## Saturday, 6 September 2014

### ELASTICITY PROBLEMS

ELASTICITY

(In these problems take 9 = 9.8 ms-2)

1. What is meant by LONGITUDINAL STRAIN?

2. What is meant by LONGITUDINAL STRESS?

3. What is HOOKE'S LAW?

4. What is meant by the ELASTIC LIMIT?

5. What is WORK HARDENING?

6. What is the difference between a DUCTILE and a BRITTLE material?

7. What is meant by the TENSILE BREAKING STRESS?

8. Write down the equations for:
(a) the Young Modulus of a material
(b) the energy stored in a wire which had been stretched by an amount e, the maximum force applied being F
(c) the energy stored in a wire per unit volume

9. A 5 kg mass is hung on a 2.5m length of copper wire of diameter 0.5 mm. If the Young modulus for copper is 1.2x1011 Pa calculate:
(a)  the extension produced.
(b) the elastic energy stored in the wire

10. A steel wire is used in a lift. If the lift has a weight of 20 000 N what is the smallest diameter cable that can be used if the breaking stress of steel is 500 MPa?

11. (a) Assuming Young's modulus for brass to be 1010 Pa, find the energy stored in a rod of cross sectional area 1 cm2 and 10 cm. in length if compressed by a load of 100 N.
(b) A uniform wire 2m long fixed at its upper end has a weight attached at its lower end. If the strain energy per unit volume of the wire is 2.5 J per m3 and the increase in length per unit length is 2 x 10-2 m, find:
(a) the Young  modulus
(b) the stress in the wire.

12. The rubber cord of a catapult has a cross-sectional area of 2.0 mm2 and a total unstretched length of 100 cm. It is stretched to 120 cm and then released to project a missile of mass 50 g. From energy considerations, or otherwise, calculate the velocity of projection.  (The Young modulus for the rubber is 5.0 x l05 Pa). State the assumptions made in your calculation.