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Solution Manual Chapter 13: Materials
Engineering
The figures below depict the situations described in Exercises 1 - 6.
13-1) A mass of M = 1.0 kg is hung from a circular wire of diameter 0.20 mm as shown
in the Figure A) above. What is the stress in the wire?
Need: Stress in wire, = ____ GPa.
Know: Stress = force/cross sectional area; g = 9.81 m/s2.
L
Diameter 0.20 mm
L
Diameter 0.20 mm
L
Diameter 0.20 mm
L
Diameter 0.20 mm
13-2) If the wire shown in Figure A) is stretched from 1.00 m to 1.01 m in length, what is
the strain of the wire?
Need: Strain in wire, ___ [0].
Know: Strain is the extension per unit length of wire.
13-3) In Figure B), when block of metal 1.00 m on a side is placed on a metal plate 1.00
m on a side, as above, the stress on the plate is 1.00 103 N/m2. What is the mass of the
metal cube?
Need: Mass of metal cube = ____ kg.
Know: Stress = force/area; g = 9.81 m/s2. = 1.00 103 N/m2 and A =
1.00 m2.
13-4) Suppose the plate described in Exercise 3 and the above figure was 0.011 m thick
before the cube was placed on it. Suppose that placing the cube on it causes a
compressive strain of -0.015. Then how thick will the plate be after the cube is placed on
it?
Need: Thickness of plate, T ___ m.
13-5) Suppose the wire Figure A) is perfectly elastic. When subjected to a stress of 1.00
104 Pa, it shows a strain of 1.00 10-5. What is the elastic modulus (i.e., Young’s
modulus) of the wire?
Need: Modulus of wire, E = ___ GPa.
13-6) A plate of elastic modulus 1.00 GPa is subjected to a compressive stress of –1.00
103 Pa as in Figure B. What is the strain on the plate?
Need: Plate strain in compression, = ___ [0].
Know: Modulus, E = 1.00 GPa = 1.00 109 Pa and a compressive stress,
= -1.00 103.
How: Hooke’s law, = E
1. Silicone rubbers are very flexible; their structure consists of polysiloxanes of formula –Si-O- in which
13-7) What is the yield strength under compression of the silicone?
Need: Compression yield strength of sample, = ____ MPa.
13-8) A flat saucer made of the above polymer has an initial thickness of 0.0050 m. A
ceramic coffee cup of diameter 0.10 m and mass 0.15 kg is placed on a plate made of the
same polymer as indicated above. What is the final thickness of the plate beneath the cup,
assuming that the force of the cup acts directly downward, and is not spread horizontally
by the saucer? Comment on your answer’s plausibility.
Need: Compressive strain on saucer made of polymer = ___ [0].
Know: Stress-strain relationship known above. Initial thickness of saucer =
0.0050 m. Contact area from diameter 0.10 m. Mass = 0.15 kg.
13-9) What is the maximum number of such coffee cups that can be stacked vertically on
the saucer and not cause a permanent dent in the plate?
Need: Maximum load on saucer that does not exceed compressive elastic
yield strength of the silicone = ___ cups.
13-10) A coat hanger like the one in the illustration below is made from polyvinyl
chloride2. The “neck” of the coat hanger is 0.01 m in diameter and initially 0.10 m long.
A coat hung on the coat hanger causes the length of the neck to increase by 1.00 10-5 m.
What is the mass of the coat? The stress strain diagram is also given below.
Need: Mass of coat = ____ kg.
Know: Stretch of neck = 1.00 10-5 m. Nominal length and diameter of
neck = 0.10 m and 0.010 m respectively.
13-11) What’s the minimum of such coats as per the previous Exercise must be hung
below the neck of coat hanger to cause the coat hanger neck to remain stretched after the
coats are removed?
Need: # coats to cause the hanger neck to yield ____ .
For Exercises 12-16, imagine the idealized situation as shown in diagram A) below for an
artillery shell striking an armor plate made of an (imaginary) metal called “armories”.
Diagram B is the stress/strain diagram for armories. Assume the stress/strain diagram is
to the armories’ failure strain.
13-12) Suppose the shell has mass 1.00 kg, and is traveling at 3.0 102 m/s. How much
TKE does it carry?
Need: TKE of shell = ___ J.
