Hi everyone, I want to discuss on Elasticity.
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Elasticity is the way by which a material when pushed down comes back to it's normal size.
The first thing one should have in mind when we talk on elasticity is Hooke's Law
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It states that the extension of an elastic material is directly proportional to the force provided that the elastic material is not exceeded. In this law one can say that
F=kE
K is constantly or proportionally called first constant or the stiffness of the elastic material.
k=F÷E
Stress and Strain
Stress; is defined as the ratio of force to area.
Stress = Force ÷ Area = Nm-²
Strain; is defined as the ratio of extension to the original length
Strain = Extension ÷ Length
From Hooke's Law, stress is proportional strain provided elastic limit is not exceeded.
Stress a* Strain
F÷A a* E÷L
As Extension and Length are the same we will cancel them. There we have;
F÷A=Constant (y)
The constant of proportionality is called Young Modulus.
Work done in Spring and Elastic String
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This is the product of average force stretching the string and the extension produce.
Average Force = initial force+final force ÷2
Where the initial force is zero (0)
Average force = 0 + F ÷ 2
Work done in an elastic string = ½F×E
F=Ek Hooke's Law
WD = ½ F E
WD = ½ ek × e
WD = ½ e² k
I think I've talked alot.
Let's solve a problem as example
A wire of length 2.00m and radius 1.0mm is stretch by 25.0mm on application of a force of 1000Newton.
Calculate the young modulus for the wire.
Solution
L = 2.00m
R = 10mm ÷ 1000 = 1×10-³m
E = 25mm ÷ 1000 = 0.025
F = 1000N
A = π r² (22 ÷ 7 × 0.001× 0.001)
A = 2.2 × 10 ÷ 7 = 3.14×10-⁶
Stress = F ÷ A = 10³ ÷ 3.14×10-⁶
Stress = 3.185×10-⁴
Note; * means a proportionality sign as I couldn't find the sign in my phone.
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With this I've come to the end of this post. Thanks for stopping by.❤️❤️❤️