Young's modulus, stretching question.

In summary, the question involves three members of steel, copper, and brass, each with identical dimensions and axial load. The Young's moduli for each material are given. Given that the steel member stretches 0.13mm, the task is to calculate the amount of elongation in the copper and brass members. The relevant equation is Young's modulus = Stress/Strain, and the approach is to assume that the strain is equal to the elongation and solve for stress, which can then be used to calculate strain for the other two members. The original length is not needed for this calculation.
  • #1
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Homework Statement


Three separate members of steel, copper and brass are of identical dimensions and are
equally loaded axially.Young’s moduli for the materials are:
steel, 210,000 N/mm^2
copper, 100,000 N/mm^2
brass, 95,000 N/mm^2
If the steel member stretches 0.13mm,
calculate the amount of elongation in the copper and brass members.

Homework Equations


The equation i believe to be relevant;
Young's modulus=Stress/Strain

The Attempt at a Solution


I am confused how to approach this question at first i believed i had to find the stress by using the elongation of 0.13mm, and because all the members would be under the same stress i could then input that information into a youngs modulus equation for the other two members. However the young's modulus equation requires strain not just the elongation and i don't know the original length.

The only way I can think of solving this question would to assume that the strain = 0.13 and solve the question like so

Steel young's modulus= stress/strain
210=stress/0.13
stress=210*0.13=27.3

Starting with brass as an example
Young's modulus = stress/strain
strain= stress/young modulus
Strain= 27.3/95 =0.29 mm

and Copper =0.27mm

Is this assumption correct, if not any hints on how i could go about solving this problem?
Thank you very much.
 
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  • #2
LordPride said:
However the young's modulus equation requires strain not just the elongation and i don't know the original length.
You don't need to know the original length, just that it is the same for each. Accordingly, the elongation will be proportional to the strain.
 
  • #3
Oh haha, thank you very much. My misunderstanding =D
 

1. 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 describes the ratio of stress to strain in a material when it is subjected to tensile or compressive forces.

2. How is Young's modulus calculated?

Young's modulus is calculated by dividing the stress (force per unit area) by the strain (change in length divided by original length) in a material. This calculation is typically done under controlled conditions, such as in a laboratory setting, to ensure accurate results.

3. What is the unit of measurement for Young's modulus?

The unit of measurement for Young's modulus is typically expressed in units of pressure, such as pascals (Pa) or newtons per square meter (N/m²). However, it can also be expressed in other units such as pounds per square inch (psi) or gigapascals (GPa).

4. What does a high or low Young's modulus indicate about a material?

A high Young's modulus indicates that a material is very stiff or rigid, meaning it will resist deformation when subjected to stress. On the other hand, a low Young's modulus indicates that a material is more flexible and will deform more easily under stress.

5. How does temperature affect Young's modulus?

The temperature can have a significant impact on Young's modulus, as materials may expand or contract with changes in temperature. In general, as the temperature increases, the Young's modulus of most materials will decrease, making them more flexible. However, this relationship can vary depending on the specific material and its properties.

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