Modulus Definition and 583 Threads

  1. chwala

    Find the modulus and the argument of ##\dfrac{2}{(4-2i)^2}##

    In my lines i have, ##(4-2i)^2 = (4-2i)(4-2i)## ##r^2 = 4^2 + (-2)^2 = 20## ##r \cos θ = 4## and ##r\sin θ = -2## ##\tan θ =-\dfrac{1}{2}## ##⇒θ = 5.82## radians. Therefore, ##|(4-2i)^2| = \sqrt{20} ×\sqrt{20} = 20## Argument = ##5.82 + 5.82 = 11.64##. also ##|2|## = ##2## and argument =...
  2. M

    Why Is My Argument Calculation for Complex Number Incorrect?

    Question 1: Find the modulus and argument of ##z=-\sin \frac {\pi}{8}-i\cos \frac {\pi}{8}##. The modulus is obviously 1. I can't prove that the argument is ##\frac {-5\pi} {8}##. I think ##\frac {-5\pi} {8}## is not correct ... What I've done: $$\tan \theta=\cot \frac {\pi}{8}$$$$\tan...
  3. P

    I Bounding modulus of complex logarithm times complex power function

    It is claimed that the modulus of ##(\log(z))^jz^\lambda##, where ##j## is a positive integer (or ##0##) and ##\lambda## a complex number, can be bounded above by ##c|z|^l## for some integer ##l## and constant ##c##. Assume we are on the branch ##0\leq \mathrm{arg}(z)<2\pi## (yes, ##0##...
  4. chwala

    Find the modulus and argument of ##\dfrac{z_1}{z_2}##

    π My take; i multiplied by the conjugate of the denominator... $$\dfrac{z_1}{z_2}=\dfrac{2(\cos\dfrac{π}{3}+i \sin \dfrac{π}{3})}{3(\cos\dfrac{π}{6}+i \sin \dfrac{π}{6})}⋅\dfrac{3(\cos\dfrac{π}{6}-i \sin \dfrac{π}{6})}{3(\cos\dfrac{π}{6}-i \sin \dfrac{π}{6})}=\dfrac{2(\cos\dfrac{π}{3}+i \sin...
  5. F

    A Is there a way to convert distance modulus to get H(z) values

    Hello, Everything is in th summary : I have a set of distance modulus and I would like to know if this is possible to convert numerically these values into a Hubble vs redshift H(z) data ( with the standard deviation). Any relation between distance modulus and H(z) are welcome. Regards
  6. Twigg

    A Lame parameter mu = shear modulus derivation (rogue factor of 2)

    Hello, I am trying and failing to derive that the shear modulus ##G## is equal to the Lame parameter ##\mu##. I start with the linear, symmetric, isotropic stress-strain formula: $$\sigma = \lambda \mathrm{tr}(\epsilon) \mathrm{I} + 2\mu \epsilon$$ I then substitute a simple (symmetric) shear...
  7. Nick Goodson

    Calculating Modulus of Resilience: Yield Stress, Yield Strain, E

    Hi, I have a problem, using the 2 different equations for calculating the Modulus of Resilience, I get 2 different answers. It seems simple, but I’m a little perplexed. For the following values: Yield Stress = 1880 MPa Yield Strain = 0.0068 E = 401 GPa [U(r) = (Yield Stress x Yield Strain) /...
  8. V

    Determine equivalent Young's Modulus

    We need to find a single wire supporting the load. But, when I think about it there can so many different types of materials we could use for the single wire and each of these single wires would have a different Young's Modulus. So, I don't get what equivalent means here? Anyways, I get the...
  9. F

    I Modulo and Modulus in math and computer programming

    Hello, I an clear on how the modulo operator ##%##, also called the remainder operator, is used in programming. It gives the remainder of the integer division. For example, ##5 % 2 = 1## because the divisor 2 fits 2 wholly times into the dividend 5 leaving behind a reminder of 1. ## 6% 3 =0##...
  10. brotherbobby

    Solve for ##x## involving modulus

    [FONT=georgia](I could solve the problem but could not make sense of the solution given in the text. Let me put my own solutions below first). [FONT=times new roman]1. Problem Statement : I copy and paste the problem to the right as it appears in the text. 2. My attempt : There are three...
  11. mgong21

    I Derivation of Voigt's Shear Modulus

    How did Voigt derive the average shear modulus of an anisotropic material, G=1/5 (A-B+3C), where 3A=c11+c22+c33, 3B=c12+c13+c23, 3C=c44+c55+c66? The original text is published in German about 100 years ago. I looked for other papers explaining this, but none has explained the derivation. They...
  12. chwala

    Find the set of possible values of ##a## - Modulus Graph

    My interest is on question 9. b(i) Find the question and solution here; I understand that ##a## should be less than ##2## because when ##a=2##, the two equations shall have same gradients which implies that the two lines are parrallel to each other. Now to my question, this solution does not...
  13. chwala

    How Can You Solve This Modulus Equation with Square Roots and Absolute Values?

    I am trying to go through my old notes ...i came across this question,i do not have the solution. Solve ##2|3x+4y-2|##+##3####\sqrt{25-5x+2y}##=##0## Ok my approach on this; ##3####\sqrt{25-5x+2y}##=##-2|3x+4y-2|## ##9(25-5x+2y)=4(3x+4y-2)^2## ##9(25-5x+2y)=4(9x^2+16y^2+24xy-12x-16y+4)##...
  14. chwala

    Solve the inequality problem that involves modulus

    This is the question * consider the highlighted question only *with its solution shown (from textbook); My approach is as follows (alternative method), ##|\frac {5}{2x-3}| ##< ## 1## Let, ##\frac {5}{2x-3} ##⋅##\frac {5}{2x-3}##=##1## →##x^2-3x-4=0## ##(x+1)(x-4)=0## it...
  15. G

    To find the modulus of elasticity of a light elastic string

    Could I please ask for help with the following question? Four uniform rods of equal length l and weight w are freely jointed to form a framework ABCD. The joints A and C are connected by a light elastic string of natural length a. The framework is freely suspended from A and takes up the shape...
  16. Leo Liu

    I (Elementary number theory) Understanding congruence and modulus

    In this question, how does the step marked with 1 become the step marked with 2? I can see that the transitivity property of congruence is used, but I don’t know what exactly is going on here. Can someone please explain? Also at which step is Congruence Add and Multiply used? Thanks...
  17. T

    MHB Complex numbers such that modulus (absolute value) less than or equal to 1.

  18. chwala

    Uncovering the Missing Solution in the Modulus Problem: k>4 and k=0

    i got ##k>4## and ##k=0## find my working... the test book gives solution as ##k>4##. Did they miss out on the second solution ##k=0##?
  19. N

    B Suggestions for Internal Assessment Project on Young's Modulus

    Hi. I am in the IB and am looking at doing a physics IA (internal assessment) on Young's modulus on an elastic material. I was thinking of doing it on the the stretchy snakes like the candy. What would I need to cover in this?
  20. J

    Relationship of Modulus to thermal expansion

    I'm trying to figure out how to relate expected thermal expansion of a uv cured polymer within a rigid cylinder to a modulus specification. The issue is the expected change in refractive index due to thermal expansion. The expansion coefficients are not available. Anybody have an idea. Do...
  21. N

    MHB How can we rewrite a modulus function?

    We can rewrite |x-3|<10 in the following way. -10<x-3<10 But can rewrite |x-3|+|x+1|+|x|<10 in the following way? -10<x-3+x+1+x<10. If we cannot, will anybody please explain why we cannot?
  22. N

    MHB Which procedure takes the minimum time to solve modulus functions?

    1) -|2x-3|+|5-x|+|x-10|=|3-x| 2) |2x-3|-|5-x|-|x-10|-|3-x|=28 3) -|2x-3|+|5-x|+|x-10|≥|3-x| How can we solve these problems? The method I know is to plug in the critical values to see which modulus becomes positive and which one becomes negative. Then find out the values of x for which the...
  23. N

    MHB Modulus problem with a negative sign

    In a video, a person discussed how to solve modulus problems with a negative sign. This is the link of that video lecture. He showed two methods to solve the problem. The first method is commonly used. Later he showed another method where he used a number line and a graph. Unfortunately, I...
  24. Buaya

    Young's Modulus of a Banana leaf

    Summary:: What is Young's modulus of banana leaf in MPa? What is Young's modulus of banana leaf in MPa? [Thread moved from the technical forums, so no Schoolwork Template is shown]
  25. A

    I When is it better to call a thing "modulus" and when "determinant"?

    In what cases it is better to call a thing "modulus" and in what cases "determinant"? In my algebra "determinant" is not a norm, discontinuous, positive for non-zero elements, not abiding triangle inequality. Should I better call it "modulus"?
  26. Amaterasu21

    B Why is Young's modulus constant below the limit of proportionality?

    Hi all, I'm a little confused about something. Force-extension graphs and stress-strain graphs are always both straight lines up until the limit of proportionality, implying both the spring constant and the Young modulus are constant up until then. For a force-extension graph, Hooke's Law...
  27. chwala

    Understanding Modulus Equations: Solving for x

    ##|2x+3|-x=1## i am getting ##x=-2## and ##x=\frac {-4}{3}## of which none satisfies the original equation, therefore we do not have a solution, right?
  28. brotherbobby

    Which points on the plane satisfy the given equation?

    Given the equation : ##|y| x = x##. Two conditions are possible : (1) ##\underline{y\geq 0}## : ##xy = x\Rightarrow \boxed{y = 1}\; (x \neq 0)##. We note that except for zero, ##-\infty<x<+\infty## for this case. (2) ##\underline{y < 0}## : ##-xy = x\Rightarrow \boxed{y = -1}\; (x \neq 0)##...
  29. jkmiller

    What Chemical Properties Affect Young's Modulus?

    I can't seem to figure out which chemical properties govern the physical property that is young's modulus. For example, any linear (or with a low degree of branching) polyethylene with no crosslinking is still a somewhat rigid and solid substance (higher ym), whereas the most linear possible...
  30. brotherbobby

    Solving a modulus inequality in ##x##

    The answer to the above problem is baffling, despite its straightforward nature. I will post the answer later, but here is my solution first. Solution : (1) ##2x+1 > x## : In this case, we have ##2x - x > -1 \Rightarrow \boxed{x > - 1}## (2) ##2x+1 < -x## : In this case, we have ##2x+x < -1...
  31. D

    Biophysics Q: Impact of stiffness (Young's modulus) on stress failure

    Hi. I'm a physician trying to understand the micromechanics of lung injury due to overdistension. The basic idea is that overstretching of the plasma membrane of the lung epithelial cell causes "stress failure" --> i.e. plasma membrane rupture --> cell death. The concepts of stress, strain, and...
  32. AN630078

    Where Do the Graphs of |3x-2| and 1/x Intersect and Diverge?

    1. I think the question is asking where is the graph of |3x-2| below the graph of 1/x. To sketch the graph of y= |3x-2| draw the line of y=3x-2 and reflect the section with negative y-values in the x-axis. Alternatively, I could set 3x-2 ≥0, meaning |3x-2|=3x-2 so draw the line of y=3x-2. Then...
  33. E

    Young's Modulus and the Poisson Ratio of Aluminium

    Hi. I've been given these sets of value. How do I calculate Young's modulus and Poisson Ratio from these set of value. I tried to create a stress vs strain graph but the graph does not look like a common stress vs strain graph but instead more of a y=x graph. The diameter of the rod is 10mm and...
  34. chriscarson

    Question involving Young's modulus (mass hanging from a wire)

    so what I did wrong?
  35. LCSphysicist

    Equation Alternatives for Young's Modulus

    I just found a definition to the Young modulus as: Is this a plausible representation of Y? That is, i know the definition , i don't think we can say this definition and the first definition is equal.
  36. LCSphysicist

    Young's modulus and compression

    See this figure: The rod is put at first between A and B shims without comprehension, suddenly a force is applied at R from an axis as the figure points. Find Fa and Fb. (the figure is a look from above) This can be solved by consider the "constant elastic" of the shims equal, but my...
  37. J

    What is the relationship between surface area and bulk modulus in a collision?

    there are two materials: Material A Material B surface area A/surface area B= 30 bulk modulus B/bulk modulus A= 11 How much more pressure is exerted through material B than material A in a collision, all else being equal?
  38. G

    Modulus of the electric field created by a sphere

    I think the right solution is c). I'll pass on my reasoning to you: R=6\, \textrm{cm}=0'06\, \textrm{m} \sigma =\dfrac{10}{\pi} \, \textrm{nC/m}^2=\dfrac{1\cdot 10^{-8}}{\pi}\, \textrm{C/m}^2 P=0'03\, \textrm{m} P'=10\, \textrm{cm}=0,1\, \textrm{m} Point P: \left. \phi =\oint E\cdot...
  39. J

    What is torsional modulus, and where is it specified?

    In the equation for minimum link length here https://www.defproc.co.uk/analysis/lattice-hinge-design-choosing-torsional-stress/ he uses a quantity Torsional Modulus, denoted as G, which I cannot seem to find either a definition for or any kind of expected value. Shear modulus (also commonly...
  40. B

    Calculating Young's Modulus from this Stress/Strain Graph

    I am trying to calculate Young's Modulus on the graph below. I have run the test through some software, now want to calculate Young's Modulus to ensure my analysis can be relied upon to be scientifically sound. This is what i have calculated from learning online. Is this correct? I have 2 more...
  41. chriscarson

    Young's modulus: Stress, Strain and Force for a Steel Bar

    As all attempts to get it right but without success this is one of the problems with my workout . Where i did wrong calculations ? The questions got the answers in brackets.
  42. chriscarson

    Calculating Force Using Young's Modulus

    How can you Calculate Force ?
  43. CPW

    Stargazing M - M as the distance modulus, and a question about the distance ladder

    I'm attempting to understand fully the distance ladder we use in astronomy to determine the distance to stars that are too far away for parallax to work. I understand we calibrate to a standard candle data of period vs luminosity for the cepheid variable stars in a group. Then from knowing the...
  44. chriscarson

    Young's modulus question with answer notation issue

    Summary:: why this answer ? I have the result of a young s modulus that is 358280256.25 and the answer the teacher gave us is 3.58 x 10 to the power of 8 . why not 358.3 x 10 to the power of 6 ? how she s deciding how many steps goes back with the point , the answer of a sum before this...
  45. karush

    MHB *gre.al.9 GRE Exam Inequality with modulus or absolute value

    given $|y+3|\le 4$ we don't know if y is plus or negative so $y+3\le 4 \Rightarrow y\le 1$ and $-(y+3)\le 4$ reverse the inequality $ y+3 \ge -4$ then isolate y $y \ge -7$ the interval is $-7 \le y \le 1$
  46. chwala

    Modulus Equation: Solving for ##p## & ##m##

    ##3√(25-5x+2y) = -2|3x+4y-2|## →##9(25-5x+2y)=4[(3x+4y)^2-4(3x+4y)+4]## →##9 (25+m)= 4[p^2-4p+4]## where ##p= 3x+4y## & ##m= 2y-5x## ##\frac{(p-2)^2}{25+m}##=## \frac{9}{4}##
  47. chriscarson

    Young's modulus — Finding the change in the length of a metal bar under stress

    A steel bar 6.00 m long and with rectangular cross section of 5.00 cm x 2.50 cm supports a mass of 2000 kg. How much is the bar stretched ? (the young s modulus of steel is 20 x 10 n\m squared)
  48. J

    Manipulating equation for Young's Modulus and Hooke's Law

    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...
  49. James Beedy

    Distance Modulus of a Star cluster

    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?
  50. T

    Young's Modulus, Stress/Strain graph and Calculating Energy

    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...
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