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Diagram of weight w attached to each of three guitar strings of initial length L zero hanging vertically from a ceiling. The weight pulls down on the strings with force w. The ceiling pulls up on the strings with force w. The first string of thin nylon has a deformation of delta L due to the force of the weight pulling down. The middle string of thicker nylon has a smaller deformation. The third string of thin steel has the smallest deformation.
The same force, in this case a weight ( w size 12{w} {} ), applied to three different guitar strings of identical length produces the three different deformations shown as shaded segments. The string on the left is thin nylon, the one in the middle is thicker nylon, and the one on the right is steel.

Stretch yourself a little

How would you go about measuring the proportionality constant k size 12{k} {} of a rubber band? If a rubber band stretched 3 cm when a 100-g mass was attached to it, then how much would it stretch if two similar rubber bands were attached to the same mass—even if put together in parallel or alternatively if tied together in series?

We now consider three specific types of deformations: changes in length (tension and compression), sideways shear (stress), and changes in volume. All deformations are assumed to be small unless otherwise stated.

Changes in length—tension and compression: elastic modulus

A change in length Δ L size 12{ΔL} {} is produced when a force is applied to a wire or rod parallel to its length L 0 size 12{L rSub { size 8{0} } } {} , either stretching it (a tension) or compressing it. (See [link] .)

Figure a is a cylindrical rod standing on its end with a height of L sub zero. Two vectors labeled F extend away from each end. A dotted outline indicates that the rod is stretched by a length of delta L. Figure b is a similar rod of identical height L sub zero, but two vectors labeled F exert a force toward the ends of the rod. A dotted line indicates that the rod is compressed by a length of delta L.
(a) Tension. The rod is stretched a length Δ L size 12{ΔL} {} when a force is applied parallel to its length. (b) Compression. The same rod is compressed by forces with the same magnitude in the opposite direction. For very small deformations and uniform materials, Δ L size 12{ΔL} {} is approximately the same for the same magnitude of tension or compression. For larger deformations, the cross-sectional area changes as the rod is compressed or stretched.

Experiments have shown that the change in length ( Δ L size 12{ΔL} {} ) depends on only a few variables. As already noted, Δ L size 12{ΔL} {} is proportional to the force F size 12{F} {} and depends on the substance from which the object is made. Additionally, the change in length is proportional to the original length L 0 size 12{L rSub { size 8{0} } } {} and inversely proportional to the cross-sectional area of the wire or rod. For example, a long guitar string will stretch more than a short one, and a thick string will stretch less than a thin one. We can combine all these factors into one equation for Δ L size 12{ΔL} {} :

Δ L = 1 Y F A L 0 , size 12{ΔL= { {1} over {Y} } { {F} over {A} } L rSub { size 8{0} } } {}

where Δ L size 12{ΔL} {} is the change in length, F size 12{F} {} the applied force, Y size 12{Y} {} is a factor, called the elastic modulus or Young’s modulus, that depends on the substance, A size 12{A} {} is the cross-sectional area, and L 0 size 12{L rSub { size 8{0} } } {} is the original length. [link] lists values of Y size 12{A} {} for several materials—those with a large Y size 12{A} {} are said to have a large tensile stifness because they deform less for a given tension or compression.

Elastic moduli Approximate and average values. Young’s moduli Y size 12{Y} {} for tension and compression sometimes differ but are averaged here. Bone has significantly different Young’s moduli for tension and compression.
Material Young’s modulus (tension–compression) Y ( 10 9 N/m 2 ) Shear modulus S ( 10 9 N/m 2 ) Bulk modulus B ( 10 9 N/m 2 )
Aluminum 70 25 75
Bone – tension 16 80 8
Bone – compression 9
Brass 90 35 75
Brick 15
Concrete 20
Glass 70 20 30
Granite 45 20 45
Hair (human) 10
Hardwood 15 10
Iron, cast 100 40 90
Lead 16 5 50
Marble 60 20 70
Nylon 5
Polystyrene 3
Silk 6
Spider thread 3
Steel 210 80 130
Tendon 1
Acetone 0.7
Ethanol 0.9
Glycerin 4.5
Mercury 25
Water 2.2

Young’s moduli are not listed for liquids and gases in [link] because they cannot be stretched or compressed in only one direction. Note that there is an assumption that the object does not accelerate, so that there are actually two applied forces of magnitude F size 12{F} {} acting in opposite directions. For example, the strings in [link] are being pulled down by a force of magnitude w size 12{w} {} and held up by the ceiling, which also exerts a force of magnitude w size 12{w} {} .

Questions & Answers

a thick glass cup cracks when hot liquid is poured into it suddenly
Aiyelabegan Reply
because of the sudden contraction that takes place.
Eklu
railway crack has gap between the end of each length because?
Aiyelabegan Reply
For expansion
Eklu
yes
Aiyelabegan
Please i really find it dificult solving equations on physic, can anyone help me out?
Big Reply
sure
Carlee
what is the equation?
Carlee
Sure
Precious
fersnels biprism spectrometer how to determined
Bala Reply
how to study the hall effect to calculate the hall effect coefficient of the given semiconductor have to calculate the carrier density by carrier mobility.
Bala
what is the difference between atomic physics and momentum
Nana Reply
find the dimensional equation of work,power,and moment of a force show work?
Emmanuel Reply
What's sup guys
Peter
cul and you all
Okeh
cool you bro
Nana
so what is going on here
Nana
hello peeps
Joseph
Michelson Morley experiment
Riya Reply
how are you
Naveed
am good
Celine
you
Celine
hi
Bala
Hi
Ahmed
Calculate the final velocity attained, when a ball is given a velocity of 2.5m/s, acceleration of 0.67m/s² and reaches its point in 10s. Good luck!!!
Eklu Reply
2.68m/s
Doc
vf=vi+at vf=2.5+ 0.67*10 vf= 2.5 + 6.7 vf = 9.2
babar
s = vi t +1/2at sq s=58.5 s=v av X t vf= 9.2
babar
how 2.68
babar
v=u+at where v=final velocity u=initial velocity a=acceleration t=time
Eklu
the answer is 9.2m/s
OBERT
express your height in Cm
Emmanuel Reply
my project is Sol gel process how to prepare this process pls tell me
Bala
the dimension of work and energy is ML2T2 find the unit of work and energy hence drive for work?
Emmanuel Reply
KgM2S2
Acquah
Two bodies P and Quarter each of mass 1000g. Moved in the same direction with speed of 10m/s and 20m/s respectively. Calculate the impulse of P and Q obeying newton's 3rd law of motion
Shimolla Reply
kk
Doc
the answer is 0.03n according to the 3rd law of motion if the are in same direction meaning they interact each other.
OBERT
definition for wave?
Doc Reply
A disturbance that travel from one medium to another and without causing permanent change to its displacement
Fagbenro
In physics, a wave is a disturbance that transfers energy through matter or space, with little or no associated mass transport (Mass transfer). ... There are two main types ofwaves: mechanical and electromagnetic. Mechanicalwaves propagate through a physical matter, whose substance is being deformed
Devansh
K
Manyo
thanks jare
Doc
Thanks
AMADI
Note: LINEAR MOMENTUM Linear momentum is defined as the product of a system’s mass multiplied by its velocity: size 12{p=mv} {}
AMADI
what is physic
zalmia Reply
please gave me answar
zalmia
Study of matter and energy
Fagbenro
physics is the science of matter and energy and their interactions
Acquah
physics is the technology behind air and matter
Doc
Okay
William
hi sir
Bala
how easy to understanding physics sir
Bala
Easy to learn
William
31. Calculate the initial (from rest) acceleration of a proton in a 5.00×106 N/C electric field (such as created by a research Van de Graaff). Explicitly show how you follow the steps in the Problem-Solving Strategy for electrostatics.
Catina Reply
A tennis ball is projected at an angle and attains a range of 78. if the velocity is 30metres per second, calculate the angle
Shimolla
what friction
Wisdom Reply
question on friction
Wisdom
the rubbing of one object or surface against another.
author
momentum is the product of mass and it's velocity.
Algayawi
what are bioelements?
Edina
Friction is a force that exist between two objects in contact. e.g. friction between road and car tires.
Eklu
Practice Key Terms 6

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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