Modulus Definition and 612 Threads

Hello, I would like to compare rods made of different materials based on the amount of force or stress they would generate when fixed at both ends. normally, I would just compare the product of the coefficient of thermal expansion ( \Alpha ), change in temperature ( \Delta T ) and modulus (E)...

We know that youngs modulus(E) is stress/strain. In case of free body thermal expansion, if the material is allowed to expand and contract freely, than there are no stresses in the body. The body has only strains. That means the stresses are zero in case of free expansion. So in this case...

Homework Statement It is just a line of equation from my Stat Mech textbook, that says B = -V(dp)/(dV) = (10U)/(9V) = (2nEf)/3 where B is the bulk modulus, V is the volume, p is the pressure, U is the energy, n is the number per unit volume and Ef is the fermi energy. Homework...

How to calculate Young's Modulus on trapezoidal shape ? Can't find the answer... Hi guys. I'm really stumbling over this question. If I'm trying to calculate the Young's modulus of a specimen that is being compressed from the top, but the contact area on top is smaller than the bottom...

Homework Statement The radius of a rod is 0.146 cm, the length of aluminum part is 1.2 m and of the copper part is 2.76 m. The rods are connected. Determine the elongation of the rod if it is under a tension of 3140 N. Young’s modulus for aluminum is 7 × 1010 Pa and for copper 1.1 × 1011 Pa...

Homework Statement A student bumps into a tray of jello. The lime jello is jiggling side to side faster than the orange jello. Both jellos have the same spatial dimensions. Which statement is true? Answer: Lime jello has a higher shear modulus than orange jello Homework Equations...

I am wondering if there is a way to solve the following: (Chinese Remainder Theorem does not apply) n == a mod(m) m == b mod(r) n == x mod(r), I need to know x, without dealing with a gigantic number(n), I can find a and b, as I chose m to give me predictable results. I appreciate any...

I'm trying to figure out how to calculate the modulus of elasticity for a board clamped to a surface plate at one end and free-floating on the other. I've measured the deflection with a 1k weight at the free end of the board. So I've got that data as well as the dimensions of the free-hanging...

I am wondering if there is a way to solve the following: n == a mod(m) m == b mod(r) n == x mod(r), I need to know x, without dealing with a gigantic number(n), I can find a and b, as I chose m to give me predictable results. I appreciate any insight...

Homework Statement Let f and g be two holomorphic functions in the unit disc D1 = {z : |z| < 1}, continuous in D1, which do not vanish for any value of z in the closure of D1. Assume that |f(z)| = |g(z)| for every z in the boundary of D1 and moreover f(1) = g(1). Prove that f and g are the...

Homework Statement Let f(z) = u(x,y) + iv(x,y) be a continuous, non-constant function that is analytic on some closed bounded region R. Prove that the component function u(x,y) reaches a minimum value on the boundary of R. The Attempt at a Solution By the minimum modulus principle...

Homework Statement Calculate the deflection at the end of a rod whose dimensions are 1m x 0.1m x 0.1m, when a load of 100N is applied. The modulus of elasticity is given as 1 x 1011 (N/m2) Homework Equations d = PL/AE where d = end deflection of bar in metres (in m) P = the applied...

Complex Analysis: Maximum Modulus Principle Homework Statement Let f(z)=u(x,y)+iv(x,y) be a function that is continuous on a closed bounded region R and analytic and not constant throughout the interior of R. Prove that the component function u(x,y) has a minimum value in R which occurs on...

I have started a home study course in mechanical engineering, I now realize that I should have started with a math’s course but any way I have a question that I could do with some help with. A designer wishes to calculate the thickness (diameter) of a steel cable for suspending a passenger lift...

Homework Statement We have a problem that basically defines an operator [·] (it's a dot inside a box) as a[·]b = (a·b) mod 6 where a, b ε ℕ. Is this operator associative? Homework Equations a[·]b = (a·b) mod 6 I tried looking for any modulus identities online but didn't have any...

Homework Statement Lets say a wire has Youngs modulus Y, Initial length L area A and is supporting some external load/force of magnitude F...its extension is dl..We say that the Potential energy of wire is 1/2(YA/L)(dl2)...But i am having a problen with the energy changes... Homework...

Young's modulus question... Homework Statement A sphere of radius 10 cm and mass 25 kg is attached to the lower ends of a steel wire which is suspended from the ceiling of a room. the point of the support is 521 cm above the floor. When the sphere is set swinging as a simple pendulum, its...

Bulk modulus question...please help Homework Statement What is the change in density of water in a lake at a depth of 400 m below the surface? The density of water at the surface is 1030 kg/m3 and bulk modulus of water is 2*109 Nm2 Homework Equations For fluid New Density= Initial...

Note: This is a laboration assignment. Homework Statement I want to theoretically determine the frequencies of the standing waves that occurs in a Chau gong when exposing it to a camera flash (Nikon sb-900) from a given distance. These shall then be compared to the frequencies obtained from...

This is a homework problem and I thought about putting it in the homework section bu since its very materials science specific I decided to put it here: For a transversely isotropic material, the “plane strain bulk modulus”, K23, is an engineering constant that is defined by the stress...

Homework Statement a hydraulic system operates at 3000 psi. Compute the percentage change in the volume of the oil in the system as the pressure is increased from zero to 3000 psi if the bulk modulus of the oil is 189000 psi.Homework Equations E=∆p/(∆V)/V The Attempt at a Solution 189 000 psi...

Homework Statement Suppose z is complex number with |z| = 1 (also assume that z is not 1 + 0*i) Let z = a + b*i where a and b are real numbers. Find a real parameter, t, such that z = (t-i)/(t+i), where i = sqrt(-1) Homework Equations |z| = sqrt(a^2+b^2) The Attempt at...

Hi, I am trying to do the multipole expansion of a point charge away from the origin, I can't understand Legendre polynomials so want to do it in Cartesian but when I try to Taylor expand the \left|\frac{1}{\vec{r}-\vec{r'}}\right| I am not sure how to handle the modulus. Any help...

out of interest does cross sectional area change when a force is applied (lets say I had a wire and I applied a force to it, the wire would stretch ) does its cross sectional area change

Homework Statement Two different materials are being considered for a safety pad below a swing. Material 1 has a Young's Modulus twice that of Material 2. Which should be chosen? A. Material 2, because the length over which the impact force acts is larger, resulting in a lower average...

Homework Statement hi there! I am new to this forum and was just wondering if anyone could help with this question on percentage uncertainty. I am supposed to find the percentage uncertainty in d^3 the info given is mass attached to the end of a strip= 0.1...

Where, on the internet, can one learn the method to solving equations modulus a number? I'd like to learn the method for finding such relations as this special case for the Erdos-Straus Conjecture, with n ≡ 2 (mod 3). Also, what is the technical name for finding the mod n relations in an...

Homework Statement A 30kg sledge hammer strikes a steel spike of 2.30 cm diameter while moving at 20.9 cm/s. The hammer rebounds with a speed of 10.0 cm/s after 0.110 s. What is the average strain in the spike during impact? Mass of hammer = 30 kg Radius of Spike = 1.15 cm or 0.0115m...

Homework Statement My prof was saying today that the modulus of a complex number isn't the absolute value. The problem is the following: Graph the set of points satisfying the following equation(s): |z-1+i|=1 The Attempt at a Solution Can I not just say that z = -i or z = 2-i...

Got exams in January so just want to make sure I am correct the questions read exactly like this a) The sample of copper wire reached its elastic limit when the stress is 1.4x10^8 Pa and the strain is 0.035 Calculate the Young's Modulus for copper. My attempt is Y= Stress/Strain => Y=...

I am trying to do this integral \int_{-\infty}^{\infty}\frac{e^{-a| \vec{r}|}e^{-\vec{b}. \vec{r}}}{|\vec{r}|} But if I write the modulus as \vec{r}=\sqrt{x^{2}+y^{2}+z^{2}} I can't figure out how to handle the annoying square root in the exponential. Would be grateful for hints, thanks...

I need to figure out the value for d in this equation, but because the numbers are large, I don't know how. (d)(13) mod (2436) = 1. d times 13 mod 2436 should be equal to 1. Is there a process I can use to find out the value of d.

Does anyone have a recommendation for a paper/source for data relating distance modulus and redshift data over a large range of redshift, such as 0 < z <= 5? I have found that combining data from different publications can be difficult given the variety of ways that distance modulus can be...

Hi, Is this right? (p+a(n/v)2)(V-nb)=nRT Just differentiate both sides with respect to P? If I do that I get 0=V+P*(dV/dP)t-nb-(an2)/V2*(dV/dP)t+2abn3/V3*(dV/dP)t (dV/dP)t=(nb-V) / (P-n2a/V+2an3ab/V3) And now to calculate the bulk modulus: kt=-1/V*(dV/dP)t = -1/V *...

Hi! Could anybody, please, tell me: whether |Cos(theta)|*Cos(theta) = Cos^(theta) , because it means that only positive values of Cos(theta) are taken. Am I right?:shy:

Hi! Could anybody, please, help me with integrate this: Integrate[ (|x| / x) dx] Thank you:)

Homework Statement If you have two materials of equal length and radius and then you join them together. Material 1 young's modulus = y1 material 2 young's modulus = y2 Homework Equations F/a = y Lchange / Lo The Attempt at a Solution Given they are of the same length and radius...

Homework Statement A mass of 225 kg is hung from a metal cable of length 1.60m and diameter 8.20mm. This causes the cable to stretch by an amount 0.668mm. Calculate the Elastic Modulus of the metal. Homework Equations E=(F/A)/(change L / orig L) The Attempt at a Solution F =...

Homework Statement Find all monic polynomials of degrees 2 and 3 in (Z/2Z)[x]. Determine which ones are irreducible, and write the others as products of irreducible factors. The Attempt at a Solution I know that factors of degree 1 correspond to roots in Z/2Z and that monic...

Hi, does higher young modulus means higher rigidity of a solide? Regards,

Homework Statement http://www.facebook.com/photo.php?fbid=1612917330439&set=a.1250823718325.2039017.1461460506&ref=fbx_album" The Attempt at a Solution I don't want to ask about the full solution for this thing, but only one thing: in that expression, which is the kinetic energy and...

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...

Homework Statement Dear Yahoo Answers, Can someone please help me with this as it's driving me crazy! We had to complete an experiment where had to calculate the Young’s modulus of Rubber, by doing an experiment. So we used a rubber band and various weights to calculate the values, to...

Homework Statement Show that the adiabatic bulk modulus of a free electron gas can be given by B= \frac{2nE_{F}}{3} where n-number density E_{F} -Fermi energy Homework Equations I started with the adiabatic bulk for an ideal gas K=\gamma P where...

Homework Statement A mass of 13.0 , fastened to the end of an aluminum wire with an unstretched length of 0.50 is whirled in a vertical circle with a constant angular speed of 130 . The cross-sectional area of the wire is 1.3×10−2 . The Young's modulus for aluminum is Pa.Calculate the...

I have to solve the equation: |12x -9| = |3 -4x| +2x -1 I was wondering if it's supposed to be like: 12x -9 = 3 -4x +2x -1 and -12x +9 = 3 -4x +2x -1 ? Or am I supposed to consider the positive and negative of 3 -4x also? I didn't attend lessons for this and I know little about modulus...

Homework Statement A particle of mass m is attached to one end of a light elastic string of natural length a and modulus mg, the other end of the sting is attached to a fixed point O on smooth horizontal surface. The particle is released from rest at horizontal distance a+L from O...

Homework Statement A suspension wire is given and the problem is to find out it's rigidity modulus. Say the wire is of length 'l' and a mass 'm' is suspended with the help of the wire. Homework Equations All i know is Young's modulus or 'Y' is Y=stress\strain The Attempt at a...

Hi all. I am now working on the uniaxial cold drawing on the plastic sheet (polybutylene succinate, a semicrystalline polymer). After uniaxial cold drawing, as expected, strength increased along the drawing direction/ machine direction (MD). Strength and elongation at break drastically...

Hi guys, Homework Statement how do i solve (or approximate if not solvable) this integral \int\int e^{-\alpha(|\vec{r}_1-\vec{r}_2|-r_0)^2} d^3\vec{r}_1 d^3\vec{r}_2 \alpha>0 Homework Equations none The Attempt at a Solution none