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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

explain how a body becomes electrically charged based on the presence of charged particles
Kym Reply
induction
babar
what are the calculations of Newton's third law of motiow
Murtala Reply
what is dark matter
apex Reply
(in some cosmological theories) non-luminous material which is postulated to exist in space and which could take either of two forms: weakly interacting particles ( cold dark matter ) or high-energy randomly moving particles created soon after the Big Bang ( hot dark matter ).
Usman
if the mass of a trolley is 0.1kg. calculate the weight of plasticine that is needed to compensate friction. (take g=10m/s and u=0.2)
Declan Reply
what is a galaxy
Maduka Reply
what isflow rate of volume
Abcd Reply
flow rate is the volume of fluid which passes per unit time;
Rev
flow rate or discharge represnts the flow passing in unit volume per unit time
bhat
When two charges q1 and q2 are 6 and 5 coulomb what is ratio of force
Mian Reply
When reducing the mass of a racing bike, the greatest benefit is realized from reducing the mass of the tires and wheel rims. Why does this allow a racer to achieve greater accelerations than would an identical reduction in the mass of the bicycle’s frame?
bimo Reply
is that the answer
nehemiah
why is it proportional
nehemiah Reply
i don't know
Adah
y
nehemiah
what are the relationship between distance and displacement
Usman Reply
They are interchangeable.
Shii
Distance is scalar, displacement is vector because it must involve a direction as well as a magnitude. distance is the measurement of where you are and where you were displacement is a measurement of the change in position
Shii
Thanks a lot
Usman
I'm beginner in physics so I can't reason why v=u+at change to v2=u2+2as and vice versa
Usman
what is kinematics
praveen
kinematics is study of motion without considering the causes of the motion
Theo
The study of motion without considering the cause 0f it
Usman
why electrons close to the nucleus have less energy and why do electrons far from the nucleus have more energy
Theo
thank you frds
praveen
plz what is the third law of thermodynamics
Chidera Reply
third law of thermodynamics states that at 0k the particles will collalse its also known as death of universe it was framed at that time when it waa nt posible to reach 0k but it was proved wrong
bhat
I have not try that experiment but I think it will magnet....
Rev Reply
Hey Rev. it will
Jeff
I do think so, it will
Chidera
yes it will
lasisi
If a magnet is in a pool of water, would it be able to have a magnetic field?.
Stella Reply
yes Stella it would
Jeff
formula for electric current
Chizzy Reply
what is that about pleace
Fokoua
what are you given?
Kudzy
what is current
Fokoua
I=q/t
saifullahi
Current is the flow of electric charge per unit time.
saifullahi
What are semi conductors
saifullahi
materials that allows charge to flow at varying conditions, temperature for instance.
Mokua
these are materials which have electrical conductivity greater than the insulators but less than metal, in these materials energy band Gap is very narrow as compared to insulators
Sunil
materials that allows charge to flow at varying conditions, temperature for instance.
Obasi
wao so awesome
Fokoua
At what point in the oscillation of beam will a body leave it?
Atambiri
what is gravitational force
Adah
what is meant by the term law
Fahd Reply
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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