# Does Young's Modulus Change When Nano-Tubes Are Connected End-to-End?

• BoanviaFx
In summary, when a force is applied to a nano-tube, it extends by a certain amount. However, when multiple tubes are connected end-to-end, the Young's modulus of the fiber remains constant, as the stress and strain remain constant. This means that the force and cross-sectional area are also constant. Therefore, the Young's modulus of the nano-tube does not change. This was confirmed by Chet's expert analysis.
BoanviaFx

## Homework Statement

A nano-tube having cross sectional area A and length L extends ΔL when a force F is applied normally to one of the cross-sectional surfaces. Show that if N tubes are connected end-to-end the then Young's modulus of the fibre does not change.

## The Attempt at a Solution

Not sure how to answer this but:

Stress on the nano-tubes regardless of how much there are will not change. So force and cross sectional area would be a constant.

I'm assuming that the total length of let's say a wire, will extend proportional to its length. So the Strain will remain constant.

So the Young's modulus of the nano-tube will not change.

Excellent analysis! Spot on.

Chet

Thanks :) !

## 1. What is Young's Modulus?

Young's Modulus, also known as the elastic modulus, is a measure of the stiffness or elasticity of a material. It is a fundamental property of solid materials and is defined as the ratio of stress to strain within the elastic limit.

## 2. How is Young's Modulus measured?

Young's Modulus is typically measured using a tensile test, where a sample of the material is pulled in opposite directions until it reaches its elastic limit. The amount of stress and strain applied to the material is then measured, and the ratio of the two gives the Young's Modulus value.

## 3. What factors can affect Young's Modulus?

The Young's Modulus of a material can be affected by various factors, including the type of material, its purity, temperature, and strain rate. Additionally, changes in the material's microstructure, such as grain size and orientation, can also impact its Young's Modulus.

## 4. Why is Young's Modulus important in materials science?

Young's Modulus is a crucial property in materials science as it helps engineers and scientists understand how a material will respond to external forces and stresses. It is also essential in designing and selecting materials for various applications, such as in construction, aerospace, and automotive industries.

## 5. How does Young's Modulus relate to other mechanical properties of materials?

Young's Modulus is one of several mechanical properties that describe how a material responds to forces and stresses. It is closely related to other properties, such as shear modulus, bulk modulus, and Poisson's ratio, which are all used to characterize a material's strength, stiffness, and deformability.

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