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Module 3-Problem Sheet - 6(a A wire 4 m long and 0.3 mm in...

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Problems: Elasticity 1. A wire 1.5 m long has a cross-sectional area of 2.4 mm 2 . It is hung vertically and stretches 0.32 mm when a 10-kg block is attached to it. Find (a) the stress, (b) the strain, and (c) Young’s modulus for the wire. 2. A 500 kg mass in hung from a 3 m steel wire with a cross-sectional area of 0.15 cm 2 . How much does the wire stretch? Y = 2.0x 10 11 N/m 2 3. A structural steel rod has a radius R of 9.5 mm and a length L of 81 cm. A force F of 6.2 X 10 4 N stretches it along length. (a) What is the stress in the rod? (b) What is the elongation of the rod under this load? What is the strain? 4. A solid copper cube has an edge length of 85.5 cm. How much pressure must be applied to the cube to reduce the edge length to 85.0 cm? The bulk modulus of copper is 1.4x10 11 N/m 2 . 5. A metal wire of length 3 m and diameter 1mm is stretched by weight of 10 kg. If Young’s modulus for its material be 12.5x10 11 dynes/cm 2 and σ for it equal to 0.26, calculate the lateral compression produced.
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Unformatted text preview: 6. (a) A wire, 4 m long and 0.3 mm in diameter, is stretched by a force of 800 gm wt. If the extension in length amounts to 1.5 mm, calculate the energy stored in the wire. (b) Find the work done in Joules in stretching a wire of cross-section 1 mm 2 and length 2m through 0.1 mm if Young’s modulus for the material of the wire is 2x10 12 dynes/cm 2 . 7. The young’s modulus of a metal is 2X10 11 N/m 2 and its breaking stress is 1.078 X 10 9 N/m 2 . Calculate the maximum amount of energy per unit volume which can be stored in the metal when stretched. 8. Calculate the work done per unit volume in stretching a uniform metal wire of area of cross section 10-6 m 2 and length 1.5 m through 4x 10-3 m. Given, Y= 2X10 11 N/m 2 . 9. Find the work done in stretching a uniform metal wire of 1 sq mm cross section and 2 m long through 0.1 mm. Given, Y = 2×10 11 N/m 2 . 1...
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