# Young's modulus problem

In summary, the conversation discusses the mass and orbit of the asteroid Ceres, and the task of estimating the change in length of a copper wire due to hanging a mass on it. The equations g=GM/r^2 and a=v^2/r are mentioned for reference. The discussion also touches on the concept of Young's modulus and its relevance to the problem on Ceres.

## Homework Statement

The asteriod Ceres has a mass of 1.11x10^21 kg and a diamter 772km. Ceres orbits the sun at an average distance of 414 million kilometers.
Estimate the change in length of a 2m length of thin copper wire caused by hanging a 1.5kg mass on the wire on the asteriod Ceres.
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## Homework Equations

$$\begin{array}{l} g = \frac{{GM}}{{r^2 }} \\ a = \frac{{v^2 }}{r} \\ \end{array}$$

## The Attempt at a Solution

Could somebody please give me some direction on how to approach these situation. Many thanks in return,

If you hung the mass from the wire on Earth, how much would the wire stretch? (Consider Young's modulus.) What's different on Ceres?

Young's modulus...never heard of it, thanks ill look into it

## 1. What is Young's modulus?

Young's modulus, also known as the modulus of elasticity, is a measurement of a material's stiffness or resistance to deformation when subjected to stress. It is defined as the ratio of stress (force per unit area) to strain (change in length per unit length) and is typically expressed in units of pascals (Pa) or gigapascals (GPa).

## 2. How is Young's modulus determined?

You can determine Young's modulus by performing a tensile test on a material. This involves applying a known force to a sample of the material and measuring how much it stretches. From this data, you can calculate the stress and strain values and then calculate Young's modulus using the formula E = stress/strain.

## 3. What factors affect Young's modulus?

The main factors that affect Young's modulus are the type of material, its microstructure, and its temperature. Materials with strong intermolecular bonds, such as metals, tend to have higher Young's moduli. The microstructure of a material, including its grain size and defects, can also influence its elasticity. Additionally, the temperature of a material can affect its Young's modulus, with most materials becoming less stiff at higher temperatures.

## 4. What are some examples of materials with high and low Young's moduli?

Some examples of materials with high Young's moduli include steel, titanium, and diamond. These materials are known for their strength and stiffness, making them useful in applications that require high durability. On the other hand, materials with low Young's moduli include rubber, foam, and certain types of plastics. These materials are more flexible and have a higher capacity for deformation under stress.

## 5. Why is Young's modulus important in engineering and materials science?

Young's modulus is an important concept in engineering and materials science because it helps us understand how materials behave under stress and strain. It is a fundamental property that can be used to predict how a material will respond to different types of loads and how it will perform in specific applications. Engineers and scientists can use Young's modulus to select the right material for a given design, ensure structural integrity, and improve the overall performance and safety of a product or structure.