# 5.3 Elasticity: stress and strain  (Page 2/15)

 Page 2 / 15

## Stretch yourself a little

How would you go about measuring the proportionality constant $k$ 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 $\Delta L$ is produced when a force is applied to a wire or rod parallel to its length ${L}_{0}$ , either stretching it (a tension) or compressing it. (See [link] .)

Experiments have shown that the change in length ( $\Delta L$ ) depends on only a few variables. As already noted, $\Delta L$ is proportional to the force $F$ and depends on the substance from which the object is made. Additionally, the change in length is proportional to the original length ${L}_{0}$ 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 $\Delta L$ :

$\Delta L=\frac{1}{Y}\frac{F}{A}{L}_{0},$

where $\Delta L$ is the change in length, $F$ the applied force, $Y$ is a factor, called the elastic modulus or Young’s modulus, that depends on the substance, $A$ is the cross-sectional area, and ${L}_{0}$ is the original length. [link] lists values of $Y$ for several materials—those with a large $Y$ 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 $Y$ 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 $\left({\text{10}}^{\text{9}}\phantom{\rule{0.25em}{0ex}}{\text{N/m}}^{\text{2}}\right)$ Shear modulus S $\left({\text{10}}^{\text{9}}\phantom{\rule{0.25em}{0ex}}{\text{N/m}}^{\text{2}}\right)$ Bulk modulus B $\left({\text{10}}^{\text{9}}\phantom{\rule{0.25em}{0ex}}{\text{N/m}}^{\text{2}}\right)$
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
Marble 60 20 70
Nylon 5
Polystyrene 3
Silk 6
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 $F$ acting in opposite directions. For example, the strings in [link] are being pulled down by a force of magnitude $w$ and held up by the ceiling, which also exerts a force of magnitude $w$ .

a thick glass cup cracks when hot liquid is poured into it suddenly
because of the sudden contraction that takes place.
Eklu
railway crack has gap between the end of each length because?
For expansion
Eklu
yes
Aiyelabegan
Please i really find it dificult solving equations on physic, can anyone help me out?
sure
Carlee
what is the equation?
Carlee
Sure
Precious
fersnels biprism spectrometer how to determined
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
find the dimensional equation of work,power,and moment of a force show work?
What's sup guys
Peter
cul and you all
Okeh
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Nana
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Nana
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Joseph
Michelson Morley experiment
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Naveed
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you
Celine
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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!!!
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
OBERT
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?
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
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?
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
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Doc
Thanks
Note: LINEAR MOMENTUM Linear momentum is defined as the product of a system’s mass multiplied by its velocity: size 12{p=mv} {}
what is physic
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
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Bala
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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.
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
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