EXERCISES
1.
Iron exhibits bcc structure at room temperature. Above 900oC, it transforms
to fcc structure. Calculate the ratio of density of iron at room temperature to
that at 900oC (assuming molar mass and atomic radius of iron remains
constant with temperature).
2.
Niobium crystallizes in body centred cubic structure. If density is 8.55 g/cm3,
calculate atomic radius (Ao) of niobium using its atomic mass 92.90
(AN = 6.02×1023).
3.
Calculate the radius of an iridium atom, given that Ir has an FCC crystal
structure, a density of 22.4 g/cm3, and an atomic weight of 192.2 g/mol
(AN = 6.02×1023)
4.
Calculate the radius of a vanadium atom, given that V has a BCC crystal
structure, a density of 5.96 g/cm3, and an atomic weight of 50.9 g/mol.
(AN = 6.02×1023).
5.
Iron has a BCC crystal structure, an atomic radius of 0.124nm, and an atomic
weight of 55.85 g/mol. Compute and compare its theorical density with the
experimental value found inside the front cover (AN = 6.02×1023).
6.
An element crystallizes in a structure having FCC unit cell with a lattice
constant of 200pm. If 200g of this element contains 24×1023 atoms, calculate
the density (in g/cc) of the elements. (AN = 6.02×1023).
7.
A metal has a body centered cubic (bcc) strtucture with a lattice constant of
288pm. The density of the metal is 7.2g/cm3. How many atoms present in
500g of the metal?
8.
At room temperature, sodium crystallizes in body centred cubic lattice.
Calculate theoretical density (g/cm3) of sodium (Na=23, rNa=1.02Ao).
(AN = 6.02×1023).
9.
A specimen of aluminium having a rectangular cross section 10mm×12.7mm
and a Young’s modulus of 69 GPa is pulled in tension with 35,500N force,
producing only elastic deformation. Calculate the resulting strain.
10.
A cylindrical specimen of a titanium alloy having an elastic modulus of
197GPa and an original diameter of 3.8mm will experience only elastic
deformation when a tensile load of 2000N is applied. Compute the maximun
length of the specimen before deformation if the maximum allowable
elongation is 0.42mm.
11.
Consider a cylindrical specimen of some hypothetical metal alloy that has a
diameter of 8.0mm. A tensile force of 1000N produces an elastic reduction
in diameter of 2.8×10-4mm. Compute the modulus of elasticity for this alloy,
given that Poisson’s ratio is 0.30.
12.
A brass alloy is known to have a yield strength of 275MPa, a tensile strength
of 380 MPa, and an elastic modulus of 103 GPa. A cylindrical specimen of
this alloy 12.7mm in diameter and 250mm long is stressed in tension and
found to elongate 7.6mm. On the basis of the information given, it is possible
to compute the magnitude of the load that is necessary to produce this change
in length? If so, calculate the load. If not, explain why.
13.
(a) A force of 100,000N is applied to an iron bar with a cross-sectional area
of 10mm×20mm and having a yield strength of 400MPa and a tensile
strength of 480MPa. Determine whether the bar will plastically deform and
whether the bar will experience necking.
(b) Calculate the maximum force that a 0.2-in. diameter rod of Al2O3, having
a yield strength of 35, 000 psi, can withstand with no plastic deformation.
Express your answer in pounds and Newtons.
14.
A cylindrical specimen of alumium having a diameter of 0.505 in. (12.8mm)
and a gauge length of 2.000 in. (50.800mm) is pulled in tension. Use the load
elongation characteristics shown in the following table to complete parts (a)
and through (e)
(a) Plot the data as engineering stress versus engineering strain
(b) Compute the modulus of elasticity
(c) Determine the yield strength at a strain offset of 0.002
(d) Determine the tensile strength of this alloy
(e) What is the approximate ductility, in percent elongation?
Load
Length
N
lbf
mm
in.
0
0
50.800
2.000
7,330
1,650
50.851
2.002
15,100
3,400
50.902
2.004
23,100
5,200
50.952
2.006
30,400
6,850
51.003
2.008
34,400
7,750
51.054
2.010
38,400
8,650
51.308
2.020
41,300
9,300
51.816
2.040
44,800
10,100
52.832
2.080
46,200
10,400
53.848
2.120
47,300
10,650
54.864
2.160
47,500
10,700
55.880
2.200
46,100
10,400
56.896
2.240
44,800
10,100
57.658
2.270
42,600
9,600
58.420
2.300
36,400
8,200
59.182
2.330
Fracture
15.
For a bronze alloy, the stress at which plastic deformation begins is 280MPa
and the modulus of elasticity is 115 GPa.
(a) What is the maximum load that may be applied to a specimen with a
cross-sectional arera of 325mm2 without plastic deformation?
(b) If the original specimen length is 120mm, what is the maximum length to
which it may be stretched without causing plastic deformation?
16.
Consider a cylindrical specimen of a steel alloy (Figure 6.21) 15.0mm in
diatmeter and 75mm long that is pulled in tension. Determine its elongation
when a load of 20,000N is applied.
17.
A cylindrical specimen of a hypothetical metal alloy is stressed in
compression. If its original and final diameters are 20.000 and 20.025mm,
respectively, and its final length is 74.96mm, compute its original length if
the deformation is totally elastic. The elastic and shear moduli for this alloy
are 105GPa and 39.7 GPa, respectively.
18.
A pipe has an outside diameter of 20mm, an inside diameter of 10mm and
length 0.30m and it supports a compressive load of 50kN. The pipe shortens
by 0.6mm when the load is applied. Determine:
(a) The compressive stress
(b) The compressive strain in the pipe when supporting this load
19.
When a circular hole of diameter 40mm is punched out of a 1.5mm thick
metal plate, the shear stress needed to cause fracture is 100MPa. Determine:
(a) The minimum force to be applied to the punch
(b) The compressive stress in the punch at this value
20.
A force of 25kN applied to a piece of steel produces an extension of 2mm.
Assuming the elastic limit is not exceeded, determine:
(a) The force required to produce an extension of 3.5mm
(b) The extension when the applied force is 15kN.
21.
A bar of thickness 20mm and having a rectangular cross-section carries a
load of 82.5kN. Determine:
(a) The minimum width of the bar to limit the maximum stress to 150MPa
(b) The modulus of elasticity of the material of the bar if the 150mm long bar
extends by 0.8mm when carrying a load of 200kN
22.
A current density of 0.05 A/cm2 is applied to a 150cm2 cathode. What period
of time (s) is required to plate out a 1-mm-thick coating of silver onto the
cathode? (dAg = 10.5g/cm3, MAg = 108g/mol, F = 96500C/mol)
23.
A 1-m-square steel plate is coated on both sides with a 0.005-cm-thick layer
of zinc. A current density of 0.02A/cm2 is applied to the plate in an aqueous
solution. Assuming that the zinc corrode uniformly, determine the length of
time required before the steel is exposed.
24.
A corrosion cell is composed of a 300cm2 copper sheet and a 20cm2 iron
sheet, with a current density 0f 0.6A/cm2 applied to the copper. Which
material is the anode? Why? What is the rate of loss of metal from the anode
per hour?
25.
At room temperature the electrical conductivity and the electron mobility for
2
copper are 6 × 107 (Ωm)−1 and 0.0030 𝑚 ⁄𝑉𝑠 respectively.
(a) Compute the number of free electrons per cubic meter for copoper at
room temperature.
(b) What is the number of free electrons per copper atom? Assume copper
has a density of 8.9 g/cm3, q = 1.6 × 10−19 𝐶, AN = 6.02×1023
26.
A cylindrical metal wire 2mm (0.08in.) in diameter is required to carry a
current of 10A with a minimum of 0.03V drop per foot (300mm) of wire.
Which of the metals and alloys listed in the table below are possible
candidates?
27.
Metal
Electrical Conductivity [(𝛀𝐦)−𝟏 ]
Silver
6.8 × 107
Copper
6.0 × 107
Gold
4.3 × 107
Aluminium
3.8 × 107
Brass (70Cu-30Zn)
1.6 × 107
Iron
1.0 × 107
Platinium
0.94 × 107
Plain carbon steel
0.6 × 107
Stainless steel
0.2 × 107
A 1-m-square steel plate is coated on both sides with a 0.005-cm-thick
layer of zinc. A current density of 0.02 A/cm2 is applied to the plate in an
aquaeous solution. Assuming that the zinc corrodes uniformly, determine
the length of time required before the steel is exposed. (d Zn = 7.14g/cm3)
28.
The metal nickel crystallizes in a face centred cubic structure. Its density is
8.9 g/cm3. Calculate:
a. The lattice constant (nm)
b. The radius of the nickel atom (Ao)
Given that the atomic weight of Ni is 58.89, (AN = 6.02×1023).
29.
Magnesium is Hcp with c/a=1.624, density = 1.74g/cm3. Find the atomic
radius (nm) of magnesium. Mg = 24, (AN = 6.02×1023).
30.
A tube of outside diameter 60mm and inside diameter 40mm is subjected to
a tensile load of 60 kN. Determine the stress in the tube.