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

    What happens when matter pops into and out of existence at Planck length scales?

    All - my first post, and as a lay person interested in quantum physics, forgive me if my questions are naive or ill-informed. Is it possible that the Universe inflated then exploded into being from a singularity smaller than Planck length? If I understand the concepts properly, the Planck...
  2. T

    Find the length of one of the sides in a triangle

    Hey! I just started study landsurveying and got a task i don't figure out how to get the right answer. My goal is to find the length of one of the sides in a triangle, but i can not use pytagoras formula. Here is the formula i am supposed to use (dont care about the text, its norwegian)...
  3. D

    Is the Upper Optical Path Longer than the Lower One in Diagram 2?

    Homework Statement for diagram 2 , i just can't understand why S1P -t + ut (upper ray ) is longer than the lower light ray (S2P) , ? if I take S2P minus ( S1P -t + ut ) , then i would get mt t (thickness ) is negative , which is indeed wrong! so it has shown that optical path of the upper...
  4. H

    Questions on length contraction in train light clock experiment?

    Hi guys, I've been thinking about this experiment for the last few hours and I have a few questions which I am deeply confused about. 1) In the light clock experiment, where light clock is set up so that light travels vertically, and the train carrying the clock travels horizontally, wouldn't...
  5. S

    Keeping uncertainty at arm's length

    It seems self-evident that mathematics must keep uncertainty at arms length. For example, to deal with probability mathematics establishes a set of assumptions. The assumptions themselves are not probabilistic - i.e. the "laws" of probability are assumed to be true "all the time", not...
  6. D

    Focal length of combined glass lens and water lens

    Homework Statement please refer to the photo, Homework Equations The Attempt at a Solution why can't I directly use the lens maker formula to get the ans ? my working is 1/f = ( (1.5-1.33) /1.33) x ( (1/20) + 0 ) ...finally , i get my f = -160cm. the radius of curvature of...
  7. H

    Short question about length contraction

    The at rest distance between Betty the astronaut and a flag in open space is 1 unit. If Betty approaches the flag at constant speed while laying out metre rulers, will she have laid out 1 unit of at rest rulers when she reaches the flag? Or will the number of rulers laid out exceed 1 due to...
  8. B

    How to re-size a sound's wave length

    In the field of acoustical physics the mathematical relationship (wavelength (lambda) = speed of sound (velocity) / frequency (cycles per sec)) indicates that lambda (wavelength) would increase if the speed of sound were increased while the frequency (cps) is held constant (e.g., 100 Hz)...
  9. E

    Focal length of converging meniscus lens filled with a liquid

    Homework Statement A converging meniscus lens is made of glass with index of refraction n = 1.55, and its sides have radii of curvature of 4.5 cm and 9 cm. The concave surface is placed upward and filled with carbon tetrachloride which has index of refraction n' = 1.46. Determine the focal...
  10. T

    Why are time dilatation & length contraction infinite at light speed?

    Considering that speed of light is constant and finite, then why are the time dilatation and length contraction infinite to a frame of reference moving at the speed of light? We know that a moving frame of reference experiments time dilatation and length contraction from the point of view of a...
  11. I

    Exploring the Relationship Between Debye Length and Ohm's Law

    Hello, I am new here. I was reading Wangsness electromagnetic fields and he delves into a short discussion about poisson-boltzman equation/Debye length before introducing the point-form of Ohm's Law. Just wondering what the significance of this was and how these two things are related.
  12. D

    MHB What is the required length of wire A?

    two wires A and B made from two different materials have temperature coefficient of resistance equal to 0.0025 and 0.0005 ohm per degree Celsius respectively. It is desired to make a coil of wire having a resistance of 1200 ohms with a temperature coefficient of 0.001, using a suitable length of...
  13. C

    Simple special relativity, length from duration

    I'm thinking about a very basic scenario in special relativity, but I've got something backwards, and I could use help understanding why it's wrong. Suppose a rod R is moving past an observer O at speed v. The observer wants to know how long the rod is, so he starts his stopwatch as soon...
  14. S

    MHB Arc Length and Rotation, Please Explain this problem

    EDIT: Okay now that the admin has cleaned up my mess, please scroll down to see the correct image and the question on the 3rd post in this thread.
  15. I

    MHB Find arc length starting from P_0

    find the arc length function for the curve $y=2x^{3/2}$ with starting point $P_{0}(1,2)$. how do i do this? this is what I've done so far. $y'=3\sqrt{x}$ $1+(3\sqrt{x})^2=9x+1$ $\int_{a}^{b} \ \sqrt{9x+1},dx$ what's my a and what's my b?
  16. I

    MHB Length of Curve $y^2=4(x+4)^3$: 13.5429

    $y^2=4(x+4)^3$ $0 \le x \le 2$ $y=2(x+4)^{3/2}$ $y'=3(x+4)^{1/2}$ $\int_{0}^{2} \ \sqrt{1+9(x+4)},dx = 13.5429$ is that right?
  17. A

    Measuring the focal length of a deformable lens

    Hello all, My lab recently purchased a deformable lens, which can change its focal length from 140 mm to 40 mm and anywhere in between, based on current applied to it. I'm wondering how to use a beam profiling camera to measure the focal length of this lens at various current levels. We...
  18. M

    Mechanical leverage to increase length?

    Hi Im trying to increase the length of a movement of a rope so when one rope is pulled the other rope movement is increased x 2 (it is attached across). So far i have tried gears whice has somewhat worked but it increases the force as well. Is there any other way to achieve this amplification...
  19. I

    MHB Find Arc Length with TI-Nspire Calculator

    how do i use the nspire to find arc length?
  20. I

    Is the Planck Length a 3d area?

    If so, is 'its half' also not a real size of space? What I am asking is pretty much; what is the meaning of the notion of a 'smallest possible' 3d area? What is the meaning of that cusp between 2d and 3d? Almost like asking what is in between 1.999999999999(repeating) and 2. Must...
  21. P

    Map Taking Proper Time to Euclidean Length

    Is there a way to map time-like curves in Minkowski space to curves in a Euclidean space such that the length of the curve in the Euclidean space is equal to the proper time of the curve in Minkowski space?
  22. W

    Role of Pipe Length in Poiseuille's Law

    I can't figure out why the length the a pipe (L) increases the change in driving pressure with respect to this law: Delta P = (8*mu*L*Q)/(pi*(r^4)) I would think that delta P wouldn't change because the fluid is incompressible. Does anyone have a conceptual explanation for the simple...
  23. M

    Focal length of a sphere with refractive index gradient

    Homework Statement We take a sphere (1mm) which has a parabolically changing refractive index, which is given in a function. Homework Equations Depending on the gradient of the refractive in the sphere, how does it correlates with the focal length. The Attempt at a Solution I...
  24. STEMucator

    Solving for Unstretched Length in Jump Problem: ##l_0 = 97.5m##

    Homework Statement The ##m = 75kg## man jumps off the bridge with ##v_1 = 1.5 m/s##. Determine the unstretched length ##l_0## of the cord in order that he stops momentarily above the surface of the water. The stiffness is ##k = 80 N/m##. Picture...
  25. T

    Focal length short and long. Which to choose?

    I'm building a telescope and one of the more important choices I'm making is what focal length to make the mirror, my understanding is the longer the focal length the closer you see far away stuff, but the field of view diminishes a bunch. I've seen both long tube dobsonians and short tube ones...
  26. B

    Focal Length of a Plano Convex Lens

    Hi, The focal length of the Plano-Convex lens as calculated by the lens maker equation: Does it work when light crosses the lens from the convex side, planar side, or both? Thanks.
  27. L

    Planck length and quantized position

    After reading an article on Planck length, I began to wonder whether or not the theoretical limit implied that position could be quantized in whole integer multiples of Planck length? To demonstrate what my question is asking mathematically I hope you will scrutinize the equations below: If...
  28. T

    What happens when a wavelength is longer than the length of coax?

    We are all taught that the TEM modes in coax have no low frequency cut-off. So this would suggest that nothing different happens for very long wavelengths that are longer than the coax itself. However, in this rather shocking paper here: http://vixra.org/pdf/1403.0964v5.pdf ...it is suggested...
  29. Albert1

    MHB QR Code Length: Examining the Fixed Size of QR Codes

    prove the length of QR is fixed
  30. A

    Maximum allowable current for ultra short pulse length

    So I'm designing a system that requires an extremely high amount of current for an extremely short pulse lengths. These pulses would be consecutively spaced at relatively large intervals from one another. I'm just wondering if there is some sort of instantaneous power limit to wires, even if the...
  31. F

    Is the Area Under a Curve Equal to its Arc Length?

    I learned in my calc 1 class that to calculate the arc length of a curve, we are to compute the integral of the function. For example, the integral of a function that describes the path of a thrown baseball would give the total distance traveled by the baseball (I hope I'm using the term arc...
  32. F

    Peak frequency of a signal depending on the length of the signal

    Hello everyone! I am generating a signal as a function of time. This is an irregular signal generated by using the superposition principle and random phase. Thus I actually have already all the frequency components of the signal. And from the frequency components I know that there is also a...
  33. L

    MHB Calculating Lever Length for Optimal Effort: 0.6 kg Bar & 200 kg Object

    a heavy bar, weights 0.6 Kg is used as a lever for pick up an object from 200 Kg situated 60 cm from the point of A support Calculate the length that should have the bar to lift the object with a minimum of effort answer 2 m ok we know 0.6x = 200.0.2 m But how can I continue?
  34. M

    The length of the curve r = cos(θ) - sin(θ), 0<θ<∏/4

    Homework Statement Find the length of the curve r = cos(θ) - sin(θ), 0<θ<∏/4 Homework Equations L=∫ds ds=sqrt(r^2 + (dr/dθ)^2) The Attempt at a Solution r^2 = (cosθ - sinθ)^2 = cos^2(θ) -2cosθsinθ + sin^2(θ) =1-2cosθsinθ dr/dθ = -sinθ -cosθ (dr/dθ)^2 = 1+2cosθsinθ...
  35. Erland

    Length contraction of rotating wheel

    Suppose that a wheel is rotating around its axis in free space with no friction, with no external forces acting on it. In theory, the wheel will rotate forever with constant angular velocity. This velocity is assumed to be small (essentially non-relativistic). Now, consider an observer O...
  36. N

    Moving an object and screen to find the focal length of a lens

    Homework Statement A convex lens is used to project the image of an object on a screen with a magnification m1 . Leaving the lens fixed, the object is moved along the optical axis by a distance Δs and the screen is moved until the image is located again. If the new value of the...
  37. A

    Proper Length Increase/Decrease: Analyzing Atom Changes

    As I've understood so far, there are theoretically many types of acceleration. In all cases except in the Born rigid acceleration the proper length of the object increases or decreases. If all parts of the object undergo the same acceleration simultaneously wrt to some IRF then the object...
  38. U

    What Determines C-F Bond Length Order?

    Homework Statement Choose correct order of C-F bond length A)C-HF2<C-H2F<C-F3 B)C-F3<C-HF2<C-H2F C)C-F3<C-H2F<C-HF3 D)C-HF2<C-F3<C-H2FThe Attempt at a Solution What factors should I look for while measuring bond lengths?
  39. M

    Find the length of curve r=cos(theta)-sin(theta)

    Homework Statement Find the length of the curve r=cosΘ - sinΘ, 0≤Θ≤∏/4 Homework Equations Arc length = ∫|v| dt The Attempt at a Solution I found r'(θ), then used the arc length formula. Arc length = ∫ sqrt (sin^2 Θ + cos^2 Θ) = ∫ dΘ and integrated it to find ∫dΘ = ∏/4 The correct answer...
  40. A

    Lorentz triangle and length contraction perpendicular to propagation

    Consider a pole of 1 light second long in the ##y## direction (the vertical line(s) in the enclosed figure). It is moving in the ##-x## direction. According SR, the pole's length is not contracted because its length is not parallel to the propagation direction. However, given the time of flight...
  41. D

    Troublesome Arc Length Problem

    1.) The problem is: Find the arc length of f(x)= x^3/3-1/(4x) from x=1 to 2 2.) Relevant formulas: ds = √(1+(dy/dx)) abs(L) = ∫ds 3.) My work so far: f'(x)= x^2+1/(4x^2) abs(L) = ∫(from 1 to 2) √(1+(x^2+1/(4x^2))^2 dx = ∫(from 1 to 2) √(1+(x^4+1/2+1/(16x^4)) dx = ∫(from 1...
  42. M

    Length change for a rod of two sections

    A rod is made of two sections joined end to end. The sections are identical, except that one is steel and the other is brass. While one end is held fixed, the other is pulled to result in a change in length of 1.20mm. By how much does the length of each section increase ? I understand that E...
  43. U

    Find the increase in the length of the rod

    Homework Statement A metal rod of length L at temperature of 0°C is not uniformly heated such that the temperature is given by the distance x along its length measured from one end when: T(x) = T_0 \sin (\pi x/L) Accordingly, points at x = 0 and x = L are also zero temperature, whereas at x...
  44. B

    Length Contraction Paradox Scenario

    Hi! I have been pondering a scenario involving a paradox with length contraction. I brought it up with my physics professor, and I somewhat understand what is supposed to happen, but I'm still somewhat confused, so I was wondering if you could help me figure out what is going on. In this...
  45. H

    Confusion over length contraction

    I understand why an object in a moving frame would be longer, but not why one in a stationary frame would be shorter. Wouldn't one in a stationary frame be the same as the object would be in the rest one? I understand the time dilation behind it, it's just that the rest of the reasoning makes no...
  46. A

    Distance dilation and length contraction

    I am trying to get another insight in what I think is currently for me a contradiction. I have searched the forums, and the web but come to the following assertion: The coordinate distance is the computation of the proper distance times the gamma-factor, while the "coordinate" length is a...
  47. J

    Length contraction/time dilation mutually exclusive?

    Hello Physics Forums! I'll try to cut right to the chase. I'm studying both length contraction and time dilation in my physics class and it seems these two occurrences are mutually exclusive. That is, in any given situation, only time will be dilated or length will be contracted. This doesn't...
  48. A

    Solving for Spiral Arc Length: A Scientist's Approach

    So here's a little background for the question: I have an arc that covers 3/4s of a circle (so it's not quite a full circumference) such that the radius from the center of the arc varies with respect to the angle (dR/d(theta)) (and it can be either positive or negative, but not constant). I am...
  49. Y

    Insulation Resistance in a coaxial cable of length L

    Homework Statement Determine the insulation resistance in a coaxial cable of length L, with conductivity, as shown in Figure assume that the current density J is radial direction. The Attempt at a Solution so i was wondering if this approach is correct, consider a sequence of...
  50. A

    The 'mechanism' of length contraction

    Let's suppose that we have a rod which is 2 meters long in its rest frame. Its rest length can be defined as a set of points which do not occupy the same place, measured in a frame which is at rest with the rod as a whole. Now if we travel relative to the rod, it gets length contracted, I...
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