Modulus Definition and 583 Threads

The bulk modulus B = - V (∂P/∂V). At constant temperature the pressure is given by P= -∂U/∂V, where U is the total energy. We can write B in terms of the energy per particle u = U/N and volume per particle v = V/N : B = v...

Homework Statement A hanging wire made of an alloy of titanium with diameter 0.5cm is initially 6m long. When a 60kg mass is hung from it, the wire stretches an amount 1.44cm. A mole of titanium has a mass of 48g, and its density is...

Hi all I need to find the relative stiffnes of certain I beams from here http://tsbluebook.steel-sci.org/EN/Browsers/Main.htm Im assuming all I need to do times the Youngs Modulus by the 2nd Moment of Area In my head I am making it more complicated than it should be so I hope this is all it...

Homework Statement Dear Mentors and PF helpers, I saw this question on a book but couldn't understand one part of it. Here the question: Solve the following inequality I copied the solution as belowHomework Equations The Attempt at a Solution I don't understand why the numerator in step...

Hey Guys, I am new to the forums but have seen you guys help a lot with pointing people in the right direction. Here is my problem: A Cylinder with a Volume of 8000m3 has a pressure of 80MPa, Bulk Modulus of 74 MPa. I need to calculate the Young s modulus and determine the material type. So...

Hello- I am running a simulation of a simple brazed copper assembly; brazed at 1050°C. I believe the Young's Modulus will drastically change after brazing at this temperature since the annealed state is "dead soft". My analyst colleague is using an annealed value for E of 15E-6 psi, which...

Homework Statement 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 (b) the shear modulus of the material. Homework Equations E=3(1−2ν)K 3. The Attempt at a Solution a) E = 3(1−2ν)K K = E /...

Homework Statement Estimate the value for Youngs Modulus from the two following graphs: Graph 1: Plot a graph of depression in metres (D) against load in kilograms (M) Graph 2: Plot a graph of log_10(D) against log_10 of Length of cantilever. Homework Equations [/B] D = 4*L^3*m*g / Y*a*b^3...

Homework Statement A rod is made up as shown [pic attached] Both have same cross-sectional area. Ep and En are Young modulus. The rod breaks when total extension = 3.0mm Greatest tensile stress that can be applied before rod breaks? Homework Equations Young modulus = stress / strain The...

There is an experiment to determine the Young's Modulus of the wood which involves bending it. The equation used to calculate it is like this E=WX3/4ZDY3 Where D=amount of bending W=force (N) which causes the bending Z=width of the wood Y=thickness of the wood X=horizontal distance between the...

Homework Statement Fermats little theorem states that ##a^{P-1} \mod P = 1 \mid ## a is coprime to P Now I'm trying to solve this equation with the help of above theorem, But I'm ending up with wrong result ##2^{133} \mod 133## Homework Equations ##a^{P-1} \mod P = 1## ##(A \times B) \mod n...

Homework Statement Q. How to find Remainder of the following expression ##32^{32^{32}}\mod{}6=?## Homework Equations The Attempt at a Solution ##32^{32}\mod{}2=0 \implies 32^{32}=2x## ##32^{32}\mod{}3=1 \implies 32^{32}=3y+1## would it help to find the remainder of ##32^{32^{32}}\mod{}6##

How to prove: $\int_{0}^{\frac{\pi }{2}} {\frac{\sin \theta}{\sqrt{Z^2+(R+h \tan \theta)^2}} K[k(\theta)]}=\frac{\pi }{2\sqrt{R^2 + (h+Z)^2}} $ where \[ k(\theta)=\sqrt\frac{4Rh \tan \theta}{Z^2+(R+h \tan \theta)^2}\] and $ K[k(\theta)] $ is the complete elliptic integral of the first kind...

Hi, I have some experimental data and I am interested to use this data to calculated modulus of elasticiy (young's modulus) and Poisson's ratio. The material for which the data is given in an anisotropic material, therefore I need to calculate modulus of elasticity and poisson's ration is x,y...

Hi, I have some experimental data and I am interested to use this data to calculated modulus of elasticiy (young's modulus) and Poisson's ratio. The material for which the data is given in an anisotropic material, therefore I need to calculate modulus of elasticity and poisson's ration is x,y...

Homework Statement Glass fibres in Nylon provide reinforcement. Young's modulus of glass fibre is 72.4GPa; Young's modulus of Nylon is 2.8GPa. If the Nylon contains 30% by volume glass fibres, what fraction of the force applied parallel to the fibre axis is carried by the glass fibre? (Assume...

I'm studying elasticity right now in my chemistry class, and I'm confused as to what exactly tensile stress (and maybe compression stress too ) might mean. It's given in N/m^2. And you're stretching the material. Is the cypher I'm given indicative of what's happening only one side? Indicative...

Isn't it amusing ?What could be the probable explanation for this?Also when operated by division operator gives the rest of the number as the quotient (Note only when the divisor is 10)

Homework Statement Grade 1020 Steel has a yield strength of 42ksi and E modulus of 30 mpsi. Another grade of steel has yield strength 132 ksi. What is its E modulus? Homework Equations E=FL/EA This is the equation i should be using to find e modulus I thing The Attempt at a Solution I don't...

Hi, I'm wondering if someone can point me in the right direction with this question. A material has a modulus of rigidity of 100 GNm-2 and a Young's Modulus of 250 GNm-2. Calculate the expected value of Poisson's Ratio for the material. Poisson's Ratio is expressed as transverse strain / axial...

Hello, I have the point ##-1 + 2i##, for which I am asked to find the modulus and argument. The modulus was simple enough, but I am having difficulty finding the angle. The point is located in the 4th quadrant, and so I need to make certain that I calculate an angle in the range ##(\frac{3...

Homework Statement Estimate the density of the water 5.3km deep in the sea. (bulk modulus for water is B=2.0×109N/m2.) Homework Equations P = F/A = Dgh The Attempt at a Solution I don't even know how to go about starting this one. Can someone point me in the right direction?

I understand that the dynamic modulus of a material is measured by inducing a sinusoidal force and measuring the strain response. Usually one gets a value for the storage and loss modulus. However, I don't understand how one would "quantify" how viscous a material is. I know a viscous material...

Does Young's Modulus change with drastic changes in size? For example, suppose you exert a force on the micro scale or maybe even the nano scale. Would the same Young's modulus uphold at such a small scale?

Homework Statement \begin{pmatrix} 5 & 8\\ 17 & 3\\ \end{pmatrix} The matrix given above is matrix A and I am trying to find A-1 mod 26 = ?Homework Equations ax+by = cThe Attempt at a Solution Well first I found the det of A which is -121 and then took -121 modulus of 26 which gave me 9. Did...

A rubber sheet (thickness 0.2mm) was mounted in an open-type Ussing chamber (6mm aperture) such that hydrostatic pressure could be applied to one side and the resulting inflation of the membrane tracked with an OCT instrument (OCT: ocular coherence tomography). From the geometry of the membrane...

I can understand the derivation of bulk modulus (K) for isotropic material. However I have difficulty to do the same for anisotropic material. to start with we have the definition: mean_stress = K * (strain_xx+strain_yy+strain_zz) My question is for anisotropic material: Is mean_stress =...

Hi guys I am looking for a dataset to use in my thesis. I am working on UNION 2.1 sample of supernovea Ia data. That dataset consist of redshift and distance modulus with uncertainty (sigma) for 590 supernovea. Do you guys know where can i find similar dataset for GRBs?

Proof that \lim_{x→p} \frac {f(x)}{x - p} = 0 \Leftrightarrow \lim_{x \rightarrow p} \frac{f(x)}{\left | x - p\right |} = 0 Relevant equations I think there is a useful theorem here, the conservation of signal: Suppose that \lim_{x\rightarrow p} f(x) = L ; L > 0 ; \forall \varepsilon...

Homework Statement A solid sphere of brass (bulk modulus of 14.0*10^10 N/m^2) with a diameter of 3.00 m is thrown into the ocean. By how much does the diameter of the sphere decrease as it sings to a depth of 1.0 km? Homework Equations Gauge pressure = density(water)*g*h Bulk...

Hi, I'm doing an IB extended essay in physics (like a 4000 word investigation) and I'm looking to do it on Young's modulus- in particular perhaps how temperature effects it. Is this legit? Like does temperature have a significant effect, in such a way that if young's modulus decreased with...

Homework Statement Why is there such a large difference between the elastic moduli of metals and polymers? Homework Equations The Attempt at a Solution I am thinking because of the different bonding between metals and polymers. Since metals have metallic bonding and polymers...

Hi pals, I am looking to find a modulus calculation using my casio fx-991 ms calculator i know how to find modulus using small numbers eg: 7 mod 3 = 1. This because 7 = 3(2) + 1, in which 1 is the remainder. To do this process on a simple calculator do the following: Take the dividend...

I was thinking... if the modulus of a vector can be calculated by ##\sqrt{\vec{v} \cdot \vec{v}}##, thus the modulus of a tensor (of rank 2) wouldn't be ##\sqrt{\mathbf{T}:\mathbf{T}}## ?

If I have a composite beam or an T beam where the top of the T is of significantly higher stiffness than the vertical part. is it true that the further a stiffness material is from the neutral axis the greater the effect on the overall stiffness is? is it possible to calculate a new flexural...

Homework Statement For any integers a and b and any positive integers k and j, if ##a \equiv 2-b \pmod{k}## and ##j \mid k##, then ##a^2 + 4b - b^2 \equiv 4 \pmod{j}## Homework Equations ##x \equiv y\pmod{q}## then q|x-y The Attempt at a Solution At first I thought this would...

I'm learning about Hooke's law and modulus of elasticity (also known as youngs modulus) but it seems I am being taught it differently in maths and physics. In maths I am taught that T=λx/l and λ is the modulus of elasticity, measured in Newtons. In physics I am taught that T=λAx/l where λ is...

How would I compute the following integral? Let t be in [0,1]. $\int_{0}^{t}|s-t|\,ds$

Homework Statement I want to know the section modulus for a beam which has a UDL of 13.5 kn/m across 10 metres. Its simply supported at both ends. max allowable stress = 255 MPa Homework Equations Z= M / max allowable stress [cm^3] The Attempt at a Solution max bending...

Homework Statement I carried out an experiment using a extensometer, had a range of values for the elongation and load. I calculated the value from the data and had 11GPa whereas it should be 200GPa. Do you know what could have gone wrong? Thanks a lot.

Homework Statement I don't need to give any information, I just need to know the best way to calculate E from a range of values for load and displacement given the length and diameter. I've calculate it for a few values and the value appears to decrease so I'm not sure where to take the value...

what is the physical meaning of first pressure derivative of bulk modulus at zero pressure. if it is ∂k/∂p, i say how it change with pressure, if it is at zero pressure?

Homework Statement I had a Young's Modulus experiment in lab. Our specimen, which was used, was mild steel. After plotting the graph I realized that there was only one yield point. However, as I read from many sources, there must be two yield points for mild steel(upper and lower). I am pretty...

In my text it's given when a cube underwents a uniform unit tensile force be applied in all six faces, bulk module=1/3(α-2β) Where α is longitudinal strain and β is lateral strain.is there a derviation for it..? And it states in x direction there will be increase in length and in y, z...

Homework Statement Consider a metal bar of initial length L and cross-sectional area A. The Young's modulus of the material of the bar is Y. Find the "spring constant" k of such a bar for low values of tensile strain. Express in terms of Y, L, and A. Homework Equations I know the...

Homework Statement A guitar string of diameter 0.6 mm and length 0.82 m is subject to a tension of 153 N. If the string stretches an amount 0.36 mm, what is Young's modulus of the string? Homework Equations Y=Stress/Strain Stress=F/A Strain=Amount of stress/Original Length The Attempt at a...

basically, i am given a function and told to sketch it. f(x)=abs(x+4) + abs(3-x) i didnt know how to do it, so i used this site ( http://rechneronline.de/function-graphs/ ) it gave this graph with a really weird shape , can anyone explain it?? i tried to google it to find the answer, but i...

Homework Statement When water freezes it expands by about 9.00% What pressure increase would occur inside your automobile engine block if the water in it froze? ( The bulk modulus of ice is 2.00*10^9 N/m^2 Homework Equations Bulk modulus = ΔPressure/(ΔVolume/Initial Volume) The...

Hi all, I am after trying to find the plastic section modulus about both local axes (x & y) after having calculated them for the global axes (n & p). Is there a way I can transform global to local using Morh’s circle to evaluate plastic section properties? Attached is the key diagram I am...

Homework Statement Three separate members of steel, copper and brass are of identical dimensions and are equally loaded axially.Young’s moduli for the materials are: steel, 210,000 N/mm^2 copper, 100,000 N/mm^2 brass, 95,000 N/mm^2 If the steel member stretches 0.13mm, calculate the amount...