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. K

    Effect of golf shaft length and flex

    Hi, I'm wondering about the effect of the shaft flex on the impact velocity between the club and the ball. I understand that as I swing down the golf club, the shaft flexes and the club head lags behind. Near the end of the point of impact, the shaft bends forward. Intuitively, I would think...
  2. M

    MHB Help finding a scaled down length? Easy for smart people, unlike me :-)

    Hi guys, I need to figure out the length of the side of a roof on a scaled down model. The picture below shows what I’m trying to calculate. The real house has a central support pole and it is 10 metres high, with length of the side of the roof at 14.67… metres. If I was to make a scaled...
  3. B

    Understanding the Human Eye: Exploring Focal Length and Retinal Distance

    I never could understand this: the lens focuses light onto the retina so shouldn't the distance between the lens and the retina be the focal distance? It does not seem to be the case while I was trying to look around for the answer on the internet. And since light is focused on the retina, the...
  4. S

    How Does a Thin Film Alter the Optical Path Length?

    Homework Statement A thin film of dielectric material of refractive index 1.455 and thickness 6.50 mm is now placed over one of the slits (say the right-hand one). By how much will this change the optical path between the slit and the centre of the screen? Homework Equations Optical Path...
  5. B

    Design a coil with a variable pitch but a constant length?

    I believe what I am attempting to do is not possible but here goes. I want to design a fixed overall length coil which I can manually adjust the pitch on. Optimally one would be able to grab the coil and by twisting it in place would be able to change it's pitch by changing its diameter but not...
  6. M

    Focal length of lens at border of two liquids

    Homework Statement I need to find optical power (reciprocal focal length) of this system with thin lens Homework Equations I tried to solve this using spherical diopter equation n1/a+n2/b=(n2-n1)/R where a is object distance and b is image distance The Attempt at a Solution equation for...
  7. J

    Help please -- convex lens problem and focul length

    Homework Statement Suppose the convex lens is placed at the 49.4 cm mark, and an image forms on the screen at the 70.5 cm mark. Find: A) The focal length of this lens: ____ cm B) the absolute value of the magnification of this lens: ________ C) the height of the image: ________cm Homework...
  8. U

    Number of phonons - Which length should I use?

    Homework Statement (a) Find debye frequency. (b) Find number of atoms. Homework EquationsThe Attempt at a Solution Part(a) [/B] Density of states is given by g(\omega) = \frac{3V\omega^2}{2 \pi^2 c^3} = N \left[ \frac{12 \pi \omega^2}{(2\pi)^2 n c^3} \right] = 9N \frac{\omega}{\omega_D^3}...
  9. S

    Calculating Focal Length of 1D Fresnel Lens

    Homework Statement Calculate the focal length of 1D Fresnel lens, whose transmittance is given as $$T(\xi)=\frac 1 2(1+\cos(\alpha \xi ^2)).$$ Homework Equations Anything you wish The Attempt at a Solution I have no idea. I tried to use the equation for diffraction image $$u_p=C\int _0...
  10. U

    What does this length represent?

    I was doing some calculations earlier and tried the ratio between a metal's fermi temperature ##T_F## and debye temperature ##\theta_D##: \frac{T_F}{\theta_D} = (6 \pi^2)^{\frac{1}{3}} \left( \frac{\lambda}{a} \right) where ##\lambda = \frac{\hbar}{2 m_e c}## and lattice spacing is ##a##. I...
  11. E

    Length contraction test in electrical circuits

    As I am sure everyone is aware, there are still folks who don’t believe SRT and GRT. While 99.9% of them are nut-jobs, there is at least one that I respect – Tom Phipps specifically. I am not familiar with any of his writing before the advent of the GPS satellites. In any case, he now accepts...
  12. A

    Length of Wire Effect on Current and Inner Electric Field.

    >Two wires of the same material are both connected to a 9-V ideal battery. They have the same cross section area but wire 2 is twice longer than wire 1. Compare the following quantities by answering if the quantity for wire 1 is smaller, equal or greater than the same quantity in wire 2. > -...
  13. M

    Determining the focal length of a gradient index lens

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  14. H

    Calculate Length of Shadow from Two Street Lamps

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  15. U

    Pressure drop per unit length of the pipe

    MODERATOR NOTE: THERE IS NO TEMPLATE BECAUSE THIS THREAD WAS ORIGINALLY MISPLACED IN A NON-HOMEWORK FORUM Viscous liquid (ρ = 1460 kg/m3, μ = 5.2×10−1Ns/m2) is pumped through a smooth pipe with a 0.1 m diameter, at a rate of 5×10−2m3/s. Using your Fanning friction factor versus Reynolds Number...
  16. M

    Charge per unit length for a charged ring

    Homework Statement If you have a ring of charge, is it valid to say lambda = Q/L, or is it lambda = dQ/dL? Homework EquationsThe Attempt at a Solution
  17. L

    Heat and increasing a rod's length

    Homework Statement A 1.0m long rod of metal has a diameter of 0.75 cm. This metal has a coefficient of linear expansion α = 4.8 × 10−5 1/K , a density of 9.7 × 103 kg/ m3 , and a heat capacity of 390 J/K . How much energy needs to be added as heat to increase the length of the rod by 7.5 × 10−3...
  18. B

    Distance from the object to objective lens and focal length

    Homework Statement 1) The medium-power objective lens in a laboratory microscope has a focal length fobjective = 3.70mm . If this lens produces a lateral magnification of -42.5, what is its "working distance"; that is, what is the distance from the object to the objective lens? 2) What is the...
  19. Vinay080

    Is the Length of an Arc Equal to its Straight Line Distance?

    Premise 1: Line is composed of points. Premise 2: Each point is associated with specific co-ordinates (x,y). Premise 3: Lines of equal length have equal number of points. Lines of greater length have greater number of points. Premise 4: Each value of x in the function f(x) gives a single...
  20. Vinay080

    What is the problem with the argument for the diagonal length of a square?

    Premise 1: All straight lines have the value of length equal to the numerical value of the end point, provided the starting point of the line is assigned the numerical value zero. Premise 2: No point can be assigned the value y.xxxxxx... or y.abcdef...(Example: 8.9999... or 8.39465..). We...
  21. B3NR4Y

    Finding New Resistance of a Length of Wire

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  22. V

    Understanding length contraction in SR

    I seem to be missing something fundamental about length contraction in SR. I would be grateful if someone can point out the error in the following logic. Suppose I have a method to measure lengths of objects in the following manner: I place a mirror at the right end of the object, send a light...
  23. A

    How does length affect the bending of a horizontal beam?

    Homework Statement We were shown this image ^ We were later told that it is suggested that the depression (y), is directly proportional to the length of the beam cubed (L3). We were asked to give reasons why this is so. EDIT: The 1kg mass is placed at L/2 Homework Equations y is directly...
  24. S

    Calculating the distance between the optical center and focal length

    -Hello everyone. At school, I studied about convex lense and concave lense. They are very interesting, we learned about how lights would be after going through the lense. But what I want to ask is how we can calculate the distance between optical center and focal (I means focal length). Focal...
  25. K

    Understanding Scattering Length in Atom Interaction: A Comprehensive Guide

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  26. W

    Finding the maximum displacement of a vertical spring using energy conservation

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  27. R

    Focal length of 2 lenses to reduce laser beam diameter

    I need to reduce the beam diameter of a laser I am using. I plan to do this by first passing the beam through a positive spherical lens with focal length f1 and then a negative spherical lens with focal length f2 and f2 < f1. By placing the lenses so that the two focal points overlap I will have...
  28. A

    MHB Calculating the length of an arc inside a circle

    A sad and strange image, I know, but better than none at all. What you see is a stake I'm trying to model using CAD software. With the dimension given (5 inches--in case it's not clear, the distance from the top of the equilateral triangle that encloses this shape to the midpoint of the red arc)...
  29. S

    Length of a Steel Wire (Standing Waves)

    Question: A copper wire and steel wire with identical diameters are placed under identical tensions. The frequency of the third resonant mode for the copper wire is found to be the same as the frequency of the fourth resonant mode for the steel wire. If the length of the copper wire is 3.44 m...
  30. P

    Finding Arc Length of a Curve: Using ##dx## and ##dy##

    The arc length of any curve defined by ##y = f(x)## is found as follows: $$ds = \sqrt{dx^2 + dy^2}$$ $$ds = \sqrt{dx^2(1 + {\frac{dy}{dx}}^2)}$$ $$ds = \sqrt{dx^2} \sqrt{1 + [f'(x)]^2}$$ $$ds = \sqrt{1 + [f'(x)]^2} dx$$ Isn't ##\sqrt{dx^2}## equal to ##|dx|##, and not ##dx##?
  31. Ookke

    Direction of length contraction in combined motion

    Left picture: There are two moving rails that cross at center (red dot) which itself doesn't move. The rails speeds are close to c, so that they are length contracted by factor 10 (roughly 0.995c). There are markings in rails at interval 10 length units in rails rest frame, so the interval is...
  32. Albert1

    MHB Find Length of Arc EF in Triangle ABC

    $\triangle ABC$,with $\angle A=70^o,$point $O$ is the midpoint of segment $\overline{BC}=12$ circle $O$(wth center $O$ and radius $\overline{BO})$, meets with $\overline{AB},\overline{AC}$ at points $E$ and $F$ respectively please find the length of arc $EF$
  33. M

    Need to find the length and deflection of bending element

    Hi, I have a task and don't know the good solution. (I add the picture of my task.) I need to find the right length and deflection and to check if the results didn't exceed the allowable stress. I know the value of "q" (force). Also I could choose myself the lenght, but I need to check, if my...
  34. Robsta

    Calculate focal length of lens by diffraction.

    Homework Statement A collimated beam from a white-light source is incident normally on a transmission grating with 500 lines per mm. The transmitted light then passes through a lens which is used to project the visible (380–780 nm) spectrum of the light source on to a strip of photographic film...
  35. A

    Focal length of a distorted window

    Homework Statement What is the focal length of a dewar window distorted by a pressure difference? As a result of the pressure difference, the radius of the first surface of the window is R1 = 100 meters. The window is 3 mm thick, with an index n = 4 at l = 4 um. Homework Equations I think I...
  36. Pull and Twist

    MHB Solve for the length of a rope when you know the work required to reel it in.

    Hey guys, I'm currently working a take home problem that's a little different then what I have been practicing in my Calc. book. I thought I set it up correctly, but yet I am not getting the correct answer. Can someone show me where I am going wrong? This is what I have so far.
  37. B

    Interaction Energies and Debye Length

    Homework Statement (c) (i) Neglecting hydrogen-bonding, calculate the interaction energy between (i) H3O+ and H2O and (ii) H3O+ and H3O+ , if each pair is separated by 0.3 nm and assuming that the aqueous solvent can be treated as a medium with constant relative permittivity. Using your result...
  38. B

    For a circular motion period to length and mass question.

    Homework Statement [/B] We are given a graph, with the information of the period, and the radius of the string. We amassed this data on our own. The graphing of it is quartic, but we have to make it into a linear graph?Homework Equations N/A The Attempt at a Solution [/B] First we tried to...
  39. T

    Length of a missing side no angle given :(

    I'm given an irregular shaped plot with 3 sides, and have been asked to find the fourth missing side, no other detail is given. Is it possible to find the missing side? If so, then how? Here is what it looks like roughly:
  40. RJLiberator

    Tricky integral from calc 3 Arc Length question

    Homework Statement Find the arc length of: r(t)=<e^t, e^(-t),sqrt(2)*t> from 0 to ln(2) Homework Equations L=integral from a to b of the magnitude of r'(t) The Attempt at a Solution Okay, this was an Exam question, the one exam question that I could not get on our Calc 3 exam. This breaks...
  41. H

    Order C-I, C-Br, C-Cl, & C-F Bonds by Length

    Arrange these bonds in order of increasing bond length. C-I, C-Br, C-Cl, C-F Is there a way to figure this out without drawing molecular orbital diagrams and determining the bond order?
  42. siddharth23

    Minimum engagement length of a bolt

    Hey guys. Could anyone give me an what the criteria for minimum engagement length of a bolt is? The bolt I'm using is M10x1. Thanks!
  43. jasonleroy

    Phase Delay Changes with Physical Length Changes

    Hopefully I can word this correctly. Consider viewing S11 of a short on a smith chart. It starts at the left and moves clockwise around the edge. If you then add a small length of line between the reference plane and the short, the phase angle wraps further around the outside in the clockwise...
  44. T

    MHB Length of a side, possible triangle side

    I have one question from my mathematics for machine technology book that has me stumped as well as my Father in-law, sister in-law and my accountant friend. I wasn't sure if I was supposed to create a right triangle and use A² + B² = C² Problem 18. B...
  45. Prashasti

    Finding Focus Length in Broken Double Convex Lens

    Homework Statement A thin double convex lens of focal length f is broken down into two halves at the axis. The two haves are then combined, as shown in the figure. What will be the focal length for the arrangements...
  46. P

    Solving Compound Microscope Lens Length Problem

    Homework Statement The barrel of a compound microscope is 15.9 cm in length. The specimen will be mounted 1.17 cm from the objective, and the eyepiece has a 5.00 cm focal length. Determine the focal length of the objective lens.Homework Equations I am using the mirror equation. The Attempt at...
  47. M

    Metal bar/tube strength by length and thickness.

    Hello guys I am working on designing somethings and I am using metal tubing. I do not know what type of metal tubing I am going to use this all depends on the math after I work my problem out. I am not sure what formulas to look up or what strength test I need to look up. For example if I have...
  48. H

    Why never any length expansion under Lorentzian Relativity?

    Lorentz believed in the ether, and developed his version of Relativity Theory based on interactions of moving charged particles (electrons, specifically) with the ether. What I don't understand is how one always gets length contraction for movement in an inertial system moving with respect to...
  49. A

    Finding Specification for Heating Nichrome Wire

    hello,If anyone of you help me in finding specification(diameter of nichrome wire required) for a 2 m nichrome wire to heat up to 65 degree Celsius .Voltage applied is 12 v. I want to use it by coiling it to cylindrical mica sheet to make a smaller heating product.Temperature should not exceed 65.
  50. RJLiberator

    Arc Length in Three Dimensions Question

    Homework Statement Find the arc length of r(t)= <tsin(t), tcost(t), 3t> from 0 to t to 2pi (inclusive) Homework Equations Integral from 0 to 2pi of the magnitude of r'(t) dt The Attempt at a Solution 1. Must find the derivative of the function. Using the product rule a few times, the...
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