Architecture and Design homework help

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  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.

Calculate:

  • The maximum weight W the filament can support without breaking.                                     [3 marks]
  • The weight W′ which will extend the filament by 0.50% of its original length.                                     [3 marks]

Total 20 Marks

  1. (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:

  • The extension of the specimen immediately before breaking.                                     [3 marks]
  • 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

  • The young modulus for glass [2 marks]
  • 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]
  • The extension just before a fibre of unstretched length 0.50 m breaks.                                     [2 marks]

Total 20 Marks