Stress-strain graph-finding elastic strain energy

In summary, the conversation discusses a discrepancy in the solution for a physics problem involving stress, strain, and Young modulus. The speaker has solved task a correctly but is unsure about their solution for task b, which is off by one zero compared to the solution given in the book. They question whether it could be a mistake in the book or in their own calculation. Another speaker agrees with their answer and mentions that mistakes in books are not uncommon. The conversation ends with the first speaker expressing relief that they did not miscalculate.
  • #1
Krashy
30
5

Homework Statement


stress-strain.png


Homework Equations


[/B]
stress = force/area
strain = extension/original length
Young modulus= stress/strain

The Attempt at a Solution



stress strain task.png

[/B]
Hi i hope you can read my handwriting. I solved task a already but even though i think i solved b correctly, the solution says its wrong. It states that its 45000 J. It could be a mistake in the book because its just off by one zero, but I am not sure it could be a mistake in my calculation too. The force and the extension is apparently right according to the solution.
Thank you very much in advance.
 

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  • #2
I agree with your answer. Such mistakes in books are not uncommon, unfortunately.
 
  • Like
Likes Krashy
  • #3
All right, thanks good to know i didnt miscalculated
 

1. What is a stress-strain graph?

A stress-strain graph is a graphical representation of the relationship between the stress (force per unit area) applied to a material and the resulting strain (change in length or deformation) it undergoes. It is commonly used to determine the mechanical properties of a material, such as its elasticity and strength.

2. How is elastic strain energy calculated from a stress-strain graph?

Elastic strain energy is calculated by finding the area under the stress-strain curve up to the elastic limit. This can be done by dividing the curve into smaller rectangles and summing their areas, or by using calculus to find the definite integral of the curve.

3. What does the slope of a stress-strain graph represent?

The slope of a stress-strain graph represents the material's stiffness or Young's modulus. A steeper slope indicates a higher stiffness and a lower slope indicates a lower stiffness. This can be useful in determining the suitability of a material for a specific application.

4. How does a stress-strain graph differ for different materials?

The shape and characteristics of a stress-strain graph can vary greatly depending on the type of material. For example, a brittle material such as glass will have a steep initial slope and then a sudden drop, while a ductile material such as steel will have a more gradual slope and a longer elastic region before reaching its yield point.

5. What is the significance of the elastic region on a stress-strain graph?

The elastic region on a stress-strain graph represents the range of stress within which a material can undergo deformation and still return to its original shape when the stress is removed. This region is important in determining the material's ability to withstand stress without permanent deformation. Beyond the elastic region, the material may undergo plastic deformation or even failure.

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