Modulus Definition and 583 Threads

Homework Statement Find the displacement (mm) in the horizontal direction of point A due to the force, P. P=100kN w1=19mm w2=15mm Homework Equations \tau = G * \gamma \tau = Shear stress = P / A \gamma = Shear strain = (pi / 2) - \alpha The Attempt at a Solution I haven't...

Homework Statement There is a 104kg uniform log hung on two steel wires, A and B, both of radius 1.00mm. Initially, wire A was 2.70m long and 2.00mm shorter than wire B. The log is now horizontal. Note that the centre of gravity (com) is not necessarily centered between the wires and the...

bulk modulus = Δp/ΔV/V Why do we need to divide change in volume by the original volume? why is it important?

I am studying Integer Modulo in my Cryptography and Data Security class. We are dealing with mainly modulo 26 [the alphabet] right now. I understand if it is addition or multiplication you just take the remainder of the result divided by, let's say 26 in this circumstance. ie: (5+25)mod26 = 4...

Homework Statement Find the modulus for: (3 - 4i)^10/(2 - i)^8 Homework Equations The Attempt at a Solution I tried putting the two terms in their exponential forms. Then do simple exponential operations and convert back to cartesian form to get the modulus. 3 - 4i =...

Homework Statement How much force is required to punch a hole ½ in. in diameter from a 1/8 in. thick steel sheet of shearing strength 4x10^4 psi. Homework Equations Shearing Modulus = Shearing Stress / Shearing Strain Shearing Stress = F/A Shearing Strain = S/L S = Length...

I am reading through some calculations in a book that refer to an average shear modulus of steel (19700)... they give no units and it has completely thrown me off track while following through the calcs can anybody help? I know the unit is imperial and if i convert some of the other units...

Homework Statement A rock at the surface has a density of 2600kg(m^(-3) 90000m down its density is 3100kg(m^(-3) Change in pressure at the depth is due to hydrostatic pressure. Whats the bulk modulus of the rock? Homework Equations Δp=p + ƿgh Δp=-B(ΔV/V) The Attempt at a...

Homework Statement how would I draw the graph f(x) = ln|3x-6| Homework Equations NONE The Attempt at a Solution So I know that the graph ln(3x-6) would be a transformation of ln(x) 6 units to the right and the stretch by scale factor (1/3) along the x-axis (i.e: divide all x...

Question: Why is it not sensible to calculate the Young's modulus of the material (steel) when the experiments was conducted? But I thought it should be possible to calculate the Young's modulus after plotting the stress/strain curve. Young's modulus can be found by finding the gradient of...

help! can someone explain to me the effect of long term oven aging on resilient modulus of ACW28

Homework Statement integrate modulus of xcos∏x within the limits -1 to 1/2 P.S I'm not allowed to use acaluculator so graphing and finding out the answer not possible Homework Equations it's using the property of definite integral ∫f(x) dx within the limit from a to b = ∫f(x) dx...

Homework Statement How much force is required to punch a hole 1/2 inch in diameter from a 1/8 inch thick sheet of steel with a shearing strength of 4x10^4 PSI? Homework Equations Formula goes like this Shearing Modulus = (Force/Area) / (Shearing Length/Length to be sheared)...

I am trying to understand what the formula v=sq rt( Bulk Modulus/density). I understand that Bulk Modulus is indicative of a Pressure force and shows how much an object resists being compressed. So if we take a solid, it will have a greater Bulk Modulus than a liquid and so sound will travel...

Homework Statement Two bars, one composed of aluminum and one of steel are place end to end as shown in Figure P11.60. The bars are both initially of length L = 24 cm, and both have a square cross section with h = 3.9 cm. If a compressive force of F = 8440 N is applied to each end, find the...

Sorry for posting two threads, these question are kind of related. i just don't understand something important here:The definition of the Maximum Principle, as given in Gamelin's "Complex Analysis", p. 88: Maximum Principle. Let h(z) be a complex-valued harmonic function on a bounded domain D...

Homework Statement Give an example to show that the modulus rule cannot be reversed. Hence give an example of a divergent sequence (a_{n}) such that (|a_{n}|) is convergent.Homework Equations The modulus rule is; "Let a_{n} be a convergent sequence. (|a_{n}|) is convergent, then lim|a_{n}|...

Does youngs modulus of elasticity depend upon temperature?

Why is it that materials with a higher bulk modulus value allow for sound waves to propagate through them faster? A material with a high bulk modulus requires a relative greater increase in pressure to contract by the same volume as a material with a lower bulk modulus, and as such sound waves...

Homework Statement Find the maximum of \left|f\right| on the disc of radius 1 in the Complex Plane, for f(z)=3-\left|z\right|^{2} Homework Equations The maximum modulus principle? The Attempt at a Solution Since |z| is a real number, then surely the maximum must be 3 when z=0...

Hey guys, Really basic question, how do I find the tensile modulus E11 from a set of data? Let the data be: stress(GPa) 0.050 0.300 0.454 0.800 strain(mm/mm) 0.002 0.0025 0.004 0.0087 I know how to find young modulus E=strain / stress When finding E...

Homework Statement Calculate the stress in a wire of diameter 0.35mm when the tension in the wire is 50N. Homework Equations Stress=F/A The Attempt at a Solution 0.25/2=0.125 0.125/100=1.25x10"-3 Pi x 0.00125"2 = 1.542x10"-5 50/1.542x10"-5 = 3242542.153 Pa Are my...

My lecturer gave this problem as an exercise: http://img839.imageshack.us/img839/2405/imagewys.jpg Uploaded with ImageShack.us I attempted to use the Maximum Modulus Principle to solve this problem but failed. Any helps/suggestions are thankfully welcome.

Homework Statement Question simply asks to calculate the Youngs modulus. I've attached the question. Homework Equations Youngs Modulus = (change in stress)/(change in strain) The Attempt at a Solution okay, what i did was simply find the gradient between each of the points...

Homework Statement Solve \frac{|x^2-5x+4|}{|x^2-4|}\le1 Homework Equations The Attempt at a Solution as |x^2-4|will be positive always cross multiply and take 1 to other side of equation solve by taking LCM we get |x^2-5x+4|-(x^2-4)\le0 on solving we get...

Hello, Quick question on how you would go about calculating this. A grade of steel has the following properties; Tensile strength = 300 N/mm^2 - (not relevant?) Youngs Modulus = 200 GPa Poisson Ratio = 0.3 The grade of steel is 2m long, with a 20mm cross sectional area. It is positioned...

[b]1. | (2-i)(3+2i)(-5-6i)(-7+3i) / (-4+i) | Homework Equations [b]3. I am pretty sure I am not computing it right but this is what i come up with. square root of 5* square root of 13* square root of 61* square root of 58 / square root of 17.

Are ballons mostly made of latex? I suppose the Young's modulus of balloon may be similar to that of latex condom. Thanks a lot.

Homework Statement Question: When water freezes it expands about 9%. What pressure increase would occur inside your automobile engine if the water froze. The bulk modulus of the ice is 2x10⁹N/m². Homework Equations B = - Δp/(ΔV/V) The Attempt at a Solution My 1st solution: Volume...

I have the function: x(\phi) = \left[(\phi - \phi_0)\frac{72~000}{360^\circ} + x_0\right]~\textrm{mod}~72~000 and I'm wondering how to invert it in order to get \phi(x) ? Also, the modulus operator is not exactly what I'm looking for here, because if x goes below 0, I want it to wrap around...

[SIZE="4"]A wire made of a particular material is loaded with a lod of 500 N. The diameter of the wire is 1mm. The length of the wire is 2.5 m, and it stretched 8mm when under load. What is the young modulus of this material? My work E= stress\strain stress= F\A r= d/2 ==>...

Homework Statement There is a structure with four legs. each leg is 6" x 6" square. The bottom of each leg is 6"W x 6"L x 3/4" H. Each leg has a foot which is 4" x 4" x 4". The foot is placed in the center of the leg. The question is how much weight can the legs support before the bottom of...

When plotting a stress against strain graph is this the right equation that fits the form y=mx+c? I got (F/A)=y(dL/L) where F is force A is area y is youngs modulus dL is change in length and L is original length. The Y is F/A. The m is y and x is dL/l (in y=mx) is this correct? Thank you

Homework Statement Here's the question, verbatim; We want to build a pressure using a block of elastic material, where the pressure applied to the top surface is measured by a strain gauge mounted on one of the side walls of the block. The gauge factor of the strain gauge is 2.5. When 1 mm Hg...

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 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...

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...