Stress/Strain and Youngs Modulus

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In summary, The work done for a Hookean process is 0.5Fe, where F is the force and e is the displacement. This is obtained by taking the integral of Fde, which gives 0.5Fe. The area of a triangle on a stress-strain graph can also be calculated as 0.5(F/A)(e/L), where F is the force, A is the area, e is the displacement, and L is the length. However, when solving for a specific triangle, the half in the equation should be taken into account.
  • #1
ravsterphysics
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Homework Statement


1.JPG


Homework Equations

The Attempt at a Solution


The shaded area is a triangle so the area of a triangle for this particular graph is this:

0.5 (Stress)(Strain) which gives:

0.5(F/A)(e/L) so the top would give work done and the bottom would give volume but we're still left with 0.5 in front of this so the answer should be A yet the answer is B? Why has the half disappeared?
 
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  • #2
The work done is not F*e because F is not constant throughout the process. The work done is the integral of Fde, which for a Hookean process is 0.5Fe
 

Related to Stress/Strain and Youngs Modulus

1. What is the difference between stress and strain?

Stress is the force applied to an object per unit area, while strain is the resulting deformation or change in shape of the object. In other words, stress is the cause and strain is the effect.

2. What is Young's Modulus?

Young's Modulus, also known as the modulus of elasticity, is a measure of the stiffness or rigidity of a material. It is the ratio of stress to strain for a given material and is typically represented by the letter E.

3. How is Young's Modulus calculated?

Young's Modulus is calculated by dividing the stress applied to a material by the resulting strain. The resulting value is a constant for a specific material and is typically expressed in units of Pascals (Pa) or Gigapascals (GPa).

4. What factors affect Young's Modulus?

The main factors that affect Young's Modulus include the type of material, its molecular structure, and the temperature at which it is being tested. Generally, materials with stronger and more tightly bonded molecules have a higher Young's Modulus.

5. Why is Young's Modulus important?

Young's Modulus is an important concept in materials science and engineering as it helps us understand how materials will behave under stress and strain. It allows us to predict how a material will deform or fail under certain conditions, and this knowledge is crucial in designing and building structures that are safe and durable.

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