BACKGROUND KNOWLEDGE:
Robert Hooke notices that the stress vs strain curve for many materials has a linear region while studying springs and elasticity. Within certain limits, the force required to stretch an elastic object such as metal spring is directly proportional to the extension of the spring. This is known as the Hooke's Law and commonly written :
F = -kx
F is the force, x is the length of extension/ compression and k is a constant of proportionality known as the spring constant which is usually given in N/m.
When calculating x, its important to take note that the spring itself will also have some nominal length L0. The total length L of a spring under extension is equal to the nominal length plus the extension , L = L0 + X. For a spring under compression, it would be L = L0 - x.
EXPERIMENT:
Objective:
To investigate the behaviour of two different elastic materials, which are both still in linear regions and a material which has gone past its elastic region(in the plastic region).
Method:
1. Three different materials are used where two of them are still in their linear regions and one is still in its plastic region.
[y1 and y2 are the first and second material acting in their linear region respectively and z is the material which is acting in its plastic region]
2. The force applied on the materials are labelled X and different values of X are applied on the material.
3. The deformation caused by the values of X on the materials are measured and recorded.
Calculations:
Given the following data:
x = 1.00, 2.00, 3.00, 4.00, 5.00, 6.00, 7.00, 8.00, 9.00
y1 = 3.00, 4.50, 6.00, 7.50, 9.00, 10.50, 13.00, 14.00, 15.00
y1 = ax + b
y2 = (a + 0.5) + c, given c = 0.2
z = x^3 + b
Data:
Graph showing deformation of material y1 and y2 against the force applied on them.
Graph 1
From this graph, the equation given is y1 = 1.5583x + 1.375
Given y1 = ax + b,
By comparing coefficients,
=> a = 1.5583
=> b = 1.375
=> y1 = 1.5583x + 1.375
=> y2 = 2.0583x + 0.2
Graph showing deformation of material z against the force applied.
Graph 2
graph is plotted with the given formula;
z=x^3 + 1.375
Finding Intersection on graph 1:
Using estimation(Estimation is done by looking at the graph)
Value of X: 2.56N
Value f Y: 4.6mm
COORDINATE OF INTERSECTION (2.56, 4.6)
Using simultaneous equation
y1 = 1.5583x + 1.375
y2 = 2.0583x + 0.2
by substituting:
1.5583x + 1.375 = 2.0583x + 0.2
0.5x = 1.175
x = 2.35
by substituting x into the equation:
y = 1.5583(2.35) + 1.375
y = 5.04
COORDINATE OF INTERSECTION (2.35, 5.04)
Discussion:
1. From Graph 1, both the line derived from the equations obeys the Hooke's Law. Hooke's Law stated that when the material is in its linear region, the extension is directly proportional to the tensile force acting on it. This clearly shows that this experiment obeys the Hooke's Law.
2. From Graph 2, the line derived from the equation obeys the Hooke's Law. It was stated that material Z is in its plastic region which also means that the extension of material and the tensile force acting on it is not proportional. Bigger force applied on the material causes greater deformation of the material. This is clearly shown in the graph as the line is deflected from a straight line. In conclusion, this experiment obeys the Hooke's Law.
3. This experiment is conducted by deforming and stretching of the three materials which causes the materials to change in shape physically.
Conclusion:
The result of this experiment is very satisfactory as it obeys the Hooke's Law concerning the behaviour of materials in linear region and plastic region when external force is acted on them. Thus, this experiment has proven the credibility of Hooke's Law.
Reference:
https://www.khanacademy.org/science/physics/work-and-energy/hookes-law/a/what-is-hookes-law
THANK YOU FOR READING. : )
F=−kxF=−kxF=−kx
