(a) A uniform metal bar, initially unstretched, has sides of length w, x and y, as shown in [Fig. 3.1]. The bar is now stretched by a tensile force F applied to the shaded ends. The changes in the lengths x and y are negligible. The bar now has sides of length x, y and z, as shown in [Fig. 3.2]. (b) A copper wire is stretched by a tensile force that gradually increases from 0 to 280 N. The variation with extension of the tensile force is shown in [Fig. 3.3].

1. (a)(i)Determine expressions, in terms of some or all of F, w, x, y and z, for: the stress σ applied to the bar by the tensile force[1]
2. (a)(ii)Determine expressions, in terms of some or all of F, w, x, y and z, for: the strain ε in the bar due to the tensile force[1]
3. (a)(iii)Determine expressions, in terms of some or all of F, w, x, y and z, for: the Young modulus E of the metal from which the bar is made.[2]
4. (b)(i)State the maximum extension of the wire for which it obeys Hooke's law.[1]
5. (b)(ii)Use [Fig. 3.3] to determine the strain energy in the wire when the tensile force is 120N.[3]
6. (b)(iii)Explain why the work done in stretching the wire to an extension of 12mm is not equal to the energy recovered when the tensile force is removed.[2]

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