Modulus Definition and 612 Threads

Equating the two equations gives me ##k = -\frac {YA}{L}## but the correct answer of the same magnitude but opposite sign. I think the nub of my misunderstanding is quite elementary (who would have guessed!) : When is it ##F=kx## and when is it ##F=-kx##? If I understand correctly, F is the...

I need to understand how to figure out the distance modulus to a star: If the distance of modulus of a star cluster is 12, what is the distance?

For part (b), I counted the number of squares underneath the 2 day sample to be roughly 33 'whole' squares (the 5by5 tiny squares is 1 whole sqaure). I then equated 33 whole square = 0.35 MJ to calculate 1 whole square to be 0.0106 MJ. I then counted the number of whole squares underneath the...

Today, while studying about bulk Modulus, I encountered a doubt. Please consider this thought experiment. I'm considering Caesium as an example as it seems to have a quite low Bulk Modulus (comparatively) of 1.6 GPa. Let's say I apply a pressure of X GPa. Volume change ratio can be given by...

Hello, natural frequencies of (circular) membrane are expressed in every textbook as: where is the m-th positive root of the Bessel Function of the first kind of order n. For m=1, n=0: ξmn = 2,405. represents the radius of membrane, and is the velocity of wave propagation...

Homework Statement If ##\text{arg}(w)=\frac{\pi}{4}## and ##|w\cdot \bar{w}|=20##, then what is ##w## of the form ##a+bi##. Homework EquationsThe Attempt at a Solution The only way for the argument of ##w## to be ##\frac{\pi}{4}## is when ##a+bi## where ##a=b \in \mathbb{Z}## right?

Hi all I was hoping someone could help explain the difference between Young's Modulus and Second Moment of Area. I know that Young's modulus is a measure of how elastic a material is and is calculated by Stress/Strain. I know that the Second Moment of Area can be defined as a objects...

Homework Statement A diver stands (80kg) at the end of a diving board, causing the board to dip 10cm. The board has a width of 34cm and a height of 6cm. If the shear modulus of the board is 2x10^6pa, what is the length of the board? (Ans: 5.2m) Homework Equations [/B] F/A=S⋅Δx/h The...

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...

Homework Statement Homework Equations Path difference is nλ at maxima, (n+0.5)λ at minima The Attempt at a Solution I think the phase difference between S1 and S2 is not 0 anymore, because the wave effectively takes a longer distance by going through S2. Thus, there is no longer a central...

Dear Everyone, I am currently in an Introduction to Complex Analysis; I have a question: Use established properties of moduli to show that when $\left|{z_3}\right|\ne\left|{z_4}\right|$: $\frac{\Re{({z}_{1}+{z}_{2})}}{\left|{z}_{3}+{z}_{4}\right|}\le\frac{\left| {z}_{1} \right|+\left|...

Hello everyone! I'd like to know if it's possible to solve an equation with a modulus like this one : $$ ( \frac{200}{15x}) mod 2 = 0 $$ Thanks in advance. Regards!

(apologies for re-posting, I am unable to find my original thread.) A material which has a Young's modulus of elasticity of 250 GN m-2 and a poisons ratio of 0.32, calculate: (a) the bulk modulus of the material 
 Relevant equation, K=E/3(1-2v) Inputting our known values...

Homework Statement Is that possible to obtain the a relationship between Young's modulus of a spring and impulse force with below information ? I personally think that we cannot if without the given cross-sectional area A and the given spring constant k. The particle is connect to a elastic...

I need to calculate Young's modulus based on deformation of sphere into ellipsoid. I assume the deforming force acting along one axes. Initial dimensions of the object before (sphere) and after (ellipsoid) deformation are known.Does anyone know or familiar with good reference?

Hello everyone, nice to be here. I am going to calculate the young modulus of 3 layers of carbon fiber laminar composite For example: 1st: 12K plain wave carbon fiber in 0 degree 2nd:3K till wave carbon fiber in 45deg 3rd:12K plain wave carbon fiber in 0 degree How can I approach to calculate...

Homework Statement if z=(x-iy)/(x+iy) then modulus of z is : Homework EquationsThe Attempt at a Solution (x-iy)/(x+iy)= (x2-y2-2x(iy))/(x2+y2) i can't get the real part and the imaginary part to take the modulus : but the answer in any way could be = 1 ? the answer in the book is 1 .

Homework Statement Homework EquationsThe Attempt at a Solution Y = (F/A)/(∆L/L) = FL/A∆L Putting values of F , L , A and simplifying Y = 2×109/∆L I don't know how to proceed . I also don't understand what is uncertainty in length and uncertainty in strain . Is uncertainty the same thing...

To start with, we need to realize that each modulus function will be defined differently depending on the value of $\displaystyle \begin{align*} x \end{align*}$. Notice that $\displaystyle \begin{align*} \left| x - 4 \right| = \begin{cases} x - 4 \textrm{ if } x \geq 4 \\ 4 - x \textrm{...

Q: Calculate the force (in N) a piano tuner applies to stretch a steel piano wire 8.50 mm, if the wire is originally 0.850 mm in diameter and 1.35 m long. (Young's modulus for steel is 20.0 ✕ 1010 Pa.) Work F=Y*A*change in L/L_0 I have no idea what is L_0 and L_f? Please help me.

Suppose that f is analytic on the disc $\vert{z}\vert<1$ and satisfies $\vert{f(z)}\vert\le{M}$ if $\vert{z}\vert<1$. If $f(\alpha)=0$ for some $\alpha, \vert{\alpha}\vert<1$. Show that, $$\vert{f(z)}\vert\le{M\vert{\frac{z-\alpha}{1-\overline{\alpha}z}}\vert}$$ What I have: Let...

Homework Statement The picture below. Homework Equations cos2x=1-2sinx sin2x= 2sinxcosxThe Attempt at a Solution I got the modulus by using the Pythagoras theorem which is 2sin theta But I faced difficulty to find the argument. I have no idea why i end up with tan a (alpha) = cot theta which...

I am searching for a shortcut in the calculation of a proof. The question is as follows: 2.12 Prove that: $$|z_1|+|z_2| = |\frac{z_1+z_2}{2}-u|+|\frac{z_1+z_2}{2}+u|$$ where $z_1,z_2$ are two complex numbers and $u=\sqrt{z_1z_2}$. I thought of showing that the squares of both sides of the...

I have a question regarding finding the Young’s modulus of a rod by loading a weight to the end and measuring the change in displacement. The experiment is part of my advanced higher physics project on Young’s modulus however it is the only experiment that I’m doing that the book “Tyler” does...

Homework Statement For the expression $$r = \frac{i\kappa\sinh(\alpha L)}{\alpha\cosh(\alpha L)-i\delta\sinh(\alpha L)} \tag{1}$$ Where ##\alpha=\sqrt{\kappa^{2}-\delta^{2}}##, I want to show that: $$\left|r\right|^{2} = \left|\frac{i\kappa\sinh(\alpha L)}{\alpha\cosh(\alpha...

Which modulus define a property of fluids?? The above mentioned question was asked in my college internals. The answer they suggested was sheer modulus. Any explanations??

Homework Statement Hi guys, i came across a paper about an Investigation of pencil-lead breaks as acoustic Emission sources by Markus G.R. Sause (it's downloadable everywhere). The Setup of the Experiment can be seen in the Picture i attached. Now the Problem i have is to find the correct...

Hi, I'm afraid I not very good at these questions just yet and would like a walk through a bit better than the one I was given by my tutors. Thank you, please refer to the inline image.

Homework Statement A specimen tested in a simple torsion testing machine , the specimen was 12.5mm in diameter and the angles were read over a gauge length of 0.75m Determine the modulus of rigidity of the material taking the torque T as 4.5Nm and the angle of twist as 4.0 degrees Homework...

Homework Statement Homework EquationsThe Attempt at a Solution [/B] A) Mean velocity is defined as <v> = total distance traveled/ total time taken = πR/Γ = 0.5 m/s B) How is part a) different from part b)? I think what Irodov means by mean velocity is mean speed in part a. It is mean...

Just want clarification on two equations. So basically, I want to calculate the time period T of the complete oscillation of a cantilever. I use this equation. Is E equal to young's modulus or is it equal to stiffness? If it is equal to stiffness, can I use this equation to calculate the...

My Aim is to determine the youngs modulus of aluminium from the data we get from tensile strength test. The attached excel sheet contains all the data i am using such as elongation,load value(which is in kN i have converted to N for calculating Stress) For stress, I am using the formula...

Homework Statement If a metal is adhered to a surface of another metal, let's say copper is plated onto aluminum, how can the elastic modulus of copper can be extracted given only the data of the thickness of the copper and aluminum, the young's modulus of the combined metal and the modulus of...

Is it true for all material that if young's modulus is high then melting point will be high and coeff of thermal expansion will be lower? Any example that doesn't follow the above statement. Many Thanks

Homework Statement Let ##f(z) = ze^z## be bounded in the region where ## |z| \leq 2##, ##Im(z) \geq 0##, and ##Re(z) \geq 0## Where does it achieve it's maximum modulus and what is that maximum modulus? Homework Equations N/A The Attempt at a Solution A theorem states that any function...

Homework Statement hi guys I am conducting an experiment for my coursework in physics and i have come across a bit of a problem. i am trying to calculate the youngs modulus of 3 different metals Aluminium steel and brass. To calculate the modulus of the material i am using a chart of Mass k/g...

Homework Statement I'm doing an experiment to determine the young's modulus involving the following equation: Homework Equations The Attempt at a Solution Finding the base units of the young's modulus with the equation resulted in the young's modulus being dimensionless, which of course is...

Homework Statement Using the equations, show the bulk modulus is about r^-4. Homework Equations The Attempt at a Solution Tried to plug Uij but it is not same as U. To be honest, I don't know where to start.

Homework Statement Find the modulus and argument of z=((1+2i)^2 * (4-3i)^3) / ((3+4i)^4 * (2-i)^3 Homework Equations mod(z)=sqrt(a^2+b^2) The Attempt at a Solution In order to find the modulus, I have to use the formula below. But I'm struggling with finding out how to put the equation in...

I'm designing a 'thing' for my masters project, which has to be 3D printed. I've designed this in Inventor, but it doesn't have PLA (Polylactic Acid), so I've been using Inventor's PMMA (Perspex) thus far. I want to get more accurate figures, so I've had a 1 cm3 block printed to get an exact...

The co-ordinates of two points are A(4,-1) and B(7, -5) The line L1: 3x+4y−12 = is perpendicular to AB. (a) Find, in terms of k, the distance between the point P (10, k) and the line L2 (b) P(10, k) is on a bisector of the angles between the lines L1 and L2 and L2 :5x+12y−20 =0...

So I'm trying to understand how the modulus works in metals. I understand that when the temperature rises, that means that the modulus decreases. But I do not understand exactly what it is or how it affects the way that the molecules would vibrate for instance, as kinetic sound energy moved...

Homework Statement [/B] So in my mechanics of materials lab, we calculated Young's modulus after measuring the strain and applying force to a beam. What I'm trying to figure out is, why are you able to use both a bending force and an axial force when calculating Young's modulus? Homework...

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...

Homework Statement A particle mass m moves in a straight line on a smooth horizontal table, and is connected to two points A and B by light elastic springs of natural lengths 2l_{o} and 3l_{o} , respectively, and modulus of elasticity λ . The points A and B are a distance 6l_{o}...

Homework Statement Homework EquationsThe Attempt at a Solution The shaded area is a triangle so the area of a triangle for this particular graph is this: 0.5 (Stress)(Strain) which gives: 0.5(F/A)(e/L) so the top would give work done and the bottom would give volume but we're still left...

Homework Statement A material is formed into a solid sphere and has a diameter of 100mm when at a pressure of 2MPa. If the diameter of the sphere reduces by 0.1mm when the pressure is increased to 6MPa, determine the bulk modulus of the material Homework Equations K=− Δp/ΔV/V0 (Δp is pressure...

Young's Modulus is usually defined as the intrinsic property of a material indicating it's stiffness, or it's ability to resist deformation. Though, it is measured in Pa, meaning it should have some statistical description. Spring constant, for example, can be define as the stiffness of an item...

I have read that Young's Modulus, like spring constant, is a measure of stiffness (how hard it is to deform a material). Though apparently, Young's Modulus is a way of doing so that applies only to the material and not its shape, where a spring constant value depends on the dimensions of the...

let equation 1: x % n1 = 0, equation 2: x % n2 =1, where n1 and n2 are known positive integers, any multiple of n1 will solve eqn1 and any multiple of n2 (and adding 1 to the multiple) will solve eqn2, but is there a short way to simultaneously solve the two equations to find x instead of...