# Young's Modulus Brass Wire Question

• gspsaku
In summary, the problem involves a 10 kg load suspended by a 10 m long brass wire that is vibrating vertically in SHM at a frequency of 10 vib/s. The Young's modulus for brass is given as 9x10^10 and we are asked to find the cross-sectional area of the wire using the equation Y = (F/A)/(delta l/l). The relationship between vibrational frequency and the mass and force constant in Hooke's law will be used to solve the problem.
gspsaku

## Homework Statement

A 10 kg load suspended by a brass wire 10 m long is observed to vibrate vertically in SHM at a frequency of 10 vib/s. Given that the Young's modulus for brass is
, what is the cross-sectional area of the wire?

So we know:
m = 10kg
l = 10m
f = 10Hz
Y = 9x10^10

## Homework Equations

Y = (F/A)/(delta l/l)

## The Attempt at a Solution

We have solved Young's modulus problems but they have been very basic. Since this one includes what appears to be some sort of vertical movement/vibration, I don't know what to do because I don't know how the vib/s or Hz comes into play...

If you have studied SHM, then you know that a body moves in SHM when the body is subject to a force obeying Hooke's law. Did you learn how the vibrational frequency is related to the mass of the body and the force constant in Hooke's law?

gspsaku
TSny said:
If you have studied SHM, then you know that a body moves in SHM when the body is subject to a force obeying Hooke's law. Did you learn how the vibrational frequency is related to the mass of the body and the force constant in Hooke's law?
We did and I'm working on it and I think I'm on my way...

At first I was so confused by the SHM because I had never seen it with any Young's mod problem but I am using Hooke's and Young's mod to find the actual stretch.

I was able to isolate the k constant and I think maybe I can solve this

Sounds good.

gspsaku

## 1. What is Young's Modulus?

Young's Modulus, also known as the modulus of elasticity, is a measure of the stiffness or elasticity of a material. It is represented by the symbol E and is defined as the ratio of stress to strain in a material under tension or compression.

## 2. How is Young's Modulus determined for brass wire?

To determine Young's Modulus for brass wire, a tensile test is typically performed. This involves applying a gradually increasing force to a sample of brass wire until it reaches its breaking point. The stress and strain values are then used to calculate the Young's Modulus value.

## 3. What is the typical value of Young's Modulus for brass wire?

The typical value of Young's Modulus for brass wire is around 100-125 GPa (gigapascals). However, this value can vary depending on factors such as the composition and manufacturing process of the brass wire.

## 4. How does temperature affect Young's Modulus of brass wire?

As with most materials, the Young's Modulus of brass wire decreases as temperature increases. This is due to thermal expansion and the increase in atomic vibrations at higher temperatures, which make the material less stiff.

## 5. What are some common applications of brass wire that utilize Young's Modulus?

Brass wire has a variety of applications in industries such as construction, electronics, and automotive. The stiffness and elasticity of the material, determined by Young's Modulus, make it useful for applications such as springs, musical instrument strings, and electrical connectors.

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