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. D

    Help with Length contraction of ruler at 60degree angle to observer

  2. M

    Helicoidal movement: acceleration vector, arc length, radius of curvature

    I have tried to solve it and I would like a confirmation, correction or if something else is suggested... :) Helicoidal movement
  3. M

    I Length Contraction & FTL Speeds: Are Lower Grades Faster?

    I’m not a physicist but let’s say hypothetically ;we have the Millennium Falcon. It’s FTL hyperdrive can go Class 0.5 past lightspeed. Then we have an X-wing which has a Class 1 past lightspeed drive. This is all from the lore. MF is 0.5 and X Wing is 1 but MF is faster. Anyway even though the...
  4. U

    How Do You Calculate the Length of a Wire in a 60W Incandescent Bulb?

    How to find the length of a wire of a 3000 Kelvin incandescent light bulb that produces L = 60W of power. The diameter of the wire is 0.00005m. I'm quite confused, as the resistivity of the bulb isn't given so I'm not sure what equation to use as resistivity = resistance × area / length does...
  5. F

    I Light pulse path, length and shape, when bouncing between two mirrors

    Hello, A light pulse moving bouncing between two mirrors (top and bottom) follows a vertical straight path w.r.t. to an inertial observer at rest relative to the mirrors. However, a moving inertial observer see the light pulse move in a zig-zag path as it bounced back and forth between the...
  6. M

    What Characteristic Length Should Be Used for Fluids in Low Gravity?

    Hi PF! Fluids in low gravity have a natural oscillation frequency ##\lambda = \sqrt{\sigma / (\rho L^3)}##, where ##\sigma## is surface tension, ##\rho## density, ##L## characteristic length. Then given a particular object, say a sphere, is ##L=D## or ##L=r##? How about a channel; would ##L##...
  7. jisbon

    Conservation of Energy and change in the length of a spring

    Hola! So my first approach to this is use both the conservation of energy and momentum equations since collision between the first two objects are elastic. Let the 3 blocks be a,b and c (from left to right) Does this means the following: whereby ##v_{a} ##= speed of block a after collision...
  8. C

    I "Spatial Width," "Coherence Length," and the Measurement Problem

    A new (short 3 pg) paper, making quite a grandiose claim, caught my eye last night: https://arxiv.org/abs/1908.07719 Abstract: We propose an experiment of two-path interference in which the optical path difference between the two interferometer arms is much larger than the spatial spread of...
  9. S

    Huge pressure drop after changing pipe length (Don't think it's loss)

    Hi All, Recently, I have been struggling to seek a solution for a seemingly simple flow question and try to rationalize my thoughts with mechanical engineering knowledge I have acquired from school but none of them can make me feel comfortable about answering the phenomenon I encountered in...
  10. Yalanhar

    Calculate the electric field due to a line of charge of finite length

    Homework Statement: A thin rod of length L and charge Q is uniformly charged, so it has a linear charge density ##\lambda =q/l## Find the electric field at point where is an arbitrarily positioned point. Homework Equations: ##dE=\frac{Kdq}{r^2}## A thin rod of length L and charge Q is...
  11. L

    MHB Year 10 Maths Find the length and width that will maximize the area of rectangle

    The question is in the image. Working out with every step would be much appreciated.
  12. E

    B Finding the length of a metre stick from a moving frame of reference

    Suppose we have a stationary metre stick with one end positioned at the origin of a stationary frame of reference, pointing along the positive x axis. The world lines of both ends of the metre stick are consequently vertical. Now consider another primed frame moving at velocity v relative to...
  13. Stormzy67

    Elastic potential energy and natural length of a spring- relation?

    I figured out that the spring constant is inversely proportional to the natural length, but there’s still an unknown change in a quantity( most likely extension).
  14. fernelau

    Understanding the Impact of Convex Lens Focal Length on Water Temperature

    Summary: Hi, I'm doing an assessment for Physics on Optics topics, but I can't really explain how the CV affect the RV CV : Focal length of convex lens RV : Temperature of water after 20 minutes under the sun How I should explain for the temperature difference? 🤔 Please help, Thanks.
  15. L

    Can a Tiny Antenna Transmit Long Wavelength EM Waves?

    Can you transmit em wave with antenna much smaller than its wavelength? For example. ELF antenna is very long. Can you make one small enough to fit in the pocket by the device constructing the long wavelength part by part?
  16. S

    Are there photodiode fabs that give the P and N length scales?

    I am interested in purchasing Si, GaAs and/or Ge PN and PIN photodiodes, where the manufacturer would also supply the length scales as well as the doping, of the P, I and N layers. Commercial suppliers don't reveal this information [moderator: solicitation removed.]
  17. DaveC426913

    B Length contraction of a pair of electrons

    I've managed to stump myself in attempting to answer a member on another forum. He is attempting to demonstrate length contraction using two electrons a known distance apart and moving at a known velocity.My thought experiment is based on his proposal; that's why I've chosen the components I...
  18. P

    Difference between time / length equations for time dilation

    What is the difference between time dilation (t is the stationary reference frame) t = Description: If two successive events occur at the same place in an inertial reference frame, the time interval 􏰋t0 between them, measured on a single clock And this equation for time, if we take t' as the...
  19. Benjamin_harsh

    What is the total moment of inertia using the negative area method?

    ##I_{total} = (I_{1} + A_{1}d_{1}^{2} ) + (I_{2} + A_{2}d_{2}^{2}) + (I_{3} + A_{3}d_{3}^{2})##(d is the distance between centroid of the individual box and centroid of whole shape.) By negative area method by joining the gaps in I section. ##I_{total} = (I_{1} + A_{1}d_{1}^{2} ) - (I_{2} +...
  20. R

    I Arc diameter as a function of arc length and chord length

    I'm trying to determine if a certain bicycle tire size will fit my bike, and that determination is based on the inflated diameter (or width) of the tire. As such, I'm trying to come up with a formula that will give me the diameter of a bicycle tire as a function of the tire's carcass width and...
  21. berlinspeed

    Squared length of 4-momentum g(p,p)?

    Explained in statement.
  22. ali PMPAINT

    A geometric proof (minimizing the length of two lines in a rectangle)

    So, I know it can be proven using calculus, but I need the geometric one. So, I got that ^c=^d and therefor, the amount of increment in one of a, is equal to the other(^e=^b). (Also 0<a+b<Pi/2) And AP'=BP'=BD/sin(a) and BP=BD/sin(a+b) and AP=BD/sin(a-b). AP'+BP'=2AP'=2BD/sin(a) and...
  23. S

    I  Find Two Equal Length Paths in a Tree Graph

    In order to try and sovle this problem, my idea here was to use an extremal argument, with two equal length maximum paths on a tree. I said that no matter where the two graphs started, they'd end up having to cross paths since if there were two distinct paths with equal lengths the graph would...
  24. A

    I Coherence length of velocity fields

    I have came across a term "coherence length of velocity field ##\lambda## ",tried to search in the internet but doesn't find any result...will anyone please give a brief summary of this in this context..
  25. Foppe Hoekstra

    I Accelerated Triangle and Length Contraction

    Two astronauts, Neil and Michael, visit a solid not revolving planet. They mount a jet engine on this planet to get it turning around its axis. Before starting the engine they put three dots on the surface with the help of an isosceles triangle, which measures 1 by 1 meter. Two dots are placed...
  26. N

    B Planck Length: Upper Limit on Photon Frequency & Momentum

    Is it known how much momentum a photon possesses if it's wavelength is at the Planck length, and what happens if it's momentum is somehow increased from that?
  27. learn.steadfast

    I Length contraction viewed with Heaviside equations

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  28. I

    Does Wire Length Affect Resistivity in Electrical Conductors?

    L=Ra/P =6x0.0006/5x10^-8 =72000
  29. babaliaris

    Torque with Infinity length can lift anything?

    I was always wondering if you can lift anything (no matter how heavy it is) if you just use a really long pipe. Or does torque increases in a way like ##e^x## , ##a^x## and after some point it barely increases? Also if this can be explained mathematically, I would love to see it.
  30. Foppe Hoekstra

    I Length Contraction: Measuring a Difference of 55 Nanometers

    If the table (with the mirrors, beamsplitter, etc.) is rotated 90 degrees, one arm will get shorter (due to lengthcontraction) because its longitudinal speed goes from zero to 30 km/s (our speed around the sun) and the other arm will get longer as its speed goes from 30 km/s to zero. So with a...
  31. f77hacker

    A Rayleigh length to electron bunch emittance

    Hello, Context is Inverse Compton Scattering with an pulsed electron beam interacting with a pulsed laser. A laser has a Raleigh length of Z_r = w_o^2 * pi / lambda w_o is the the radius of the spot size, lambda is the laser frequency. I want to match this spot size to a pulsed electron bunch...
  32. R

    Testing PhD viva - Length of starting presentation

    I have my PhD viva in about a months time, part of it is to give an introductory presentation. Since I'm sure some members here examine PhD students in their viva, I would like to ask what they would consider a good lenth of time for the presentation? I don't want to annoy the examiner by having...
  33. T

    MHB Finding Chord length given arc length and arc height?

    I am in the process of making a tent and need to get two curved surfaces to meet. I need to find the length of a Chord of a circle given that I have the Arc length and Arc Height (that's all), no radius or anything else. I suspect that I will need a radius to find this. Or am I missing a...
  34. F

    I Human eye and its focal length range....

    Hello, The human eye has an average diameter of ##2.5 cm## and an optical power between ##60D## and ##64D##. An object can be brought as close as the near point which is about ##25 cm##. If ##d_{o}=0.25m## (object distance) and ##d_{i}= 0.025m## (distance to the retina), the optical power...
  35. multiversetheory

    I Is it possible for something to be smaller than a Planck length?

    After watching a youtube video 2 years ago, the video said the smallest thing known is at Planck length, but could there be something smaller than Planck length
  36. J

    I Vacuum energy length scale detectable by the Casimir effect?

    According to Sean Carroll's The Cosmological constant(https://arxiv.org/pdf/astro-ph/0004075.pdf) (Eqn.20) cosmological observations imply that the magnitude of the vacuum energy density in natural units is given by $$|\rho^{(obs)}_\Lambda|\le (10^{-12}\ \rm{GeV})^4.$$ Does this imply that the...
  37. Zack K

    Trapezoidal rule to estimate arc length error

    I got the first part of it down, $$L=\int_1^5 \sqrt{1+(\frac{1}{x^2})}dx$$ I just want to know if it's right to make your ##f(x)=\sqrt{1+\frac{1}{x^2}}## then compute it's second derivative and find it's max value, for the trapezoidal error formula.
  38. ntdiemai

    Critical Reynolds number and characteristic length

    What are the critical Reynolds number for fluid and characteristic length when a cylinder immerses and then rotates in the fluid (The fluid is initially static)? Please suggest the critical number for the transition from concentric flow to laminar and from laminar to turbulent flow. I would...
  39. J

    Focal length of converging thin lens graphs

    I tried -M=pq = f/(f-p) = f/f - f/p = 1-(f/p) => M+1= -f/p => -Mp-p=f But since it’s the y intercept, p will equal zero and so the focal length will be 0?
  40. T

    Derive thermal expansion of area from length

    I tried following: $$ \Delta l = \alpha l_0 \Delta T $$ $$ (\Delta l)^2 l_0 = \alpha l_0^2 \Delta T \Delta l $$ $$ \Delta A l_0 = \alpha A_0 \Delta T $$ $$ \Delta A = \frac{ \alpha A_0 \Delta T }{ l_0 } $$ If we remember that: $$ \Delta l = \alpha l_0 \Delta T $$ So we have $$ \Delta A = \frac{...
  41. J

    Comp Sci Computing the Length & Area of a 3D Triangle

    I have computed the total length of a 3D triangle and its area. The code is shown below. I want to use file output instead of cout. The file name, cw2task1output, was just given as part of the task, in this case should I make an empty text file named cw2task1output then attach it to the resource...
  42. S

    A What is the relationship between focal length and focus point in convex lenses?

    First of all, Let me present some of the things I found from research. (considering convex lens) Interpretation 1 => Focal length is the distance from the center of the lens to the point where all rays converge. Interpretation2 => Focal length is the distance from the point of convergence to...
  43. opus

    Finding the Length of a Polar Curve Using Desmos and the Arc Length Formula

    Homework Statement Use Desmos to graph the spiral ##r=\theta## on the interval ##0\leq\theta\leq4\pi##, and then determine the exact length of the curve and a four decimal approximation. Hint: ##\int \sec^3(x)dx=\frac{1}{2}\sec(x)tan(x)+\frac{1}{2}\ln\left|\sec(x)+\tan(x)\right|+C## Homework...
  44. J

    I The Planck length and string theory

    String theorists frame much of their studies in the context of Planck length. The theories are meant to fold together QM and general relativity. The equation for Planck length includes the gravitational constant, G. It seems to me the theorists are assuming the gravitational laws extend to...
  45. babaliaris

    Projectile Motion: Path's length?

    So I just learned about projectile motion. I understand why you can study it as two independent straight line motions . But this can give you a way to calculate total velocities or accelerations, just by adding its individual component of each vector. If the initial position of the projectile...
  46. patric44

    Calculating the Length of a Water Column in a Beaker

    Homework Statement a Basin contains water , a beaker is put upside down to a depth of 3m inside it , if the volume of the beaker is 250 cm^3 . and its C.S area = 200 cm2 calculate the length of the water column which rises inside the baker , supposed that their is no air leakage from the...
  47. karush

    Chord Length: A Mathematical Observation

    Ok this should be just an observation solution .. But isn't the equation for chord length $$2r\sin{\frac{\theta}{2}}= \textit{chord length}$$ Don't see any of the options Derived from that..
  48. Alexanddros81

    A glider of length 12.4 cm moves on an air track

    Homework Statement Serway Physics - P2.40 A glider of length 12.4 cm moves on an air track with constant acceleration (Fig P2.39). A time interval of 0.628 s elapses between the moment when its front end passes a fixed point A along the track and the moment when its back end passes this pont...
  49. Mr Davis 97

    Length of median is less than half of adjacent sides

    Homework Statement ##ABC## is a triangle, the midpoint of ##AB## is ##H##. Prove that ##2CH < AC+CB##. Homework EquationsThe Attempt at a Solution Note that by the triangle inequality that ##CH \le HA + AC## and that ##CH \le HB + BC##. Adding these two inequalities gives $$2CH \le HA+HB+AC+CB...
  50. DJ_Juggernaut

    I On The Length of a Meter Stick

    Can a single meter stick be one meter per A and less than a meter per B? If so, isn't this is a simple paradox? Does anyone here see it that way?
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