Name – Jack Maggs     Username – jm30g13     Student ID – 26272172

"I am aware of the requirements of good academic practise and the potential penalties for any breaches".

1. Robert Hooke

Figure 1. Robert Hooke

Robert Hooke was born on July 18th, 1635, on the Isle of Wight. He died on 3rd of March 1703 in London. He studied at Oxford University and here he became an assistant to the famous Robert Boyle. Robert Hooke first stated Hooke's law in 1660.

2. Hooke's Law 

“Hooke’s law states that the force needed to stretch a wire or spring is directly proportional to the extension of the material from its natural length.”

Hooke’s law:

                         Force, F = k∆L                                                  [1]

Where (k) is the spring constant and (∆L) is the change in length from its original length (L). (F) is the force applied to the spring 

Unit of F = N

Unit of k = Nm^-1 or kgs^-2

Unit of L = m 

Figure 2. Force against extension graph

Elastic region - Hooke's law is obeyed, force (F) is directly proportional to the extension (∆L) However once the spring has gone past the elastic limit, the spring will not return to its original length.

Plastic region - Hooke's law is no longer obeyed, therefore force (F) is no longer proportional to the extension (∆L). Here the wire loses strength and becomes narrower at its weakest point.

Fracture - This is the point at which the spring breaks 

3. Experiment





Figure 3. Experimental setup



1. Set up the apparatus as shown in figure 1.
2. The spring is attached to a fixed support and a known force (F) is applied
3. The extension (∆L) of the spring is measured by using a ruler
4. Experiment is repeated using a different force to extend the spring
5. The results are then tabulated and a graph is constructed
6. Repeat experiment for all materials

Click on figure 3. for more information on the experiment

4. Results

Table 1. Shows the results of the extension of the 3 materials when a different forces were applied.

Material 1 + 2

Figure 4. Graph of y1 and y2 against x 

Graph analysis 

Both lines on figure 4. obey Hooke's law as the force applied is proportional to the extension of the materials. This means that both of the materials are still in their elastic region. However as you can see on the blue line (y1 = ax + b) there is a kink in the graph, this result is called an anomaly. An anomalous result is a result that doesn't fit in with the general trend of the results. This could be down to an error that occurred during the experiment.

The gradient of the graph represents the 'spring constant' of the spring or the 'stiffness'. The orange line has a steeper gradient than the blue line meaning that the material that represents the orange line is 'stiffer' than the other material. 

Finding the point of intersection by solving simultaneously 

Y1 = ax + b                               [2]
Y2 = (a + 0.5)x + c                    [3]



Plugged the numbers into [2] and [3]


Y1 = 1.5583x + 1.375               [2]
Y2 = (1.5583 + 0.5)x + 0.2       [3]


Equate [2] and [3]


1.5583x + 1.375 = (1.5583 + 0.5)x + 0.2
1.5583x + 1.375 = (2.0583)x + 0.2
1.5583x + (1.375 - 0.2) = 2.0583x

1.5583x + (1.175) = 2.0583x 1.175 = 2.0583x - 1.5583x 1.175 = 0.5x x = 1.175/0.5 x = 2.35 Sub [x] into [2] Y1 = 1.5583x + 1.375  Y1 = (1.5583*2.35) + 1.375 Y = 5.03 Point of intersection - (2.35 , 5.03)   Material 3 Figure 5. Graph of z against x Graph analysis The line on figure 5. shows that this material does not obey Hooke's Law, this is because the force applied is never proportional to the extension of the material. The line on the graph is an exponential function meaning that the material is in its plastic region. Conclusion The results show that materials 1 + 2 obey Hooke's Law, as the force applied is proportional to the extension of the material. This shows the material is in its elastic region. The results for material 3 show that the force applied is not proportional to the extension. This shows the material is in its plastic region. Errors There are a number of possible errors that could have occurred when conducting this experiment: High chance of human error when reading the extension values due to the scale being in millimetres and being hard to read accurately. The extension not being read at eye level, therefore giving a different value for the extension. This is called a parallax error. When reading the extension, the overall system may not have been at rest. When working out the simultaneous equations both the values were recurring meaning that they had to be rounded up. This is referred to as a rounding error. The mass stated may not have been the same mass that was actually applied to the material. References Jim Breithaupt (2008). AQA Physics A AS Physics. Cheltenham: Nelson Thornes. 164-171. http://www.tutorvista.com/content/physics/physics-iii/solids-and-fluids/hookes-law.php

http://m.everythingscience.co.za/grade-12/07-mechanical-properties-of-matter/07-mechanical-properties-of-matter-02.cnxmlplus

http://www.cyberphysics.co.uk/topics/forces/hooke.htm

http://www.s-cool.co.uk/category/subjects/a-level/physics/stress-and-strain

http://www.ucmp.berkeley.edu/history/hooke.html