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. Amirul96

    Calculate Pipeline Length: Pressure Drop & Parameters Explained

    Hi, I want to ask how to calculate the length of pipeline..From what i have searched, one of the way to calculate it is from the equation of pressure drop. However, it seems i don't have info about the pipe length and pressure drop (it means i need to calculate it). Is it possible to calculate...
  2. Leo Liu

    Is the length of the arm r in a polar coordinate a function of the angle?

    My textbook says ##\vec r (\theta) = r \hat r (\theta)##, where ##\hat r (\theta)## is the terminal arm (a position vector in some sense). It can be seen that both ##\vec r (\theta)## and ##\hat r (\theta) ## are function of ##\theta##; whereas, the length of the vector ##r## is not. I...
  3. Flying_Dutchman

    I Length Contraction: Traveling in a Space Ship

    Suppose I'm traveling inside a spaceship at speed comparable to light between two points A and B. According to me the distance between the two points will be shortened due to length contraction. But actually my spaceship passes through every point between A and B so the distance measured by...
  4. E

    B Why Do We Draw Dimensionless Unit Vectors in Diagrams?

    A unit vector, ##\frac{\vec{v}}{|\vec{v}|}##, has dimensions of ##\frac{L}{L} = 1##, i.e. it is dimensionless. It has magnitude of 1, no units. For a physical coordinate system, the coordinate functions ##x^i## have some units of length, e.g. ##\vec{x} = (3\text{cm})\hat{x}_1 +...
  5. PainterGuy

    MATLAB Matlab command question: length max([x+y-1,x,y])

    Hi, I'm not sure if I should be asking this but I couldn't make sense of the following Matlab command: length max([2+3-1,2,3]). The result is "16". I couldn't the operation of this command and why it produces the result of "16". Could you please help me with?
  6. P J Strydom

    B Length contraction and Time dilation calculation

    I was absent for a while due to personal constraints but I did keep myself busy with the Time dilation equation some member sent me a while back. I decided to set a time limit for myself to learn and understand time Dilation and length contraction, which must be before December 2020, or I will...
  7. J

    MHB Finding the Length of a Dividing Line in a Trapezoid

    A trapezoid with a base of 100m and 160m is divided into 2 equal parts by a line parallel to the base. Find the length of dividing line.
  8. E

    The maximum length that a spring can stretch in reality

    In detail, I came up with 424m for the stretched length of a spring in order to change the mass of an object by 10^-9kg which originally was 1 kg. Problem said, "is it feasible?" In my opinion, there is no spring that can be stretched for this long, so it is not feasible. However, I'm not sure...
  9. anemone

    MHB Length of Shortest Side In a Triangle

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  10. Uchida

    I Length Perception & Spacetime Warp: Is it Warped?

    If I make two rods with 1 meter length here on the surface of earth, and send one of them near a black hole that is at rest relative to earth, placing it there with its length alligned in the radial direction of the black hole, would I see the rod close to the black hole with a length shorter...
  11. G

    B Length Contraction Thought Experiment: Spot Mistake/Wrong Assumption

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  12. jeremiahrose99

    I Solution to the 1D wave equation for a finite length plane wave tube

    Hi there! This is my first post here - glad to be involved with what seems like a great community! I'm trying to understand the acoustics of a finite plane-wave tube terminated by arbitrary impedances at both ends. So far all of the treatments I've managed seem only to address a different...
  13. Tony Hau

    How to find the length of a vector expressed in polar coordinates?

    The velocity of a particle below is expressed in polar coordinates, with bases e r and e theta. I know that the length of a vector expressed in i,j,k is the square of its components. But here er and e theta are not i,j,k. Plus they are changing as well. Can someone help convince me that the...
  14. R

    B Is There a Connection Between Planck Length and Planck Time in Relativity?

    If Planck length is 10^-35 of a meter and Planck time is 10^-43 of a second, doesn't that mean that as the relative speed gets closer to the speed of light and time acceleration and length contraction are happening, they are happening at a different rate, since length contraction has to reach...
  15. alexm

    Motion of rotating rig, find the angle variation with control rod length

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  16. George Keeling

    I Comparing Planck's Mass, Length, Time and Energy

    Sean Carroll gives the Planck's set of four dimensioned quantities: Planck's mass, length, time and energy. I wanted to compare them with actual things.\begin{align} m_p=\sqrt{\frac{\hbar c}{G}}&=2.18\times{10}^{-8}\rm{kg}&\rm{{10}^{7}\ E. coli}\phantom {100000000000000000000}&\phantom...
  17. D

    How Many Seconds Make Up Eternity in The Shepherd Boy?

    I have read a short story by the Grimm Brothers, named "The Sheperd Boy" and there is a riddle that sounds like this: So we have a mountain made of pure diamond, and it takes 1 hour to climb it, 1 hour to go around it and 1 hour to go down into it (I assume from its peak to its base). And...
  18. Adrian555

    A Geodesics of the 2-sphere in terms of the arc length

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  19. Mikkel

    Python Numerical modeling of a glacier's length -- Coding error(s)

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  20. B

    Balance length for a potentiometer circuit

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  21. S

    Correct statement regarding the load vs length graph of a rubber band

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  22. chriscarson

    How can you calculate change in length without force and area units?

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  23. chriscarson

    What is the Relationship Between Strain and Change in Length in Hooke's Law?

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  24. 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)
  25. P

    Understanding Gauss's Law in Cylindrical Shells of Non-Infinite Length

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  26. Charlie Cheap

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  27. Saracen Rue

    I How to find the maximum arc length of this equation?

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  28. Edwin1974

    I True length of sidereal year in 6000 b.c.e.

    Hi there :smile: Anybody out there able to explain to me how to calculate what the true length of a sidereal year was about 6000 years ago ? Kind Regards Edwin.
  29. M

    B Help! Solving Einstein's Length Contraction Problem

    I have to admit that my "best" math days are long gone. That said, I wonder if anyone can help me? I'm stuck in part 1 of Einstein's book on 'Relativity, The Special & General Theory: The behaviour of measuring rods & clocks in motion', specifically on the second equation : √(1-v^2/c^2) used to...
  30. marielescobal

    Calculation of bond length using Raman spectra

    Hi, I really need your help. Suppose I have a Raman spectra of a hydroxyapatite, how do I calculate the bond length from the spectra? I've been trying to understand the concept of Badger's rule but I really cannot understand. Please help.
  31. jnorman34

    I Planck Length & Singularity: Point or Sphere?

    Since Planck length is a distance unit of space-time which cannot be further subdivided, would that not imply that an electron, or singularity, or any other point particle cannot actually be a “point”, but must rather be a spherical volume with a Planck length diameter? i realize this may well...
  32. G

    MHB Calculate the length of the fourth side edge.

    The three lateral edges of a pyramid based on a square are 6016, 2370 and 4350 long. Calculate the length of the fourth lateral edge. We assume that edges 6016 and 2370 extend from the opposite tops of the base.
  33. C

    Optics focal length and optical power Question

    1/f = 1/dₒ + 1/dᵢ = 1/1.0 + 1/0.33 = 4.03 m (focal length) Power: 1/4.03 m or 0.248 (0.25) *around to the2 decimal points? or leave it as a fraction? ((Did I do this correctly? I am not sure if this is correct and is it okay to be in meters not centimeters?)) Please let me know!
  34. O

    Diffraction pattern due to a lens with focal length f

    Suppose one light up with a laser on a grid with grid constant g. The grating is followed by a focusing lens with a focal length of f. In the focus (or immediately in front of it) the maxima have a distance d. How large was the distance of the maxima immediately after the grating? scheme: Laser...
  35. M

    Draw and find the Length of x=t+4 , y=t2+1

    Hi, my try: Do you agree with me? Thanks
  36. B

    Length of a string over a 2 pulley system

    Hello all, I am working on a lab report for physics, and am a bit stuck on one aspect. The basic layout of the pulley system is attached. (This is a diagram I made, so if there are any inaccuracies in this one either, I am happy to fix it. So, I mostly understand the lab. My TA said, though...
  37. B

    Determining Radiation Length in Air

    The radiaton length for air is about $$X_0 = 30420cm$$. This is the length at which the electron has decreased to 1/e of it´ s initially value. I also know that the maximal value of interactions for a specific energy is given by $$ n_{max} = \frac{ln(\frac{E_0}{E_c})}{ln(2)} $$, where E_c is...
  38. N

    B Clarification on Length Contraction

    The rule for length contraction seems to be inconsistent with the lorentz transformations for distance. The rule for length contraction is: ## x = \gamma x ^\prime ## and ## x ^\prime = \frac {1} {\gamma} x ## But the lorentz transformations for distance are ## x = \gamma x ^\prime + \gamma vt...
  39. B

    Propagation of Error for Focal Length

    Homework Statement: Propagation of Error for Focal Length Homework Equations: f = (s'*s) / (s' + s) In my lab, we had to calculate the focal length of a lens based on object distances (s) and image distances (s') that we measured. The object distances were measured with an uncertainty of...
  40. B

    I Time Dilation, Length Contraction & Massive Bodies

    For instance, if a stream of muons were released from a box near a massive object and traveled on a straight path slowly (at a non-relativistic velocity) away from that object, a faraway observer would notice that the particles would take longer to decay than a muon typically would in empty...
  41. S

    B Length Contraction in Accelerated Frame

    I was wondering, would there be a length contraction (or expansion) in the z and y axis' if an object was accelerating in x axis? I know that in special relativity there is no deformation in the y and z axis' if the object is moving in the x axis. I was looking a this paper for clarification.
  42. Z

    Switching speed of ICs vs gate length

    Why is it that the smaller the gate length, the higher the max operating frequency becomes? In particular, I think I saw somewhere that a 6 um gate length, seems to limit ICs to 100kHz, where as 1 um is around 1MHz (all rough ball bark numbers, and can be persuaded otherwise). Was wondering if...
  43. D

    Physical optics -- counting interfence fringes to measure a length change

  44. A

    I How time dilation is a permanent change and length contraction not?

    Comparing high precision atomic clocks, one flying in a airplane and one on the ground had demonstrated permanent time dilation presumably due to special relativity (speed) and/or general relativity (gravity) . While similar experiment with a ruler would demonstrate length contraction only...
  45. ColdheartedGod

    B Schwarzschild radius of an object is smaller than Planck length

    I had this idea when some people said that LHC can produce black hole. Based on the calculation of Schwarzschild Radius, any mass than 9.375×10^7 kg have a Schwarzschild radius smaller than the plank length. Particles inside LHC or other particle accelerator have clearly radii smaller than that...
  46. Telemachus

    Magnetostatics and Ampere's law on a finite length wire

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  47. U

    Understanding the Math Behind A: Minimum Length of Plane Mirror

    15. What is the minimum length of a plane mirror in order for you to see a full view of yourself? A 1/2 your height B 1/4 your height C 3/4 your height D your full height Q Why is answer of A given is the correct one, I understand pictorially how it is, since visually if you were to draw a...
  48. S

    B Can a wavelength be smaller than a Planck length?

    According to this article https://physics.stackexchange.com/questions/321229/why-dont-we-have-proton-neutron-microscopes, they seem to hint that heavier objects have a shorter wavelengths and give better resolution. If I kept increasing the mass of a particle and kept it's speed at .9c would I...
  49. DaTario

    A Increase of coherent length in stimulated emission

    Hi All, When I teach the basic structure of a laser setup, stimulated emission appears as a fundamental phenomenon. But in no reference I found a description that could account for the increase of coherent length of the EM laser field. According to my knowledge, one photon typically doesn't...
  50. D

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

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