What is Length: Definition and 1000 Discussions

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. P

    Exploring Quantum Entanglement Paradoxes: Length Contraction Clue?

    Could any of the experts here say whether there could be a clue here as to how to resolve the apparent paradoxes of quantum entanglement? I mean if a distance is reduced to zero, in a photon' s frame, then we should not be surprised that measurements made on one of a pair should be reflected...
  2. V

    Length Contraction & Galaxies: Time Dilation Adjustments

    Since galaxies are moving away from us, shouldn't they be contracted in length than they would be if they were at rest (wrt us)? In other words, are we observing increasingly shrunken galaxies as we look deeper into space? When measuring supernova light curves, we do adjust for time dilation...
  3. Dopplershift

    Are length and time Trade-offs in relativity?

    In special relativity, When an object travels at speeds near the speed of light, time slows down for the person on traveling at that speed, thus you gain more time. Also, you have length contraction. So my question is this, with the idea of 4-dimesional space-time, is what you gain in time...
  4. M

    Length Contraction of Bridge rotated 30 degrees

    Homework Statement A Train is driving with a uniformed velocity. v=1/4 c. The train is driving under a bridge, which is rotated \theta=30 degree in relation to the railway. The bridges length is 20 m long in a reference frame of the bridge (stationary bridge). Calculate the length of the...
  5. Anton Alice

    Dopplershift, using changing optical length

    Hello, again a simple question: consider a mirror, with a transparent layer (index of refraction n) of certain thickness on it. If a ray is reflected by the mirror, while the mirror is moved normal to the plane, then one could observe a dopplershift. But what happens if the mirror is fixed...
  6. Anton Alice

    Time dependent optical path length vs coherence

    Hello, I have a simple question. Suppose a perfect point source in front of a mirror. The virtual image of the point source acts like a second point source. Now let's look at the interference of the direct point source light and the virtual point source, at some position. Since the path...
  7. CMATT

    Wave Speed & Wavelength of Harmonic Oscillation on Slinky

    (a) A wave traveling on a Slinky® that is stretched to 4.5 m takes 2.6 s to travel the length of the Slinky and back again. What is the speed of the wave? For this one, I did v = d/t = 4.5 m / 2.6 s = 1.73 m/s Then I did v = (1.73)(2) = 3.46 m/s This is correct (b) Using the same Slinky...
  8. I

    Special Relativity - time dilation and length contraction

    Homework Statement The highest energy protons have gamma factors around ##1.0*10^{12}##. (a) Our galaxy has a disk diameter of 30 kpc, which is ##9.3*10^{20}m##. If a photon and one of these high energy protons start traversing the galaxy at the same time, by how long will the arrival of the...
  9. mhsd91

    Negative Critical Correlation Length Exponent (Nu)

    Hi everyone, I've encountered a curious problem I just can't figure out, and any input would be much appriciated!This is a personal project I'm working on, and as far as I know, there is no one else working on exactly the same. However, the computational study of critical phenomena is quite...
  10. D

    Relativity time dilation and length contraction

    Homework Statement can somebody help my figure out what t0 l0 l and t is? For instance: A girl an her dad are in an airplane, the girl starts running 20m in 8 seconds. There is also a boy standing beneath the plane (lets pretend that the airplanes floor is seethrough. Homework EquationsThe...
  11. P

    Calculate length of wire needed for solenoid

    Hi, I'm trying to calculate the length of wire that I need to wound a coil using a spool and wire of known dimensions. I was trying to use this converter but I'm not getting good results: http://www.had2know.com/technology/solenoid-coil-wire-calculator.html For instance: with a wire radius of...
  12. Buzz Bloom

    Q: Calculate average length of photon path: emit->absorb

    Assume a very large volume of a gas of a specific molecule. This molecule can absorb a photon and spontaneously quickly re-emit a photon of the same energy before the molecule can physically interact with another molecule. Therefore the energy of these photons never participate in the...
  13. Syed Khairi

    Optimum Length & Turns for a Search Coil of a Fluxmeter

    Hello, I'm investigating the relation of the length and number of turns of a search coil of a fluxmeter (measure magnetic flux). I got to an equation B= qR/nA where q is the quantity of charge passed through search coil R is the combined resistance of search coil and fluxmeter n is the number...
  14. NicolasPan

    Comp Sci Error while calculating arc length of curve in Fortran

    The program must calculate the length of the curve of ƒ=3.1*x^2-5.3/x between x=1/2 and x=3/2.The legth should be calculated as the sum of n line segments starting with n=1 and ending with n=20. I really can't find why the result I'm getting is wrong.Thanks in advance I am giving you the code...
  15. marif

    Correlation length from intensity profile

    I want to calculate the correlation length of a rough surface from the intensity profile of diffuse and specular reflectance from that rough surface. By fitting with the Gaussian curve, I calculated FWHM of the intensity profile.Generally it is considered thatcorrelation length = 2/FWHMI also...
  16. ptownbro

    Electron Energy Level Fall at a Given Wave Length

    1. Homework Statement An electron in the H atom falls from n=(?) to n=3. The wave length of the emitted photon is 1100 nm. From what level did the photon fall? Homework Equations Used the following to get the Energy. w = c / v E = h * v E = h * (c/w) w = lambda (couldn’t figure out how to...
  17. m4r35n357

    I Is it time to "retire" time dilation and length contraction?

    Considering the enormous number of questions posed on this forum and other places, the concepts seem fundamentally flawed (because both are formally and practically unobservable). The calculations themselves (together with the Lorentz Transform) are highly error-prone and the results misleading...
  18. T

    Time dependence of the Ratio Hubble length to scale factor

    Let's assume a universe like ours which after inflation expands decelerated and accelerated thereafter. How will the ratio Hubble length ##1/H## to scalefactor ##a## evolve over time? And how could one calculate the time dependence of this ratio. Any help appreciated.
  19. J

    Calculating Jean's length for neutral hydrogen cloud

    Homework Statement What is the Jean's length in parsecs for a typical neutral hydrogen cloud, which has a density of n(H I) ~10^8 atoms/(m^3) and a temperature of 100K? Homework Equations jean's length = sqrt[(15*K*T)/(4pi*G*u*p)] where: 'K' is the Boltzmann constant 'T' is the temperature of...
  20. J

    Length of a line between origin and edge of a circle

    For a circle with radius R centered at R along the X-axis so that the edge of the circle touches the origin, what is the length of a line drawn between the origin and an edge of the circle in terms of the angle between that line and the X-axis? This isn't a homework problem, just something I'm...
  21. I

    A rod in free fall with varying length

    Suppose you have a weightless rod with at the endpoints two masses. This is a special rod whose length varies in time as a function L(t). If I consider this rod in free fall my intuition is that this rod will rotate for suitable L(t). However, I want to write down the equations of motions for...
  22. A

    Question about Length of Action of Involute gears

    Homework Statement Length of action Z(Length of line of action) is Z=\sqrt{(r_{p}+a_{p})^{2}-(r_{p}cos\phi )^{2}}+\sqrt{(r_{g}+a_{g})^{2}-(r_{g}cos\phi )^{2}}-Ccos\phi How can I drive it? Homework EquationsThe Attempt at a Solution
  23. Kompewt

    Focal length of thin converging lens

    Homework Statement An outdoor security camera has a simple lens with focal object length fo = 6.00 cm and perfectly focuses the image of a bird onto its detector located 9.00 cm away from the lens. The animal then flies away from the lens and the new focal distance is 8.00 cm. (a) How far did...
  24. N

    No mass for mass per unit length

    Homework Statement A ski gondola is connected to the top of a hill by a steel cable of length L and radius R . As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took T seconds for the pulse to return. What is...
  25. T

    Length of ramp to stop vehicle

    A Ford Ranger with a mass of 2430 kg is traveling at a velocity of 85 mph down a mountain road. The brakes fail and the driver elects to use a "run away" truck ramp to stop the vehicle. The ramp has an incline of 15.0 degrees. What is the minimum length the ramp must be in order for this...
  26. T

    Does Length Contraction affect measured velocity?

    First, let me clarify if my understanding of length contraction is correct. Is it accurate to say that relativistic velocities not only affect the measured length of an object in the direction of motion, but also the distance to the object from an observer in the direction of motion? For...
  27. S

    How would you calculate the length of a year on a planet?

    Homework Statement How would you calculate the length of a year in Earth years on a hypothetical planet? (given the mass + radius of the planet) I understand Kelper's law is used somehow, but is orbital velocity needed?
  28. DrClaude

    Understanding Magnetic Field in Length Gauge

    I've having trouble understanding one of the consequences of using the length gauge. The length gauge is obtained by the gauge transformation ##\mathbf{A} \rightarrow \mathbf{A} + \nabla \chi## with ##\chi = - \mathbf{r} \cdot \mathbf{A}##. Starting from the Coulomb gauge, we have $$...
  29. W

    [SQL] Rule of Thumb for Queries: Length of String vs Speed?

    Hi all, Just curious as to whether it is a good rule of thumb ( though not an actual rule) that out of two effective queries (i.e., two queries q1, q2 that return the desired result) , the query that is shortest as a string, i.e., has the fewest total words, will run faster? I understand the...
  30. astrololo

    The natural length of a spring

    Homework Statement A block is fixed on the extremity of a mobile ideal spring that is horizontal and which has the other side of it fixed (Non mobile). When the length of the spring is 50 cm, the block has a force of 5 N on the right; When the length of the spring is 80 cm, the block has a...
  31. Ian Limjap

    Heat transfer -- length of the tube required to heat water....

    Homework Statement Water flowing at the rate 3.5 kg s−1 through a tube with an inner diameter of 2 cm is to be heated from 20 to 40◦C. If the tube wall temperature is maintained at 90◦C, determine the length of the tube required. Homework Equations Q'=Cp*m*(DeltaT) Q=2*pi*r*L*Q' The Attempt...
  32. P

    Equivalent focal length of two lenses

    Homework Statement Two thin lenses have focal lengths of -5cm and +20cm. Determine their equivalent focal lengths when (a) cemented together and (b) separated by 10cm. Homework Equations ##\frac{1}{f_{eq}}=\sum_{n=1}^k \frac{1}{f_n}## The Attempt at a Solution So the first part was easy since...
  33. R

    What is the formula for spacing wire around a conical Christmas tree?

    So here's my problem. For the past few years i have built a very large christmas tree in my front yard. 1200 lights or so... looks awesome it is 6m high, a 2m ring at the bottom and is a constant cone shape to the top point. To install the lights i start from the bottom and progress to the top...
  34. R

    Calculating load per unit length

    I am having the hardest time calculating q, the load per unit length. This question is in relation to my previous question I posted here. I have a cylinder laying horizontally that is fixed on its ends. The cylinder is filled with water. To calculate the deflection I am simplifying the problem...
  35. D

    Planning an experiment to show resistance is proportional to length....

    Homework Statement My task is to plan and carry out experiments which show that the resistance of a conductor is proportional to the conductor's length. I have access to the following equipment: http://imgur.com/a/GuqUX Amperemeter, voltmeter, electricity, ruler som other werid things and...
  36. adi adi

    Arc Length Circle Quadrant 1: Solve ∫√(1+(dy/dx)2)dx

    Homework Statement find the arc length of a circle in the first quadrant with an equation x2 + y2 = a2 Homework Equations arc length = ∫ √(1 + (dy/dx)2) dx The Attempt at a Solution i got stuck on how to solve the integral
  37. C

    Length of Sides of a clock

    Homework Statement I'm trying to create a clock face in Python and can't quite figure out where I'm going wrong. Statement: For a clock of radius 100 units, what will be the distance between two adjacent numbers? If a turtle walks along the path joining two adjacent numbers, by what angle...
  38. T

    Calculate mean path length of a magnetic circuit

    Given this magnetic circuit: With these dimensions: With this equivalent circuit: If I am using F = HL to calculate the mmf drops in RcoreAB(see equivalent circuit) and RcoreBCDA(see equivalent circuit) then how would I calculate L in the formula ?
  39. brotherbobby

    Proving "Rotation Matrix is Orthogonal: Necessary & Sufficient

    I'd like to prove the fact that - since a rotation of axes is a length-preserving transformation, the rotation matrix must be orthogonal. By the way, the converse of the statement is true also. Meaning, if a transformation is orthogonal, it must be length preserving, and I have been able to...
  40. J

    Energy unit to kelvin, seconds, density, length

    Homework Statement Convert 1 ##Gev## to Kelvin, and convert ##GeV^{-1}## to meters, seconds, and convert ##GeV^4## to density ##(kg/ m^3).## Homework Equations natural units ##c=h=k_B=1## The Attempt at a Solution I know to convert energy to meters, I can use ##\lambda =hc/E##, I get the...
  41. O

    De Broglie wave length, average electron energy and momentum calculation

    Homework Statement Calculate the average electron energy of an electron in an electron gas at thermal equilibrium. Temperature is 315K. Calculate the average electron momentum. Calculate the de Broglie wave length of the electron Homework Equations 3*kT/2 The Attempt at a Solution [/B] Part...
  42. 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...
  43. 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 ??
  44. 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...
  45. 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...
  46. 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...
  47. 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...
  48. 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...
  49. 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...
  50. 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
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