Calculating Young's Modulus with Force and Extension Measurements

In summary, the conversation is about someone asking for help in calculating Young's Modulus using given data. They are provided with a table of force and extension values, as well as the area of the material. The formula for Young's Modulus, E, is given as E=stress/strain, and the equations for stress and strain are also mentioned. The person is unsure about which data to use from the table and whether they need to plot a graph. They also ask for clarification on the term "area 50mm by 5" in the data. Eventually, they are able to calculate the Young's Modulus using the formula E=Fl/Ae.
  • #1
ACCC12
5
0
hi

i have been given these results in order to work out the young's modulus can any 1 tell me how i go about doing this

Force (kN) Extension (mm)
0.5 0.003
1 0.011
1.5 0.019
2 0.021
2.5 0.024
3 0.032
3.5 0.040
4 0.043
4.5 0.050
5 0.060
5.5 0.064
6 0.070
6.5 0.076
7 0.081

Area 50mm by 5

thanks for all your help
 
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  • #2
[tex]E=\frac{stress}{strain}[/tex]


Write the formula for stress and the formula fopr strain and then simply the formula for Young's Modulus,E.
 
  • #3
i know the equation but i didnt know which part of the data to use, do i just take any part of the data from the table or do i have to plot a graph! thanks for all you help!
 
  • #4
ACCC12 said:
i know the equation but i didnt know which part of the data to use, do i just take any part of the data from the table or do i have to plot a graph! thanks for all you help!

what is meant by "area 50mm by 5 " in your data ? please explain.
 
  • #5
[tex]E=\frac{\frac{F}{A}}{\frac{e}{l}}[/tex]


[tex]E=\frac{Fl}{Ae}[/tex]

Right?


From your graph, what does the fraction F/e represent?
 
  • #6
50mm length, 5mm diameter
 
  • #7
got the answer to be 5.3 is that correct!

equation used

2.5 x 50
----------
981.75 x 0.024
 
  • #8
any takers! thanks
 

1. What is Young's modulus?

Young's modulus, also known as the elastic modulus, is a measure of the stiffness of a material. It is defined as the ratio of stress (force per unit area) to strain (change in length per unit length) in a material under tension or compression.

2. How is Young's modulus calculated?

Young's modulus is calculated by dividing the applied stress by the resulting strain. This can be represented by the equation E = σ / ε, where E is the Young's modulus, σ is the stress, and ε is the strain.

3. What units is Young's modulus measured in?

Young's modulus is typically measured in units of pascals (Pa) or newtons per square meter (N/m²). However, it can also be expressed in other units such as gigapascals (GPa) or megapascals (MPa).

4. What factors affect Young's modulus?

The Young's modulus of a material can be affected by various factors, including the material's composition, microstructure, and temperature. It can also be influenced by external factors such as stress, strain rate, and the presence of impurities or defects.

5. How is Young's modulus used in materials science?

Young's modulus is a fundamental property of materials and is commonly used in materials science and engineering to characterize the mechanical behavior of different materials. It is particularly useful in predicting how a material will respond to external forces and stresses, allowing for the design and development of new materials for various applications.

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