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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 Δ L , size 12{F=kΔL} {}

where Δ L size 12{ΔL} {} is the amount of deformation (the change in length, for example) produced by the force F size 12{F} {} , and k size 12{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 Δ L size 12{ΔL} {} —it is not constant as a kinetic friction force is. Rearranging this to

Δ L = F k size 12{ΔL= { {F} over {k} } } {}

makes it clear that the deformation is proportional to the applied force. [link] shows the Hooke’s law relationship between the extension Δ L size 12{ΔL} {} 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.

Hooke’s law

F = kΔL , size 12{F=kΔL} {}

where Δ L size 12{ΔL} {} is the amount of deformation (the change in length, for example) produced by the force F size 12{F} {} , and k size 12{k} {} is a proportionality constant that depends on the shape and composition of the object and the direction of the force.

Δ L = F k size 12{ΔL= { {F} over {k} } } {}
Line graph of change in length versus applied force. The line has a constant positive slope from the origin in the region where Hooke’s law is obeyed. The slope then decreases, with a lower, still positive slope until the end of the elastic region. The slope then increases dramatically in the region of permanent deformation until fracturing occurs.
A graph of deformation Δ L size 12{ΔL} {} versus applied force F size 12{F} {} . The straight segment is the linear region where Hooke’s law is obeyed. The slope of the straight region is 1 k size 12{ { {1} over {k} } } {} . For larger forces, the graph is curved but the deformation is still elastic— Δ L size 12{ΔL} {} will return to zero if the force is removed. Still greater forces permanently deform the object until it finally fractures. The shape of the curve near fracture depends on several factors, including how the force F size 12{F} {} is applied. Note that in this graph the slope increases just before fracture, indicating that a small increase in F size 12{F} {} is producing a large increase in L size 12{L} {} near the fracture.

The proportionality constant k size 12{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 Δ L size 12{ΔL} {} 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 size 12{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 that about 0.1% or about 1 part in 10 3 size 12{"10" rSup { size 8{3} } } {} .

Questions & Answers

what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
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?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
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?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Abe advanced level physics. OpenStax CNX. Jul 11, 2013 Download for free at http://legacy.cnx.org/content/col11534/1.3
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