# 13.2 Elasticity: stress and strain

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• State Hooke’s law.
• Explain Hooke’s law using graphical representation between deformation and applied force.
• Discuss the three types of deformations such as changes in length, sideways shear and changes in volume.
• Describe with examples the young’s modulus, shear modulus and bulk modulus.
• Determine the change in length given mass, length and radius.

We now move from consideration of forces that affect the motion of an object (such as friction and drag) to those that affect an object’s shape. If a bulldozer pushes a car into a wall, the car will not move but it will noticeably change shape. A change in shape due to the application of a force is a deformation    . Even very small forces are known to cause some deformation. For small deformations, two important characteristics are observed. First, the object returns to its original shape when the force is removed—that is, the deformation is elastic for small deformations. Second, the size of the deformation is proportional to the force—that is, for small deformations, Hooke’s law is obeyed. In equation form, Hooke’s law    is given by

$F=k\Delta L,$

where $\Delta L$ is the amount of deformation (the change in length, for example) produced by the force $F$ , and $k$ is a proportionality constant that depends on the shape and composition of the object and the direction of the force. Note that this force is a function of the deformation $\Delta L$ —it is not constant as a kinetic friction force is. Rearranging this to

$\Delta L=\frac{F}{k}$

makes it clear that the deformation is proportional to the applied force. [link] shows the Hooke’s law relationship between the extension $\Delta L$ of a spring or of a human bone. For metals or springs, the straight line region in which Hooke’s law pertains is much larger. Bones are brittle and the elastic region is small and the fracture abrupt. Eventually a large enough stress to the material will cause it to break or fracture. Tensile strength is the breaking stress that will cause permanent deformation or fracture of a material.

## Hooke’s law

$F=\mathrm{k\Delta L},$

where $\Delta L$ is the amount of deformation (the change in length, for example) produced by the force $F$ , and $k$ is a proportionality constant that depends on the shape and composition of the object and the direction of the force.

$\Delta L=\frac{F}{k}$

The proportionality constant $k$ depends upon a number of factors for the material. For example, a guitar string made of nylon stretches when it is tightened, and the elongation $\Delta L$ is proportional to the force applied (at least for small deformations). Thicker nylon strings and ones made of steel stretch less for the same applied force, implying they have a larger $k$ (see [link] ). Finally, all three strings return to their normal lengths when the force is removed, provided the deformation is small. Most materials will behave in this manner if the deformation is less than about 0.1% or about 1 part in ${\text{10}}^{3}$ .

what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
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What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
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Rafiq
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
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Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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research.net
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sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
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absolutely yes
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Maciej
Abigail
for teaching engĺish at school how nano technology help us
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NANO
how can I make nanorobot?
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what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
how did you get the value of 2000N.What calculations are needed to arrive at it
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