Young's Modulus: Calculate from Length, Radius, Elongation & Weight

[monkeymak7]

Homework Statement

A wire, of length 250 centimeters, and radius 0.3 millimeters is stretched by hanging on a weight of 12 kilograms, and the elongation produced is 8 millimeters. Calculate the value of Young’s modulus for the wire.

Homework Equations

The Attempt at a Solution

I have no idea because we never went over this...please please guide me in the right direction

 

[Dickfore]

In atomic units, where the unit of length is 1 bohr radius ($a_{0} \equiv \hbar^{2}/(m_{e} \, k_{0} \, e^{2})$, the unit of mass is the electron mass $m_{e}$ and the unit of energy is 1 hartree ($E_{0} = m_{e} \, (k_{0} \, e^{2})^{2}/\hbar^{2}$), the unit for Young's modulus (pressure) is:

$$[Y] = [F]/[A] = \mathrm{T}^{-2} \, \mathrm{L}^{-1} \, \mathrm{M} = \frac{[E_{0}]}{[a_{0}]^{3}}$$

$$Y_{0} = \frac{27.2 \, \mathrm{eV} \times \frac{1.602 \times 10^{-19} \, \mathrm{J}}{1 \, \mathrm{eV}}}{(5.29 \times 10^{-11} \, \mathrm{m})^{3}}.$$

I believe the answer to your question is:

$$Y = \frac{Y_{0}}{226}$$

 

[monkeymak7]

Where are you getting all the values for this equation? I apologize, but this is like reading a different language! I'm just not understanding where 27.2, 1.602, and 5.29 are taken from...

 

[PhanthomJay]

Look up the stress strain relationships for elastic materials where the stress (P/A) is linearly proportional to the strain (elongation/length). Watch your units.

 

[monkeymak7]

I think I've figured it out! Thanks for your help. I posted another question and still haven't had any responses. I've been trying to research this question for a few days and still haven't a clue as to what needs to be done. Do any of you know what the heck this question is asking and how I go about solving it. (The book I have for my class has nothing like this in it, nor have I seen anything like this throughout the chapters I have studied).


A balance, the beam of which is 30 centimeters long and weighs 40 grams, is deflected through 1° by an excess of 1 milligram in one of the pans. What is the distance of the center of gravity of the beam below the central pivot?

 

[eoneil]

Young’s Modulus, E= tensile stress/tensile strain= (F/Ao)/(∆L/Lo)
F= force applied to object= ma= mg= (12kg)(9.81m/s2)= 117 N
Ao= cross-sectional area through which force is applied= πr2= 2.8 x 10^-8
∆L= amount by which length of object changes= 0.008m
Lo= original length of the object= 0.25m

So, E= (mg/Ao)/(∆L/Lo)= (117N/2.8x10^-8)^2/(0.008m)(0.25m)= 0.0165 Gpa,

Gpa=gigapascals