PHY 2311

PHYSICS 231Lecture 20: material science and

pressure

Remco ZegersWalk-in hour: Tue 4-5 pm

Helproom

gas liquid solid

PHY 2312

quiz

A child runs toward a merry-go-round and jumps on theedge. As a results, the merry-go-round starts to spin.Next, she moves towards the center of the merry-go-round. If no net torque is applied to the child ormerry-go-round then:

a) they will start to spin faster while she moves to the center b) the rotational velocity will not change while she moves to the centerc) the will start to spin less fast while she moves to the the center

PHY 2313

States of matterSolid Liquid Gas Plasma

diffi culttodeform

easy todeform

easy todeform

easy todeform

diffi culttocompress

diffi culttocompress

easy tocompress

easy tocompress

diffi cultto flow

easy toflow

easy toflow

easy toflow

notcharged

notcharged

notcharged

charged

PHY 2314

Phase transformations

PHY 2315

solids

amorphousordered

crystalline

PHY 2316

The deformation of solids

Stress: Tells something about the force causing the deformation

Strain: Measure of the degree of deformation

For small stress, strain and stress are linearly correlated.

Strain = Constant*Stress

Constant: elastic modulus

The elastic modulus depends on:• Material that is deformed• Type of deformation (a different modulus is defined for

different types of deformations)

PHY 2317

The Young’s modulus

LA

FL

LL

AFY

Y

0

0

0

2

/

/

L/L :strain tensile

](Pa) Pascal[N/mF/A :stress tensile

strain tensile

stress tensile

Beyond the elastic limit an objectis permanently deformed (it doesnot return to its original shape ifthe stress is removed).

PHY 2318

exampleAn architect wants to design a 5m high circular pillar witha radius of 0.5 m that holds a bronze statue that weighs 1.0E+04 kg. He chooses concrete for the material of the pillar (Y=1.0E+10 Pa). How much does the pillar compress?

5m

0

2

0 /

)/(

/

/

LL

RgM

LL

AFY pillarstatue

R=0.5 m L0=5m Y=1.0E+10 Pa M=1.0E+04 kg

L=6.2E-05 m

PHY 2319

question

0/

/

LL

AFY

Given:

A rod with a cross section A of 1 cm2 is stretched by 1 mmif a force of 1000 N is applied. If on a rod of the samematerial but which is 2x loner and has a cross section of2 cm2 a force of 2000 N is applied, it will stretch by:

a) 1 mmb) 2 mmc) 4 mmd) 8 mm

Fx2, Ax2, L0x2 so L must be twicelarger to keep Y constant

PHY 23110

Ultimate strength

Ultimate strength: maximum force per unit area a materialcan withstand before it breaks or fractures.

Different for compression and tension.

PHY 23111

example

A builder is stacking 1 m3 cubic concrete blocks. Each blocksweighs 5E+03 kg. The ultimate strength of concrete forcompression is 2E+07 Pa. How many blocks can he stackbefore the lowest block is crushed?

The force on the low end of the lowest blockis: F=Nmblockg. N: total number of blocksmblock=mass of one blockg=9.81 m/s2

Ultimate strength: 2E+07=F/A=Nmblockg/1

N=408 blocks.

PHY 23112

The Shear Modulus

xA

Fh

hx

AFS

S

/

/

x/h :strainshear

](Pa) Pascal[N/mF/A :stressshear

strainshear

stressshear

2

x

PHY 23113

Moving earth crust

30 m

100 m

A tectonic plate in the lower crust (100 m deep) of the earth is shifted during an earthquake by 30m.What is the shear stress involved, if the upper layerof the earth does not move? (S=1.5E+10 Pa)

hx

AFS

/

/

strainshear

stressshear

F/A=4.5E+09 Pa

PHY 23114

Bulk Modulus

Compressibility: 1/(Bulk modulus)

pressureP

VV

P

VV

AFB

B

00

0

2

//

/

V/V :strain volume

](Pa) Pascal[N/mF/A :stress volume

strain volume

stress volume

PHY 23115

example

What force per unit area needs to be applied to compress1 m3 water by 1%? (B=0.21E+10 Pa)

0/

/

VV

AFB

V/V0=0.01 so, F/A=2.1E+07 Pa !!!

PHY 23116

Some typical elastic moduli

PHY 23117

Density

)/( 3mkgV

M

)4(/

Cwatermaterialspecific o

PHY 23118

Pressure

Pressure=F/A (N/m2=Pa)

Same Force, different pressure

PHY 23119

example

A nail is driven into a piece of wood with a force of 700N.What is the pressure on the wood if Anail=1 mm2?A person (weighing 700 N) is lying on a bed of such nails (his body covers 1000 nails). What is the pressureexerted by each of the nails?

Pnail=F/Anail=700N/1E-06m2=7E+08 PaPperson=F/(1000Anail)=700/1E-03=

7E+05 Pa (about 7 times the atmospheric pressure).

PHY 23120

Force and pressure

A P=0Vacuum

Air (P=1.0E+5 Pa)

F

Force due to pressure difference: Fpressure=PAIf A=0.01 m2 (about 10 by 10 cm) thena force F=(1.0E+5)*0.01=1000N is needed to pullthe lit.

What is the force needed to move the lit?

Fpressure-difference= PA

PHY 23121

Magdeburg’s hemispheres

Otto von Guericke (Mayor of Magdeburg, 17th century)