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).

View More On Wikipedia.org
Recent contents Top users
  1. P

    How is the focal length of an objective calculated?

    Hi, I am using an objective lens to illuminate my object by a collimated beam. The magnification and NA is available on the objective. How can I calculate the focal length from this information? The objective is not infinity corrected. Thank you
  2. U

    MHB Wire Length w/ 0.068 Ohms & 2.8mm Diameter: ~11.56 ft

    The electrical resistance of a wire varies directly with the length of the wire and inversely with the square of the diameter of the wire. If a wire 50 feet long and 2 millimeters in diameter has a resistance of 0.265 ohms, find the length of a wire of the same material whose resistance is 0.068...
  3. Q

    How to measure the length of metal sheet coil?

    Hi everyone, I have been trying to find an equation to measure the length of a coil. The coil is a metal sheet that wraps around the loops as it creates. It looks like a roll of tape. I have been using two different formula, but it is not giving me the right results. 1. L = 0.065449 (OD^2 -...
  4. Grinkle

    Plank length / space expansion question

    Do models of the expansion of space-time manifest that expansion by an increase in Plank-length, or by additional Plank-lengths appearing in between existing particles? I think it must be the latter because the Plank-length is not an empirically measured value and the constants it derives from...
  5. C

    Day length and orbital period + apparent luminosity

    Homework Statement I am actually an MD student, but I have been working on writing a novel. I wanted to create exoplanets that were suitable for human habitation, and I had a guy help me over the summer come up with plausible numbers for a variety of variables. Where I am having trouble now is...
  6. T

    Uniform rope of length L and mass M, work to pull it up.

    Homework Statement A uniform rope of length L and mass M is held on a frictionless table by a force F. One fourth of its length (¼L) is hanging over the edge. Find the work required to pull the hanging part back onto the table. Homework Equations W=Fd The Attempt at a Solution I have no...
  7. gfd43tg

    Length of slab for infinite temperature

    Homework Statement An explosive is to be stored in large slabs of thickness 2L clad on both sides with a protective sheath. The rate at which heat is generated within the explosive is temperature-dependent and can be approximated by the linear relation ##\dot Q_{gen} = a + b(T - T_{\infty})##...
  8. Q

    Length contraction and time dilation in spacetime

    Observers that pass each other with a relative speed close to the speed of light will observe length contraction and time dilation at the other observer. In a spacetime diagram, this would be represented by two worldlines making an angle, right? Some textbooks suggest that some of the length...
  9. G

    Solving Physics Homework: Spring Length & Work Done

    Homework Statement A vertical spring is 10.0 cm long when supporting a 20.0 kg mass, and it is 12.0 cm long when supporting a 32.0 kg mass. Assume the stretch is linear with the load. a) What is the length of the spring with zero load? (0.06666667) b) How much work would be done in...
  10. A

    Simple Harmonic Motion equation question: which length and why

    Homework Statement I solved this physics question, but I am unclear about why Amplitude was the amount the spring was stretched by (which should be the new equilibrium point), instead of the amount the person pulled the mass down by (which should be the amplitude). Can anyone help? On your...
  11. mesa

    How to figure out tube length to heat Argon to 700 C from ambient

    If one were trying to heat Argon gas from ambient (~20oC) through a mild steel tube of some diameter 'd' how long would it need to be? Additional unknown includes flow rate of Ar gas so some general function would be adequate. Unfortunately my thermo-book is limited and does not go into enough...
  12. chwala

    Finding the length and width of rectangle

    Mod note: Thread originally posted in a technical math section, so is missing the homework template. I am trying to solve this problem it states as follows "A piece of wire 24 cm long has the shape of a rectangle. (a) Given that the width is W cm, show that the area, A cm^2 of the rectangle is...
  13. B

    Speed of light and planck length

    I was thinking about the special theory of relativity and how as one approaches the speed of light, ones length contracts. what I would like to know is: If I had an object and I accelerated it towards the speed of light and it contracts in the direction of travel, what happens when it reaches...
  14. Ookke

    Length contraction in diagonal motion and something strange?

    Object A goes horizontal line and object B diagonal line in 45 degrees angle (Fig 1). A and B have the same velocity ##v## in x-direction. In y-direction, B has velocity ##v##, A has none. The magnitude of ##v## is not very important, but the total speed of B must be below ##c##. In their own...
  15. R

    How does one get time dilation, length contraction, and E=mc^2 from spacetime metric?

    How does one get time dilation, length contraction, and E=mc^2 from the spacetime metric? Suppose all that you are given is x12 + x22 + x32 - c2t2 = s2 How do you derive time dilation, length contraction, and E=mc^2 from this? What is the most direct way to do this?
  16. admbmb

    Conceptual trouble with derivatives with respect to Arc Length

    Hi, So I'm working through a bunch of problems involving gradient vectors and derivatives to try to better understand it all, and one specific thing is giving me trouble. I have a general function that defines a change in Temperature with respect to position (x,y). So for example, dT/dt would...
  17. A

    Find the arc length parametrization of a curve

    Homework Statement Find the arc length parametrization of the curve r = (3t cost, 3tsint, 2sqrt(2)t^(3/2) ) . Homework Equations s(t)=integral of |r'(t)| dt The Attempt at a Solution I was able to get the integral of the magnitude of the velocity vector to simplify to: s(t) = integral of...
  18. H

    Focal Length of a Plane Glass: How to Measure and Understand Its Infinite Power

    Homework Statement what is the focal length of a plane glass ? Homework EquationsThe Attempt at a Solution place a plane glass in a plane and allow light to pass through it measure its focal length (i think its focal length is infinite )
  19. D

    MOSFET Channel length modulation

    In Sedra&Smith's microelectronic circuits they have the following expression for the drain current in a MOSFET in saturation iD = 1/2µpCox(W/L)Vov2(1+VDS/VA)But I don't see how this can be correct. Wikipedia also has another expression, see...
  20. Quarlep

    Is there a definitive measurement in the universe?

    In Every measurement there must be uncertanity.In length or In time everything.Lets assume we have a ruler and a rope.If I measure the rope I get a result but I can't say this is exactly true because there's a unncertanity in measurement.Lets suppoe the rope is 100 cm minus or plus 0.5 mm.The...
  21. Pezz

    Length Contraction: Why Must dx be Measured in the Prime Frame?

    The Lorentz transformation for motion in the same direction along the x-axis of two frames can be used to derive the length contraction formula. Say we are converting from dx to dx'. The t would obviously have to be 0. That would leave us with dx'=gamma(dx). My question is why dx here has to be...
  22. L

    Length Contraction: Sally & Sheldon's Meter Stick

    Homework Statement Sally and Sheldon have identical meter sticks. Sally is on earth, and sheldon is in a spacecraft that moves at 0.5c relative to sally. Sheldon leaves the spaceship at 0.1c relative to the spacecraft in a launch pad, moving away from sally. according to sally, what is the...
  23. S

    Question about circle arc length formula

    Now i haven't checked yet whether or not this is correct, but the formula for the length of an arc that subtends a central angle can also be expressed this way: AC/360 Where: A: Central Angle C: Circumference Is this correct? Thank you for your help.
  24. S

    Length-Norm inequality to root-n times Length (using 2|uv| <= |u|^2 + |v|^2)

    I've been reading "The Qualitative Theory of Ordinary Differential Equations, An Introduction" and am now stuck on an inequality I am supposed to be able to prove. I am pretty sure the inequality comes from linear algebra, I remember seeing something about it in my intro class but I let a friend...
  25. S

    Mass in Equilibrium with Variable Length Cable

    Homework Statement Consider the diagram below. A 1000 kg block being suspended in equilibrium by cables c and a. Cable c is on a pulley which can vary the length of the cable. Write the constraints of equilibrium. Find the tension in each cable based on varying lengths of cable c between 1.2 m...
  26. L

    Calculating Arc Length of a Curve: A Calculus II Problem

    Homework Statement Find the exact length of the curve: y= 1/4 x2-1/2 ln(x) where 1<=x<=2 Homework Equations Using the Length formula (Leibniz) given in my book, L=Int[a,b] sqrt(1+(dy/dx)2) I found derivative of f to be (x2-1)/2x does that look correct? The Attempt at a Solution I found f'...
  27. T

    Simple Pendulum: The gradient of the graph of T^2 against length

    I've been asked to investigate the value of g. My graph shows that the gradient is around 4.4 as when the length was 0.27m, the squared time period was 1.18s (since this is a T2 against L graph). My question is, of course, why? If I am detecting g, which is 9.81 on earth, why did I get such...
  28. K

    Finding the focal length of a negative lens without another lens.

    Homework Statement A simple method for determining the focal length of a negative lens is shown below. Prove this is true. Homework Equations The Attempt at a Solution The linear magnification formula relates magnification, the distance from the lens to the image (i), the distance from...
  29. J

    MHB Solve Circle Radius Given Trapezoid Height & Length

    I don't know if this can be calculated. I have tried for hours and days to isolate/calculate the radius and angles of the circle in order to be able to calculate length 1. I have tried using cos/sin-relation formulas and triangle formas - but Iam stuck. Any hints would be greatly appreciated...
  30. D

    Difference between optical and geometrical length in optical path

    I'm searching for a week from now and can't find out difference between optical and geometrical length in optical path. Can anyone explain or give me idea or how can I find it out?
  31. C

    Calculating Arc Length of a Curve: y^2 = x^3, (1,-1) to (1,1)

    Homework Statement A curve has the equation y2 = x3. Find the length of the arc joining (1, - 1) to (1, 1). Homework Equations The Attempt at a Solution I took the integral of the distance and tried to evaluate from -1 to 1. L = [intergral (-1 to 1) sqrt (1+(dy/dx x^3/23/2)2 dx] Evaluated I...
  32. C

    Find Arc Length of Particle Moving on Curve

    Homework Statement Find the length of the path traced out by a particle moving on a curve according to the given equation during the time interval specified in each case. The equation is r(t) = a(cos t + t sin t)i + a(sin t - t Cos t)j, 0</=t</=2pi, a>0Homework Equations Arc length =...
  33. Math Amateur

    MHB Modules of Finite Length - Cohn, page 61

    I am reading "Introduction to Ring Theory" by P. M. Cohn (Springer Undergraduate Mathematics Series) In Chapter 2: Linear Algebras and Artinian Rings, on Page 61 we find a definition of the length of a module. Some analysis follows, as does a statement of Theorem 2.5. I need help to understand...
  34. D

    How Do You Calculate the Focal Length of a Telescope's Objective?

    Homework Statement An optical telescope with a 12mm eyepiece makes the Moon appear to have an angular diameter of 30 degrees. What is the focal length of the telescope's objective? Homework Equations magnification=focal length of objective/focal length of eyepiece The Attempt at a...
  35. O

    Resistance and the length of the wire

    Hi! The question is simple, seemingly... Doubling the length of a wire, doubles the resistance of the wire... Why? There is one interesting point to it: Doubling the length of the wire also makes the ELECTRIC FIELD weaker TWO times. That automatically makes the current smaller two times...
  36. D

    Find the frame length with derivative

    Find the optimum frame length nf that maximizes transmission efficiency for a channel with random bit erros by taking the derivative and setting it to zero for the following protocols: (a) Stop-and-Wait ARQ (b) Go-Back-N ARQ (c) Selective Repeat ARQ My work has been uploaded I am a bit rusty on...
  37. T

    Solving Lorentz Transform problem using only length contraction

    Homework Statement A traveler in a rocket of length 2d sets up a coordinate system S' with origin O' anchored at the exact middle of the rocket and the x' axis along the rocket’s length. At t' = 0 she ignites a flashbulb at O'. (a) Write down the coordinates t'_F, x'_F, and t'_B, x'_B for...
  38. I

    MHB Interval for the Length of an Arc

    find the length of an arc of a helix r(t)=(sint,cost,t) from the point (0,2,0) to (0,5,2pi) would the interval when integrating be from 0 to 2pi because t in the case is (z=t)? please say yes. please say yes.
  39. I

    MHB Arc Length C: Origin to (6,18,36)

    let C be the curve of intersection of the parabolic cylinder $x^2=2y$ and the surface $3z=xy$. find the exact length of C from the origin to the point (6,18,36). please help! this is the last question i have left from this assignment and i have no idea how to do it. i have grading to do and a...
  40. B

    (length contraction)the distance travel or the object length shorter?

    Consider the following case: First frame S, which is earth. Second frame S', which is rest relative to rocket. Rocket are moving in speed of v relative to earth. Problem: Due to time dilation, from frame of S, the clock in rocket is running slower. Likewise, due to time dilation, from...
  41. S

    Polar Arc Length: Solve Integral of r=6cos6θ

    Homework Statement Find the arc length of one of the leaves of the polar curve r= 6 cos 6θ. Homework Equations L = ∫sqrt(r^2 + (dr/dθ)^2) dθ (I use twice that since the length from 0 to π/12 is only half the petal) The Attempt at a Solution I seem to get an integral that can't be...
  42. Kaustubh sri

    Find the length of largest square

    Find the length of largest square accommodated in a right angled triangle whose perpendicular length is 16 m and base's length is 8 m. My attempt I have tried a lot to find the length but every time it comes in fraction , i think that the figure i have made is wrong . The answer I am getting is...
  43. W

    Length, time and velocity in relativity (special?)

    10. The average lifetime of a pi meson in its own frame of reference is 2.6 x 10^-8 s. If the meson moves with a speed of 0.95c, what is (a) its mean lifetime as measured by an observer on Earth and (b) the average distance it travels before decaying, as measured by an observer on...
  44. C

    What are the physics of length contraction?

    Objects in motion relative to an inertial frame S are measured to have contracted lengths in S in the direction of motion. How does Special Relativity view this contraction physically? For a concrete example, suppose I have a bar of steel moving lengthwise and, as it moves past me (in frame...
  45. S

    Children's Slide, given slide length and angle, solve speed at bottom

    Homework Statement Hi guys! Here is my problem: A Children's slide is 20 ft long and makes an angle 30° with the horizontal. If the coefficient of sliding friction is 0.05 and the child starts from rest at the top, with what speed does he reach the bottom? I want to say it is about...
  46. Shackleford

    What is the arc length parametrization of α(t) and why is the s so tiny?

    Of course, I need to find the first derivative and integrate its norm. α'(t) = (1, 0, (1/2)t^2 - (1/2)t^-2) ∫ [1 + (1/4)t^4 + (1/4)t^-4]^(1/2) dt, t = 1 to t = 3. Have I simply forgotten useful integrals? α'(t) = (e^t, -e^-t, root2) ∫ [e^2u + e^-2u + 2]^(1/2) du, u = 0 to u = t.
  47. W

    Relativistic Time, Length, Mass

    Reposting to this section of the forum instead of the Introductory Physics homework section. So let's say a guy travels at 0.5c in a spaceship from planet 1 to planet 2. Am I right in saying that: proper time = time measured inside space ship proper length between planets = length the...
  48. T

    Limits of the Path Length of B-field induced gyroradius

    Hi, I am trying to derive the path length of a charged particle in a B-field. I am assuming the particle will travel a distance L along the applied field. Using the following equations for the path length of a helix and gyroradius: Helix defined as [a*cos(t),a*cos(t),b*t] for t on [0,T] has...
  49. P

    Chemistry Calculate persistence length of a single dsDNA molecule

    Hello! 1. The problem statement and all variables AIM: Calculating persistence length P of a single dsDNA molecule from a data set of force F (to the molecule) vs. extension x measurements. Experimental background: pN forces were applied to a single dsDNA molecule spanned between two...
  50. P

    Calculate persistence length from force extension data of a single DNA

    Hello! From a data set of F-x measurements of a single dsDNA molecule I want to calculate the persistence length P . So I plotted \frac {1} {\sqrt{(F)}} vs. x and fitted these data points (linear). According to an interpolation formula the extension x of a worm like chain with contour...
Back
Top