Mechanical Properties of Solids

Solids have a definite shape and size, but when forces act on them they can be stretched, compressed, twisted or bent. A body that regains its original shape when the deforming force is removed is called elastic, while one that does not is called plastic. This chapter explains the elastic behaviour of solids in terms of interatomic forces. It defines stress, the restoring force per unit area, and strain, the fractional change in dimension. Stress may be tensile, shearing or hydraulic. Hooke's law states that, for small deformations, stress is proportional to strain, and the constant of proportionality is a modulus of elasticity. You will study the stress-strain curve of a metal, showing the proportional limit, yield point, elastic region, plastic region and fracture point. Young's modulus, the shear modulus and the bulk modulus are defined and compared for common materials. Finally, the chapter explains applications of elastic behaviour: the design of crane ropes, the shape of beams and girders, and why mountains on Earth cannot be much taller than about 10 km.

Detailed Worksheet: Mechanical Properties of Solids Section A - Definitions (10 marks) 1. Define stress and strain. (2 marks) 2. State Hooke's law. (2 marks) 3. Why is steel more elastic than rubber? (2 marks) 4. Define bulk modulus and compressibility. (2 marks) 5. What are elastomers? Give one example. (2 marks) Section B - Calculations and Applications (15 marks) 6. A steel wire 4 m long with a cross-section of 2 mm^2 is stretched by a force of 200 N. Find the extension. Take Y = 2 x 10^11 Pa. (3 marks) 7. Two wires of the same material have lengths L and 2L and radii r and 2r. They are stretched by equal forces. Find the ratio of their extensions. (3 marks) 8. Find the fractional change in volume of water when it is subjected to a pressure of 100 atm. Take the bulk modulus of water as 2.2 x 10^9 Pa. (3 marks) 9. Distinguish between elastic and plastic bodies with one example each. (3 marks) 10. Why are the girders of bridges given an I-shaped cross-section? (3 marks) Section C - Diagrams (10 marks) 11. Draw a typical stress-strain curve for a metal and mark the proportional limit, yield point, ultimate tensile strength and fracture point. (4 marks) 12. Draw a diagram showing a shearing force acting on a cube and mark the shear strain. (3 marks) 13. Draw the stress-strain curve for the aorta, an elastomer, and explain how it differs from that of a metal. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. Define Young's modulus, shear modulus and bulk modulus. Write their formulas and explain which of them applies to solids, liquids and gases. (5 marks) 15. A square lead slab of side 50 cm and thickness 10 cm is subjected to a shearing force of 9 x 10^4 N on its narrow face. The lower edge is fixed. Find the displacement of the upper edge. Take the shear modulus of lead as 5.6 x 10^9 Pa. (5 marks) 16. A crane must lift loads of up to 10^4 kg. If the yield strength of steel is 3 x 10^8 Pa, find the minimum radius of a steel rope that can be used. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Take g = 9.8 m/s^2. Give answers in SI units.