phy 231 1 physics 231 lecture 20: material science and pressure remco zegers walk-in hour: tue 4-5...
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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)