Young's modulus of a steel post, finding change in length

In summary, Superman pulls on a steel post with a cross-sectional area of 30cm^2 and a length of 2m with a force of 6X10^6N to trap a supervillian. By using the equation F/A= Y(of steel post) ⋅ΔL/Li to calculate the change in length, the result is 1.9mm. However, if the Young's modulus is changed to 200000 N/mm^2 instead of 210000 N/mm^2, the result is 2 cm, which may have been rounded down to 1.9mm.
  • #1
DracoMalfoy
88
4

Homework Statement


Superman pulls on a steel post to trap a supervillian. The post has a cross-sectional area of 30cm^2 and a length of 2m. If Superman applies a force of 6X10^6N by how much is the length of the post increased?

A)
2mm

B) 7mm

C)
1.2cm

D)
1.7cm

E)
2cm

Homework Equations



F/A= Y(of steel post) ⋅ΔL/Li

F= 6x10^6N
A=30cm^2= .3m^2
Li=2m[/B]

The Attempt at a Solution


[/B]
I know I'm supposed to find the change in length, but when I use this equation, I'm getting 1.9 which isn't an answer choice. I'm not sure what I'm doing wrong here.
 
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  • #2
DracoMalfoy said:

Homework Statement


Superman pulls on a steel post to trap a supervillian. The post has a cross-sectional area of 30cm^2 and a length of 2m. If Superman applies a force of 6X10^6N by how much is the length of the post increased?

A)
2mm

B) 7mm

C)
1.2cm

D)
1.7cm

E)
2cm

Homework Equations



F/A= Y(of steel post) ⋅ΔL/Li

F= 6x10^6N
A=30cm^2= .3m^2
Li=2m[/B]

The Attempt at a Solution


[/B]
I know I'm supposed to find the change in length, but when I use this equation, I'm getting 1.9 which isn't an answer choice. I'm not sure what I'm doing wrong here.

I also obtain 19 mm. But if I use 200000 N/mm^2 instead of 210000 N/mm^2, the calculation yields 2 cm exactely. Maybe it was rounded down ...
 

1. What is Young's modulus?

Young's modulus, also known as the elastic modulus, is a measure of a material's stiffness or ability to resist deformation when a force is applied. It is represented by the letter E and is measured in units of pressure, such as newtons per square meter (N/m²) or pounds per square inch (psi).

2. How is Young's modulus calculated?

The formula for Young's modulus is E = (stress/strain), where stress is the force applied to a material and strain is the resulting change in length or deformation. This ratio is also known as the modulus of elasticity and is a constant value for a given material.

3. What is the significance of Young's modulus for a steel post?

Young's modulus is an important factor in determining the strength and flexibility of a steel post. A higher modulus indicates a stiffer material that can withstand greater forces without breaking or deforming. This is why steel, with a high Young's modulus, is commonly used in construction and engineering projects.

4. How is the change in length of a steel post calculated?

The change in length of a steel post can be calculated using the formula ∆L = L x (strain), where L is the original length of the post and strain is the change in length divided by the original length. This change in length can be determined by applying a known force to the post and measuring the resulting deformation.

5. What factors can affect Young's modulus of a steel post?

Young's modulus can be affected by various factors, such as temperature, pressure, and the material's microstructure. In the case of a steel post, the type and quality of steel used, as well as any heat treatments or mechanical processes it has undergone, can also impact its modulus. Additionally, external factors like corrosion or fatigue can also affect the post's stiffness and overall performance.

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