# 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

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:

(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__