooke’s Law.
Although the results are as expected, there are some anomalies. For example, the line of best fits do not pass directly through the origin. It seems that the most likely cause of this was the use of apparatus in this experiment, the slotted weights. The slotted weights used were too small compared to the elastic constant of the materials, thus the y-intercepts of the graphs represents the negligible weighs that do not cause any extension on the materials. To reduce this error, a greater value of slotted weights should be used to widen the range of forces applied as well as extensions of materials and thus, the best fit lines will be closer to the origin. Besides, this error might caused by the parallax error when taking the measurements of the extensions where the eye level is not perpendicular to the ruler readings.
(Annexe 2)
CONCLUSION:
The graph of y1 and y2 against x, which are both
still in their elastic regions, forms linear trend lines which shows the
behaviour of Hooke’s Law as the force applied is proportional to the extension.
On the other hand, the graph of z against x, which has gone past its elastic
region, shows a curve trend line which explains that the material no longer
obeys Hooke’s Law once it exceeds the elastic limit. Thus, it is noted that the
elasticity of a material behaves differently in elastic and plastic region. In
this experiment, Hooke’s Law theory is shown.
REFERENCE:
- Hosch W. L. (2006). Hooke’s Law. [Online]. Available at: https://www.britannica.com/science/Hookes-law
(Accessed: 20 October 2019)
- Williams M. (2015). What is Hooke’s Law? [Online]. Available at: https://phys.org/news/2015-02-law.html
(Accessed: 20 October 2019)
APPENDICES:
The intersection point of the graph y1 and y2 against x can be found by using matrix method in Microsoft Excel:
