Young’s Modulus
When stress is applied to a material, strain is produced in the material. The strain is proportional to the stress, provided the stress does not exceed a limit known simply as the ‘limit of proportionality’. Within this limit, the value of is a constant for that material, and is known as the Young Modulus for the material.
The Young Modulus (E) =
Provided the limit of proportionality is not exceeded.
Before we can work out the Young Modulus we need to know about stress and strain. Stress is defined as the tension (force) per unit area applied normal to that area. Strain is defined as the extension per unit length.
- Stress is proportional to strain up to the limit of proportionality, P. The gradient OP is equal to the Young Modulus.
- The elastic limit, E, beyond, which the spring becomes permanently stretched.
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The yield point, beyond the elastic limit (Y1) is where the spring suddenly gives a little. The stress increases until Y1 where the stress drops a little when the sample is stretched a little. Further stretching increases the stress to the point Y2.
- Plastic behaviour – beyond the elastic limit, the wire loses its elasticity. Its behaviour is described as plastic because it does not regain its initial shape when the forces applied are removed.
- The maximum stress, the point where the spring has its greatest strength it is sometimes called the ultimate tensile strength (UTS) of the material.
- B, stands for the breaking point.
Prediction
I predict that increasing (F) force or load will increase the deflection (∆d). I also predict that Hooke’s Law is correct and that; ‘ The deformation of a material is proportional to the force is applied to it, provided the elastic limit is not exceeded’.
Variables
Independent variable - Weight
Dependent variable- Extension
Control variable – Ruler position, same ruler.
Safety
- Be careful, the ruler might break.
Fair test
- Use the same: - G Clamp
Ruler
Table
Only change one variable in each investigation.
Equipment
G-Clamp
Ruler (x2)
O.5 Newton Weights (x8)
Edge of the Table
Clamp Stand
Diagram
Method
- Set up the apparatus as shown in the diagram above.
- Set the over-hang to 90cm.
- Start putting the weights on, one at a time.
- Record the results.
- Then repeat the experiment at least three times.
Results Table
Analysis
From the results I have found out that the larger the load the larger the causes a larger deflection, which is just as I expected. The load is proportional to the extension, as found as evidence to Hooke’s Law. ‘ The deformation of a material is proportional to the force is applied to it, provided the elastic limit is not exceeded’. However, my results do not show that there is a bend limit. This is probably because I did not put enough load on the end of the ruler to find this out.
Evaluation
I thought the investigation went well. My prediction turned out to be correct. I did have some anomalous results in my results but they were not totally wrong, they just were not as accurate as I would have liked them to be.
If I had to repeat the experiment I would like to use a more accurate ruler that had a scale down to one tenth of a millimetre, rather than a one-metre ruler with a scale down to millimetres.
Unfortunately, I could not use larger masses because the ruler might fracture and it could have disastrous results.
I believe that it really was a fair test. I used the most accurate method possible to measure the deflection of the ruler with the resources available.
Bibliography
Breithaupt, Jim (1995) Understanding Physics. Third Edition
Stanley Thornes Publishers Ltd. Cheltenham
Johnson, Brian (1986) Physics for GCSE. First Edition
Heinemann Educational Books Ltd. London
Shepherd, Michael (1996) GCSE Physics. First Edition
Letts Educational Ltd. London
