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

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## 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 $w$ .

Pls guys am having problem on these topics: latent heat of fusion, specific heat capacity and the sub topics under them.Pls who can help?
Thanks George,I appreciate.
hamidat
this will lead you rightly of the formula to use
Abolarin
Most especially it is the calculatory aspects that is giving me issue, but with these new strength that you guys have given me,I will put in my best to understand it again.
hamidat
you can bring up a question and let's see what we can do to it
Abolarin
the distance between two suasive crests of water wave traveling of 3.6ms1 is 0.45m calculate the frequency of the wave
v=f×lemda where the velocity is given and lends also given so simply u can calculate the frequency
Abdul
You are right my brother, make frequency the subject of formula and equate the values of velocity and lamda into the equation, that all.
hamidat
lExplain what happens to the energy carried by light that it is dimmed by passing it through two crossed polarizing filters.
When light is reflected at Brewster's angle from a smooth surface, it is 100% polarizedparallel to the surface. Part of the light will be refracted into the surface.
Ekram
What is specific heat capacity?
Specific heat capacity is the amount of heat required to raise the temperature of one (Kg) of a substance through one Kelvin
Paluutar
formula for measuring Joules
I don't understand, do you mean the S.I unit of work and energy?
hamidat
what are the effects of electric current
What limits the Magnification of an optical instrument?
Lithography is 2 micron
Venkateshwarlu
what is expression for energy possessed by water ripple
what is hydrolic press
An hydraulic press is a type of machine that is operated by different pressure of water on pistons.
hamidat
what is dimensional unite of mah
i want jamb related question on this asap🙏
What is Boyles law
it can simple defined as constant temperature
Boyles law states that the volume of a fixed amount of a gas is inversely proportional to the pressure acting on in provided that the temperature is constant.that is V=k(1/p) or V=k/p
what is motion
getting notifications for a dictionary word, smh
Anderson
what is escape velocity
the minimum thrust that an object must have in oder yo escape the gravitational pull
Joshua
what is a dimer
Mua
what is a atom
how to calculate tension
what are the laws of motion
Mua