Question on stress and strain
1. Find stress, strain and Young’s modulus of elasticity in the case of a wire 1.5 m long and 1m×m ^ 2 in cross-section, if it increases by 1.55 mm in length, when a weight of 10 kg is suspended from it. [Ans. 9.8× 10 ^7 Nm ^- 2 1 ,33×10 ^ – 3, 9.487×10 ^10Nm ^- 2 ]
2. A structural steel rod has a radius of 10 mm and a length of 1 m. A 100 kN force stretches it along its length. Calculate (a) the stress (b) elongation and (c) strain on the rod. Given that Young’s modulus of the structural steel is 2×10 ^11 Nm ^-2
[Ans. (a) 3.18×10 ^8Nm ^- 2 (b) 1.592×10 ^- 3m
(c) 1.592×10 ^- 3 ]
3. What force is required to stretch a copper wire 1cm ^ 2 in cross-section to double its length? Y for copper is 1.26×10 ^ 12 dyne cm ^-2
[Ans. 1.26×10^12 dyne]
4. Determine the force required to double the length of a steel wire of area of cross section 5×10 ^-5m ^ 2 Young’s modulus of steel = 2 x 10^11 N m^-2.
[Ans. 10 ^ 7 N ]
5. A load of 2 kg produces an extension of 1 mm in a wire 3 m in length and 1 mm in diameter. Calculate the Young’s modulus of elasticity of the wire.
[Ans. 7.487×10^10 Nm^-2 ]
6. Calculate the percentage increase in length of a wire of diameter 2 mm stretched by force of 1 kgf. Young’s modulus of the material of wire = 15.10 ^ 10Nm^-2 .
[Ans. 0-0021%]
7. Find the maximum length of the steel wire that can hang without breaking. Given that breaking stress for steel = 7.9× 10 ^ 11 Nm ^-2 and density of steel = 7.9 * 10^3 kg m^- 3
[Ans. 1.2×10^7 m ]
8. A silica glass rod has a diameter of 1 cm and is 10 cm long. Estimate the largest mass that can be hung from it without breaking it. Given that Young’s modulus of silica 6-5 x 10^10 N m^-2 and breaking stress for silica 5 x 10^7 N m^-2.
[Ans. 400-7 kg]
9. A steel wire of length 5 m and cross-section 3 × 10^ – 5 m^2 stretches by the same amount as a copper wire of length 3 m and cross-section 4 × 10^- 5 m ^ 2 under a given load. What is the ratio of Young’s modulus of steel to that of copper?
[Ans. 2.22]
10. A mass of 5 kg is hung from a copper wire of 1 mm diameter and 2 m length. Calculate the extension produced, if Young’s modulus for copper = 1.1 × 10^11 N m². What should be the minimum diameter of the wire, so that it is does not break. Given that breaking stress for copper = 1.5 x 10^8 N m-2
[Ans. 1-134 mm; 0-645]
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