P.23Crystal structures
Kinds of bonds formed
- Hydrogen bond
- Ionic bond
- Covalent bond
- Metallic bond
Size and shape
- fcc
- bcc
P.24Size of a molecule
Using Avogadro constant
nm14.0r
cm109x6x
64r
3
4
cm109x6x
64=atomeach of volume
106x=atomsCu of number
cm9
64=Cu of volumemolar
gcm9=Cu ofdensity
64=Cu of mass atomic
323
3
323
23
3
3-
P.25Hooke’s Law
The extension is proportional to the force in a wire if the proportional limit is NOT exceeded.
P.25Stress and Strain
Strength
The Greatest force a material can withstand before breaking
Stiffness (force constant)
The opposition a material sets up to being distorted by having its change of size and/or shape.
Stress
The force acting on unit cross-sectional area
Stress = F / A
Strain
The extension of unit length
Strain = e / l
P.26
Stress S=(Weight W) / (Area A)
New volume V’ = 23 V = 8V
New weight W’ = V’ g = 8 V g = 8 W
New area A’ = 22 A = 4 A
New Stress S’ = (8 W) / (4 A) = 2 S
P.28Young’s modulus E
Under elastic limit, stress α strain
Estress
strain
F
Ae
( )
( )
E
F
Ae
F
eA
FEA
e ke
( )
( )
( )
EA
Stiffness
P.26
mg = ke
E = (F l) / (A e)
F = [(E A) / (l)] e
k = [(E A) / (l)]
For same material, Young modulus will be the same
New l’ => new k’=2k
m’g = k’e’ + k’e’
2m g = 2ke’ + 2ke’
e’ = (0.5) e
P.30
Q: larger strain before break
P: E=stress/strain = slope = stiffnessstrength = greater breaking stress
P.31
=/E. Strain is independent of the unstretched length
NNY
=/E =(F/(EA)). When A increases, decreases.
=/E =(F/(EA)). Ebrass < Esteel. When E decreases, increases.
P.31
%E = %m + %g + %l + 2%d + %e
%l = 0.51%
%d = 1.64%
%m = 0.1%
%e = 2.56%
%g = 1.02%
ed
mgl
er
lmg
Ae
FLE 22
2
)(
)(
P.31Energy stored in a wire
1
21
21
2
2
Fe
EAee
EAe
( ) )
( E =F / A
e /
W FeEAe
e EAe
1
2
1
2
1
2
2
( )
P.32
Energy on the wire
FeW2
1
Ae
FlE
)(1
)1.0(2
)02.0(101105
22
1 2682
Jl
EAee
l
EAeW
2
2
1..1 mvEKW
)/(20 smv
P.32
7542.28
1
00019998.0)21022.1(103.12 2310
l
EAeF
00019998.010004.1'
0004.102.01' 22
lle
l l’
o854.88
5002.0
1tan
)(115.010/)854.88cos(7542.282/cos2 kggFm
mg
P.32
Their extensions should be the same.
2brassE
E
F
Fconst
E
F
l
EAeF steel
brass
steel
x
Taking moment at point O
O
)(600
9005.0
)900(
mmx
xx
xFxF steelbrass
P.33
These two wires are connected in series. They have same force.
2122
21
1
1 eekel
AEe
l
AEF
l
EAeF combined
1
11 /
l
AEFe
2
22 /
l
AEFe combinedkFee /21
combinedkFl
AEF
l
AEFee ///
2
2
1
121
1221
21
2
2
1
1
2
2
1
1
lElE
AEE
lAE
lAE
lAE
lAE
kcombined
P.33
mg = k x
YYN
m x
x = mg / k x depends on weight of the ball and force constant k
The ball eventually stopped, energy is lost due to air resistance.
P.38
Stiffer material needs a greater stress to produce same strain. Young modulus is larger which has steeper slope.
Y
YY
Stronger material can withstand a greater stress before breaking
Z breaks at strain=1.6, hence e = 1.6l . The length of Z at breaking point = 2.6 l
P.38
Ductility is independent of its melting point.
Young modulus is a measure of stiffness. It is NOT a direct measurement of the ductility of material.
Copper has performed plastic deformation between the elastic limit and the facture point. Glass has narrow gap only.
Extension under same stress depends on the proportional part. It is independent of plastic deformation.
P.40Equilibrium spacing of molecules
Stable equilibrium occurs when P.E. is minimum.
)(
1
11
11
0
qbpa
r
rr
rr
qp
o
qp
qp
o
qb
o
pa
F
qbpaF
P.40Elasticity and Hooke’s Law
Near ro, F-r curve is nearly a straight line
kdF
dr
EF A
e
/
/
Er r r
F E r r ro o
o o
force between two molecules F / r 2o
( ) /
( )
P.40Thermal expansion
At higher temperature, molecules have some energy and oscillate between X and Y.
Due to asymmetry, mean position will be G.
Metal is expanded.
At very high temperature, the molecule separation will be very large. The corresponding energy needed is called latent heat or binding energy.
P.41
kdF
dr
EF A
e
/
/
Er r r
F E r r ro o
o o
force between two molecules F / r 2o
( ) /
( )
1183 105.1106.4/109.6 EESlope ro
P.41
126 r
b
r
aV
0126
130
70
r
b
r
a
dr
dV
6
1
0
2
a
br 6
06
0
22
2min 22422 r
a
ar
a
b
a
ab
b
aba
V
P.41
137
126
r
b
r
a
dr
dVF
015642
1482
2
r
b
r
a
dr
Vd
dr
dF
0
6
16
16
06
1
7
13
7
13
7
26r
a
ar
a
br
137
126
r
b
r
aF
130
6
13
60
70
6
7max
713
6
713
6
r
ar
r
aF
13
71
13
76
70
6
7
6
7
max
r
aF
6
7
70
max 13
7
13
36
r
aF
P.41
(1) : Spacing of molecules at equilibrium
(2) : Max. distance before breaking
(3) : force constant => stiffness
(4) : max. tension that the material can tolerate before breaking, it is called tensile strength.
P.42
A1 is +ve energy that the system repel back to eq. pt.
A2 is -ve energy that the system attract back to eq. pt. with max. attractive force.
A3 is -ve energy that the material breaks and go to infinity
A2 + A3 is energy needed to move the molecules from eq. pt to infinity