1. 3.4.2 mechanical properties of matter

2. previously
Hooke’s Law applies to the straight line section of the curve.
Force (F)  Extension (x)
F = -kx
F is the force causing the extension in the spring.
–kx is negative as it indicates that it is a restoring force.
© Pearson Education Ltd 2008
This document may have been altered from the original

3. Straight-line graph of tension against extension
The area under this graph is equal to the work done to stretch the spring
© Pearson Education Ltd 2008
This document may have been altered from the original

4. The work done in stretching the object is stored in it as elastic potential energy E.
E = work done in acheiving the stretch
E = average force x extension
Average force = F/2
so E = (F/2)x
E = (kx/2)x
E = 1/2 kx2
E = 1/2 k x & E = 1/2Fx
Total work done W = Fx , so where has the other half of the energy gone?
© Pearson Education Ltd 2008
This document may have been altered from the original

5. Stress (Pa) = Force (N) / Area (m2)
Key terms
Ductility - A material is said to be ductile if it can be permanently stretched.
Brittleness - A material is said to be brittle if it cannot be permanently stretched. It will break soon after it has passed its elastic limit (point beyond which it will not return to its original shape / length).
Strain - The extension per unit length. This has no unit.
Stress - A measure of the force per unit cross sectional area applied to a material.
Stress (Pa) = Force (N) / Area (m2)
 = F / A

6. PAG 2

7. Young’s modulus – a measure of stiffness
We know that stress is a measure of the force per unit cross sectional area applied to a material and that strain is the extension per unit length. Therefore;
Young’s Modulus (E)
E = stress / strain
E = (F/A) / (L/L)
E = FL
AL
The units of Young’s Modulus are……. PA

8.  8mm Permanent extension Strain is the percentage extension.
Stress is the Force per unit cross sectional area.
If the wire tested here was 1m long how much permanent extension was there?
Permanent extension 
8mm
© Pearson Education Ltd 2008
This document may have been altered from the original

9. Stress / Pa
Strain
(0,0)
Brittle material breaks here.
Ductile material stretches permanently beyond its elastic limit.
Release of stress.
Permanent Deformation.
If a material is stiff, it produces little strain so will have a steeper gradient.

10. Using pencils to stretch a copper wire
When you do this you can feel a change in the way the copper wire stretches. You should be able to feel what is going on in the graph on the next slide.
This should also be the shape of the graph achieved when the wire was stretched in the Young’s Modulus experiment.
© Pearson Education Ltd 2008
This document may have been altered from the original

11. Stress-strain graph for a ductile material Limit of Proportionality
Yield Point
Elastic Limit
Permanent
Deformation
© Pearson Education Ltd 2008
This document may have been altered from the original

12. Stress-strain graph for a brittle material eg cast iron or glass
© Pearson Education Ltd 2008
This document may have been altered from the original

13. Stress-strain graph for a rubber band
Graph shows an increase in the force needed to try and stretch the band as it stretches. It “goes solid like string”.
Also the band shows a very large amount of extension relative to it’s length – strain axes very long!
© Pearson Education Ltd 2008
This document may have been altered from the original

14. Hysteresis Here it matters if you are loading or unloading Stress
/ 109 Pa
Strain
(0,0)
0.5 1
Stress
/ 109 Pa
Strain
(0,0) 6 1
Polythene
Rubber

15. Factsheet 27
Materials Support
S&C Scaling up
Calculation sheet 6
Calculation sheet 6.2
Practical 6.3 – Strawberry laces
Practical 6.4 – Determining YM