Length Definition and 1000 Threads

Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the International System of Units (SI) system the base unit for length is the metre.
Length is commonly understood to mean the most extended dimension of a fixed object. However, this is not always the case and may depend on the position the object is in.
Various terms for the length of a fixed object are used, and these include height, which is vertical length or vertical extent, and width, breadth or depth. Height is used when there is a base from which vertical measurements can be taken. Width or breadth usually refer to a shorter dimension when length is the longest one. Depth is used for the third dimension of a three dimensional object.Length is the measure of one spatial dimension, whereas area is a measure of two dimensions (length squared) and volume is a measure of three dimensions (length cubed).

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  1. J

    How to find composition series of Z_n^* of length k?

    Hi, I'd like to find easily-accessible composition series of an interesting lengths say 10 or so (to study some theorems about subgroup series experimentally). I'm thinking the integer mod unit groups, that is ##\mathbb{Z}_n^*=Z_0\rhd Z_1\rhd Z_2\rhd \cdots \rhd Z_9\rhd Z_{10}=\{1\}##. Would...
  2. terryds

    Does Wire Length Affect Resistance?

    In https://in.answers.yahoo.com/question/index?qid=20120918081153AARHhnA, It says that "1.When the length of the wire is doubled,its volume remains constant, " How come ? Volume is Area times the length.. How come it remains constant if the length of wire is doubled ??
  3. goonking

    Frequency and Length: Solving for String Length

    Homework Statement Homework EquationsThe Attempt at a Solution for the first harmonic, the wavelength is twice the length of string. so 0.296m x 2 = 0.592m is the wavelength with the wavelength and frequency known, we solve for v in v = ƒλ v = 0.592m x 440 Hz = 260 m/s then to solve for...
  4. fluidistic

    Length contraction via Lorentz transformation matrix

    1,2,3. Homework Statement I tried to derive the length contraction using the Lorentz transformation matrix and considering 2 events. I reached the correct result but there's a step that I had to assume that I don't understand. Consider a ruler of length L along the x-axis for an observer at...
  5. A

    Find length of spring in its equilibrium position

    As shown in Figure Q1a, a frictionless, massless, piston, supported by two springs, A and B, is held by a pin in a vacuum inside a rigid-walled container. The properties of the springs are: spring constants kA = 3,859 and kB = 3,090 (in N/m), natural lengths LA0 = 0.03 and LB0 = 0.1 (in m). When...
  6. A

    Find length of spring A in equilibrium position

    As shown in Figure Q1a, a frictionless, massless, piston, supported by two springs, A and B, is held by a pin in a vacuum inside a rigid-walled container. The properties of the springs are: spring constants kA = 3,859 and kB = 3,090 (in N/m), natural lengths LA0 = 0.03 and LB0 = 0.1 (in m). When...
  7. Chrono G. Xay

    Predicting Initial Length of String Needed Before Stretch

    I have put together an equation whose purpose is: With a desired 'magnitude of static friction' ( μ_s ), 'fundamental frequency' ( f ), and 'tension' ( T ), initial conditions such as 'string breakover angle' ( Θ_0 ), 'nut-tuner distance' ( L_{h,0} ), and 'string diameter' ( d ), and...
  8. A

    Conservation of energy for a system

    Homework Statement Figure shows a massless wheel of radius R on which at a point a mass m is fixed and a uniform chain of mass 2m is tied to it which passes over the rim of the wheel and half of its length is hanging on other side as shown in the figure. When a small clockwise jerk is given to...
  9. G

    What is the Relationship Between Force Magnitude and Length in a Scale?

    Homework Statement In this notes , I was told that the f2 is min when the length is the shrtest ( when f2 is prependicular to fr ... why ? Is the length represent the magnitude of the force ? the shorter the length , the smaller is the force ? Homework EquationsThe Attempt at a Solution
  10. klotza

    Insights A Hand-Wavy Discussion of the Planck Length - Comments

    klotza submitted a new PF Insights post A Hand-Wavy Discussion of the Planck Length Continue reading the Original PF Insights Post.
  11. S

    MHB Count the number of strings of length 8...

    Count the number of strings of length $8$ over $A = \{w, x, y, z\}$ that begins with either $w$ or $y$ and have at least one $x$ I don't understand this question at all. First of all, this is a set A that contains 4 elements $w,x,y,z$ correct? They are asking me to count the number of strings...
  12. Jimster41

    The Impact of Cosmological Expansion on the Planck Length: A Quantum Perspective

    I get that Planck length is derived from h, G and c. But as a theoretical measure of length how is it affected or not affected by cosmological expansion?
  13. G

    Capacitance per length unit of coaxial cable

    Homework Statement Coaxial cable has double layered dielectric. a=2mm, b=4mm, c=8mm, εr1=3, εr2=4.5, Uab=1000V 1. Calculate capacitance per unit length of a cable. 2. Calculate inner and outer charge densities of a cable. 2. Homework Equations Gauss law C'=Q'/U σ = nD σp = nP 3. The Attempt...
  14. G

    Capacitance per unit length - two cylindrical conductors

    Homework Statement Two cylindrical conductors, of distance between them d and radius a (a<<d), have dielectric layer of relative permitivitty εr and thickness a. Calculate capacitance per unit length of this system. Homework Equations Capacitance per unit length, C'=Q'/U Gauss law, cylindrical...
  15. M

    Which length has to be taken to compute magnetic resistance?

    In general I read that: R_m =\frac{l}{\mu A} But considering for example the following transformer: I don't understand why the lengths taken from the sketch by the solution's procedure are the following: For the right and left part resistance: R_r = R_l = \frac{(\frac{1}{2} + \frac{1}{2}...
  16. N

    Dimensional Analysis of Planck Length

    Hello! So in looking at black hole thermodynamics, I came across the equation ## l_p = \sqrt{G\hbar} ## But in doing a dimensional analysis of ## \sqrt{G\hbar} ## I get ## [\sqrt{G \hbar}] = \sqrt{ \frac{Nm^2}{kg^2} \frac{m^3}{kgs} } ## This obviously doesn't amount to a length. What...
  17. Titan97

    Why is the Bond Length of CF3Cl Shorter than CH3Cl Despite Bent's Rule?

    Taken from 'Concise Inorganic Chemistry - J.D.Lee': "According to Bent's rule, more electronegative atom not only prefers to stay in the orbital having more p-character but can also increase the p-character in its attached orbital of the central atom depending on the circumstance... With an...
  18. Justice Hunter

    Why does length contraction not cause Black holes?

    So i was watching this video : And it got me thinking... i began wondering why, when space contracts from someones frame of reference (In the video, this would be the frame of reference of the cat), why is it that the protons don't become black-holes when the space contracts? If the density...
  19. DaTario

    Coherence length of a single photon

    Hi All, Is there any experimental evidence that photons may have attached to itself a coherence length? Best Regards, DaTario
  20. M

    MHB Calculating Curve Length: A Shortcut for Solving Complex Equations?

    Hi everyone, I have an exercise I haven't solved yet, please help me. Find the length of the curve: y = \frac{{x}^{5}}{6} - \frac{lnx}{4}, 2 \le x \le 4.
  21. K

    Dimensional analysis on equation including scattering length

    Hi all, I post a question about the dimension of wave function in position space before and people help me to identify that the unit of wave function should be in the unit of ##\text{m}^{-1/2}##. I am verifying that by doing the dimension analysis on Schrodinger equation...
  22. T

    Grashof Number Calc for Greenhouse: 1.5m x 2m x 2m

    Homework Statement Hello. This should be rather easy. I am trying to figure out what the Characteristic length I should use in calculating the grashof number for a greenhouse. The dimensions given for the greenhouse are 1.5 m wide x 2 m long and 2 m high. What characteristic length should I...
  23. Y

    {Geometry} Find length of the equilateral triangle

    Homework Statement http://i.imgur.com/lnk7e0D.png CDE is an equilateral triangle inside a circle, with side length 16. FGH is also an equilateral triangle and F is the mid point of DE. Find the length of the side FGH. Should be expressed as Asqrt(B)-C. Where A B and C are positive integers...
  24. D

    Focal length of magnifying glass for VR?

    Hi the standard focal distance seems to be 45mm for vr headsets such as google cardboard. In other words there's a pair of convex lenses in front of your eyes with the screen being 45mm away from the lenses ... I am not sure why you can't use different lenses to reduce the focal distance to the...
  25. neosoul

    Schools Do Graduate schools care about length of undergraduate career

    Hey PF, I'm currently double majoring in engineering and physics. I want to be a licensed engineer and go on to grad school to study molecular engineering or something similar. However, I love my physics department. It's smaller so students get more funding and attention and way more...
  26. F

    Length of Base to support weighted pillar

    Hi all, I need to find base length x which would support the pillar and wouldn't topple over (weight of 2.1kg on right hand side of pillar) Thanks in advance
  27. P

    Exploring the Relationship Between Wire Length and Voltage in a Circuit

    Homework Statement We conducted an investigation into wire length, current and resistance but kept track of the voltage rather than relying on the power pack setting. We noticed the voltmeter (measuring across the power pack) reading increased as the length of the wire increased though by only...
  28. R

    A question on length contraction

    Just wondering if someone could check that I am understating this aspect of length contraction correctly... I am in a spaceship moving at say a speed of 0.6c relative to some imaginary ruler in space which has increments set 1 meter apart. (1 meter in the ruler's rest frame.) I am moving along...
  29. caters

    The problemFind side length using trig

    Homework Statement $AB = 20 cm$, $m∠A = 30°$ , and $m∠C = 45°$ . Express the number of centimeters in the length of $BC$ in simplest radical form. Homework Equations $sin A = sin C$ The Attempt at a Solution $AB = 20, BC = x$ D is the point where this obtuse triangle separates into 2 right...
  30. C

    Ground state in an infinite square well with length doubling

    Homework Statement Assume a particle is in the ground state of an infinite square well of length L. If the walls of the well increase symmetrically such that the length of the well is now 2L WITHOUT disturbing the state of the system, what is the probability that a measurement would yield the...
  31. Tali

    In mechanics: doea the length of the wire affects the angle?

    Homework Statement general question: if I give a ball velocity (He is tied to a wire (tension)) and consider that the wire has no mass. Does the length of the wire affects the angle? If I solve this with energy tools then I get that the longer the wire the smaller the angle. it does not settle...
  32. K

    Length Contraction & Relativistic Aberration: Is 1 Formula Enough?

    I have been coding a speed of light simulator and I am having a bit of trouble with a few aspects of the project. My first question is: Are the length contraction and relativistic aberration formulas BOTH needed in my calculations or does the relativistic aberration formula already account for...
  33. Dethrone

    MHB Arc Length Formula: Understanding the Proof

    I'm reading about Line Integrals, so I thought I'd review the proof for the arc length formula. However, there's something I don't quite understand about the proof that I either overlooked or understood before. From what I see, the arc length formula holds because the MVT guarantees that there...
  34. Nicholas Morse

    How to determine length of a spring

    Hi Everyone, Kind of a tough question here. How do I determine the length of a spring if we don't have any visual information about it? All we have is the spring rate & change of object position from when the spring is uncoiled, to fully coiled. Anyone have any ideas on this? I tried the...
  35. Ookke

    Distant stars and length contraction

    Please see the picture. Red dots are stars, lines are the path that light takes, our observer is at center. Assuming that stars are somewhat uniformly spread around us, I suppose that stationary observer (left picture) sees about as many stars in every direction, but an observer moving in...
  36. Kairos

    Time dilation, length contraction, but velocity invariant

    If a frame is moving at constant velocity relative to an observer, this observer perceives a time dilation and a length contraction. But in this case how the velocity (length/time) can appear constant ? It is expected to be contracted.. Thank you in advance for the explanation
  37. eftrsd

    Understanding the Vacuum Debye Screening Length: Importance and Calculation

    What is the correct value for the vacuum Debye screening length?
  38. S

    How to use DWT when sample size is smaller thn filter length

    Hi, I am new member over here. I wanted to know how to perform discrete wavelet transform, probably using symmlet 8 wavelet with 16 Low/High pass filter coefficients using matrix transformation method when decomposing to a certain level the approximate coefficients i.e. sample size becomes less...
  39. Mentz114

    Length contraction and the speed of light

    I hope to lay to rest two of the misconceptions about special relativity that are evident in the many questions asked here. 1) Why is the speed of light a constant ? Everybody believes Pythagoras's theorem that the length of the hypotenuse of a right angle triangle is ##\sqrt{s_1^2+s_2^2}##...
  40. Tonia

    How fast must a meter stick be moving if its length is....

    Homework Statement How fast must a meter stick be moving of its length is measured to shrink to 0.500 meters? Homework Equations v/c = sqrt(1 - (1/L)^2) = sqrt(1 - 1/4) = sqrt(3/4) = sqrt(3)/2 or use v = sqrt(3)c/2 The Attempt at a Solution (squrt 3c/2) = squrt 450000000 = 21213.203 =...
  41. Amr Elsayed

    Length contraction and direction of tavel

    Hi all, I want to make sure of a particular information. Length is contracted only in direction of motion. If I am on a spacecraft moving with high speed, I shall see the universe is contracted just in front of me that I am going to, but there would be no contraction If I look to regions that...
  42. Stephanus

    Exploring Twins Paradox & Length Contraction

    Dear PF Forum I want to know about these questions that are still bothering me, Does the universe have preferred frame of refference? Why there's twins paradox? Motion is relative, why 1 clock experiences time dilation while the other doesn't? V = \sqrt\frac{3}{4} ≈ 86.6\% If V define ratio of...
  43. A

    Muon length contraction confusion

    Muon created by fast cosmic ray has speed 2.99X10^8 m/s and life time 2.2 micro sec. According to this numbers muon should travel only 0.66Km with respect to Earth in his life time. however it travels more than 10 km (10.4km) due to time dilation. in muon frame of reference, Earth travels only...
  44. ChrisVer

    Can momentum be calculated to achieve a 2mm decay length for a tau particle?

    Hi, I'm looking for the momentum so that the decay length of a tau (mean lifetime ##t_{lft}=2.9 \times 10^{-13}s##) can be ##2mm##. I was wondering whether someone can use the formula I got: l_{lab}= t_{lab} u = \gamma u t_{lft} \Rightarrow pc= m \gamma u = m \frac{l_{lab}}{t_{lft}}? (Looking...
  45. V

    MHB Calculating Ribbon Length for Decorating Cylindrical Flower Containers

    A florist delivers single stemmed flowers in a sealed plastic container that is cylindrical in shape. Each container has a bade radius of 4cm and a height of 45cm. the florist wished to decorate each container with a very thin coloured ribbon. The ribbon will wind around the body of the...
  46. Dyatlov

    Need help with a triangle's length side/ angle relation.

    Hello. I am trying to wrap my head around where from did he got the x = sin of theta equation at the 32:44 mark of the video: . Isn't sine of theta x over the hypotenuse in the diagram ? Thanks in advance!
  47. R

    Arc Length. Simplify expression

    Homework Statement I'm trying to find Arc Length of F(x) = (e^x + e^-x)/2 0< x < 2]Homework Equations L = integrate sqrt ( 1 + (dy/dx))^2)The Attempt at a Solution (dy/dx)^2 + 1 = 1/4e^2x + 1/4e^-2x + 1/2] I don't know how to take the square root of the above function so I can be able...
  48. E

    Beat frequency and length question. (grade 11)

    Homework Statement Two pipes, Identical in length and closed at one end are producing notes. You are very, very annoyed because the notes are creating an audible beat frequency of 20Hz. If one pipe is producing a note at 10Hz and the temperature is 15C (which correlates to a speed of sound of...
  49. J

    Length generated by all atoms contained in 1 gram of iron

    Hi, I tried to calculate the distance resulting from Na iron atoms contained in 1 g. scaled in meters and by juxtaposing them in a single thread (segment). I did the following calculation with: Atomic radius : 140 E-10 meters Na : 6 E23 atoms in 56 g. of iron => ( 2 x 140 E-10 x 6 E23 )/56...
  50. saadhusayn

    Why Does Length Contraction Differ When Calculated at an Angle?

    Hi, My question concerns the following problem from chapter 4 of Special Relativity by A.P. French. A statement of the problem: 4-15 A flash of light is emitted at point O and is later reabsorbed at point P. In frame S, the line OP has a length l and makes an angle θ with the x axis. In a...
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