Order Description 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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