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Question 1 (5 marks)
A rectangular section beam (l = 20 cm, w = 4 cm, d = 2cm) of auxetic foam is
submitted to a normal tensile load (along its length) of 1 kN. For this foam, Young’s
modulus E is 0.06 GPa, Poisson’s ratio ? equals -0.2. What are the dimensions of the
beam under load?
Question 2 (5 marks)
2(a) (1 mark)
Sketch the primitive cell of a FCC (face centre cubic) crystal in a clear diagram.
2(b) (2 marks)
Represent the ?212? plane on the same diagram.
2(c) (2 marks)
Indicate the [031] direction on the same diagram.
(Indicate your choice of axis)
Question 3 (5 marks)
Calculate the density for nickel at 500°C, given that its density at room-temperature
(20oC) is 8.902 g/cm3. Assume that the volume coefficient of thermal expansion, av, is
equal to 3al. (The value of ?l for nickel is 13.3 ? 10-6 (?C)-1).
Question 4 (15 marks)
The potential energy of interaction of two atoms in a molecule is given by the Morse
potential:
? ?
? ? ? ?
? ?
?
?
? ?
?
?
??
?
?? ? ? ?
? ??
?
??
? ? ?
?
a
r r
a
r r
U r D o o 2exp
2
exp ,
with D = 8 eV, r0 = 3.5Å, and a = 2.5 Å. (for information, 1Å = 10-10 m, and 1eV =
1.6 10-19 J, but express your results in Å and eV)
4(a) (4 marks)
Sketch (approximately) the potential form in a graph, and annotate important features.
4(b) (6 marks)
What is the distance at which the atoms form a stable bond? What is the potential
energy value at this distance?
4(c) (5 marks)
Find the critical separation at which the molecule breaks.

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