1. (a) A certain spring which obeys Hooke’s law has a force constant k 0f 60 Nm-1. Draw a graph of the stretching force F against extension x for this spring for a range of x from 0 to 25 mm. show all calculations used to determine the plotting points. [10 marks]
(b) Use your graph to determine the work required to stretch the spring from an initial extension of 5 mm to final extension of 25 mm. [4 marks]
(c) the figure below shows a vertical nylon filament with a weight suspended from its lower end. The cross-sectional area of the filament is 8 x 10-7 m2, the young modulus is 2 x 109 Pa and the ultimate tensile stress is 9 x 107 Pa.
(i) The maximum weight W the filament can support without breaking. [3 marks]
(ii) The weight W′ which will extend the filament by 0.50% of its original length. [3 marks]
Total 20 Marks
2. (a) State Hooke’s Law and explain why wires used as guitar strings must have elastic properties. [3 marks]
(b) The data below are for a thin steel wire suitable for use as a guitar string.
Ultimate tensile stress: 1.8 x 109 Pa
Young Modulus: 2.2 x 1011 Pa
Cross-sectional area: 2.0 x 10-7 m2
In a tensile test, a specimen of the wire, of original length 1.5 m, is stretched until it breaks. Assuming the wire obeys Hooke’s law throughout, calculate:
(i) The extension of the specimen immediately before breaking. [3 marks]
(ii) The elastic strain energy released as the wire breaks. [4 marks]
(c) Glass is described as a brittle material with an amorphous structure. Explain the terms ‘brittle’ and ‘amorphous’ [4 marks]
(d) The graph below shows the tensile stress against strain for a glass fibre.
Use this graph to calculate
(i) The young modulus for glass [2 marks]
(ii) The strain energy per unit volume just before fibre breaks, i.e. where the graph line ends. State your answer with suitable SI unit. [2 marks]
(iii) The extension just before a fibre of unstretched length 0.50 m breaks. [2 marks]
Total 20 Marks