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).

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

    I Length contraction in General Relativity

    In GR, a free falling object when viewed by a distant observer appears to be length contracted and slows down as it approaches the event horizon of a black hole. The length contraction piece, however, seems counterintuitive. I would have thought that the leading edge of the object would...
  2. VVS2000

    I Finding focal length of the lens using "u-v" method

    I was just checking out this experiment for finding focal length of a lens that I did few years back. the method used was called as the u-v method(https://www.concepts-of-physics.com/pdf/uv-method.pdf), and here in this method, object distance u and image distance v is measured from the sharp...
  3. Keith Koenig

    B Length, Time, and Velocity -- Which are fundamental quantities?

    We think of length and time as the first fundamental quantities and velocity as the first derived quantity but any two determine the third so we would be completely justified in defining velocity as a fundamental quantity and one of length or time as the other, with the remaining being the first...
  4. G

    Length of spin vector for spin-½ particle

    My answer so far in |S| = √3 /2 *hbar but the question states it must be an angular momentum. Is this an angular momentum or am I missing something? Thanks
  5. PainterGuy

    Time dilation and length contraction for a rocket

    Hi, It's not a homework but still thought to post it here as advised in the past. A rocket is going to leave Earth's surface and it is decided that a data pulse encoding emission time of pulse will be sent every second from Earth station to the rocket, and the rocket would do the same. The...
  6. P

    I Between a Zeptometer and the Planck length

    What exists between approximately 1 X 10 E-21 meters (preon length?) and the Planck Length of 1.6 X 10 E-35 meters?
  7. M

    Help identifying a length for this paper edge

    Hi PF! Two years ago my lab launched experiments aboard the ISS. The experiment was simple: place two water droplets on a substrate, set camera above the drops, and watch them coalesce. However, the exact size of the drops is unknown (approximately 1 cm radii, though this number is debated)...
  8. Istiak

    Find focal length of electron for a parabolic motion

    Here I was going to use ##\int \vec F \cdot d\vec l = \frac{1}{2}mu^2## What I got that is ##l=\frac{mu^2}{2eE}##. Here the question is what is ##l## (I took ##x## while doing the work but here I used ##l## instead of ##x##)? I was assuming that it's ##x## since I am calculating work in the...
  9. S

    Finding the length of this side of similar figures

    Is it possible to find the value of ##x##? I feel like the information is not enough to find it. I have found EF, which is 19.8 cm (if this is helpful) Thanks
  10. karush

    MHB - Length of curve to 4 decimal pl

    8.1.1 find the length of the curve to four decimal places $y=xe^{-x},\quad 0 \le x \le 2$ eq from book $L=\int_c^d\sqrt{1+[g'(y)]^2}\, dy$ ok I haven't done this in about 2 years and only did a few then so trying to review rare stuff kinda desmos graph
  11. guyvsdcsniper

    B Check my understanding of Time Dilation and Length Contraction

    I just started learning about Special Relativity and have come upon the topics of Time dilation and Length contraction. Its a bit abstract for me and I just want to cross ref my knowledge here and see if someone can tell me if I am understanding this correctly. I've attached an excerpt of a...
  12. alexandrinushka

    B Any plausible explanation for dynamical length contraction?

    I am new here, so pardon my ignorance. First of all, I am aware of the impossibility to distinguish experimentally between SR (Special Relativity) and LET (Lorentz Ether Theory). I know there is a PF policy article on LET and the Block Universe. I must admit though that LET is more appealing...
  13. JD_PM

    How to determine the minimum grid length | Numerical Plasma Physics

    Summary:: I am learning particle-in-cell (PIC) python 3X code. PIC currently represents one of the most important plasma simulation tools. It is particularly suited to the study of kinetic or non-Maxwellian effects. I am learning particle-in-cell (PIC) python code. PIC currently represents one...
  14. hutchphd

    B Exploring Relativistic Mass & Length to Help STEM Students

    Comments please Is there good sobriquet to use for relativistic length ? Just a thought to aid the struggling college frosh STEM students
  15. C

    Comp Sci Complexity for generating strings of length k from CNF grammar

    Here's the following code I've written for generating strings of length k given a CNF grammar ( Chomsky Normal Form grammar ) ( The code is a recursive variant of the CYK algorithm ). The algorithm is recursive and uses memoization. def generate_language(rule_dict, start_var, k): mem =...
  16. S

    I Because of length contraction, does absolute position exist?

    I know that I have heard that GR proves that there is no absolute time, so does this go for location too? If so, could it be said that particles have a superposition in position/location the same way that particles do in QM?
  17. B

    I Judge Original Time & Length Special Relativity

    How to Judge original time and original length of special relativity
  18. M

    Guitar string tension: effect of total length - continued

    This wiki page offers an incomplete equation for calculating tension over a length of string. Can you please help complete the equation? https://en.wikipedia.org/wiki/String_bending It is referenced here in this thread post #23...
  19. O

    I Linear Accelerator Length Contraction

    I am trying to understand the effect of relativistic length contraction on the electron bunches in a linear accelerator. Figure B is for nonrelativistic speeds, successive cylinder lengths are progressively longer. However, wikipedia says "At speeds near the speed of light, the incremental...
  20. alan123hk

    B The Paradox of Relativity Length Contraction

    A rigid rod with length ## l_0## slides on a smooth and flat tabletop along the length at speed of ## ~\frac {\sqrt{3}}{2}c~ ##, there is a hole of width ##~l_0~##on the table. The observer who is stationary relative to the desktop thinks that the length of the rigid rod ##~ l=l_o...
  21. karush

    MHB B20.<= to the length of the dividend

    Do the division using the c-strips to make a train of as many of the divisor as possible such that the length of the train you make is less than or equal to the length of the dividend, and if you were to add one more of the divisor to the train, it would be longer than the dividend. If the train...
  22. Y

    Does wire length difference create phase shift?

    When wiring a 240 volt AC circuit, I've always assumed that it's important for L1 and L2 wires to be the exact same length, in order to avoid introducing a phase shift that would reduce peak voltage. Length differences can accumulate when the wires enter a panel and need to go slightly...
  23. D

    Uncertainty of pendulum period and pendulum length

    I'm doing a lab report where I manually measure the time taken for a bifilar pendulum to do 10 oscillations. Is there a rule or a method that I should follow to calculate its uncertainty? Or is the uncertainty just an estimation of human reaction time and judgment? I also need to know the...
  24. D

    Need help with this unequal length bifilar pendulum

    [Mentor Note -- Three threads on the same problem have been merged into this one] Hi, I'm doing a lab report on the relationship between the period of oscillations in an unequal length bifilar pendulum. The set up is like below Can anyone help me derive a formula for the period of oscillations...
  25. Horizont22

    I Shorten the lens distance while having same focal length?

    Hello Everybody, I'm David from Spain, and happy to be here. We have a LED that needs a FL50mm collimator which is focused to infinite, because we want parallel rays. So the lens is at a distance 50mm (approx) from the led. However, 50mm is too much distance for our design, so the question is...
  26. knotted_pine

    Engineering Finding arc length of a pipe between two tanks

    I can't seem to find the arclength between A and B. I tried using L = integral (0.6 to 0.4) of sqrt (1+ (dz/dx)^2) to no avail. Would it be roughly similar to 400 km (the length from A to B) since the change in elevation could be considered negligible? Furthermore, how might I go about...
  27. Twigg

    What causes variations in delay in coax cable of the same length?

    Hey all, I was doing some tests in lab when I noticed that between two 4.5m RG174 SMA cables, there was a 1ns difference in delay at 4MHz between the two cables. To clarify, theory says 4.5m of RG174 (66% velocity factor) at 4 MHz should have a delay of 22.7ns. I measured one cable at 22ns and...
  28. S

    B Is length contraction (Lorentz transformation) an illusion or real?

    My textbook (from first year university physics) says that length contraction is actually real. But how can it be real when two different observers can measure two different lengths? For example, if I am in a spaceship going close to the speed of light relative to people on Earth, they will...
  29. Harli

    Mechanical Waves Recorded after an Earthquake

    .
  30. M

    B Distance Length Contraction at Light Speed

    I know it's not possible to travel at light speed so this is just theoretical. As I understand it at relativistic speeds the distance you need to cover to travel to a destination are length contracted. If you were traveling at light speed is the distance between you and any object ever zero?
  31. O

    Arc length of vector function - the integral seems impossible

    The vector equation is ## v(x)=(e^x cos(2x), e^x sin(2x), e^x) ## I know the arc-length formula is ## S=\int_a^b \|v(x)\| \,dx ## I found the derivative from a previous question dealing with this same function, but the when I plug it into the arc-length function I get an integral that I've...
  32. MisterH

    A Minimum sample length to estimate the frequency of a sinusoid

    Given a discretely sampled horizontal sinusoid of length p, and unknown amplitude, what is the minimal number of consecutive points on a window that is required to correctly estimate its total length, starting at any random point on the wave? Initially I would think it would be either p (full...
  33. M

    Area of interior triangle of pyramid normal to a side length

    This isn't homework, but I figured it's fine if I make it a HW problem and post here (if not, please let me know). Let ##z^*=0## be the vertex of the pyramid, and let ##z^*## run the altitude. It's easy to show the area of the base normal to the altitude is ##A = 4 \left.z^*\right.^2...
  34. B

    MHB Find Vector of Given Length in Particular Direction

    Question:
  35. Safinaz

    Understanding the Mass-Length Relation: Solving for V in Simple Equation

    Hello, If i have this relation: ## M_p^2 = M^3_s V ## where ##M_p ## and ##M_s ## are masses in GeV and V is a length. Let ## M_p = 10^{18} ~ ## GeV and ##M_s = 10^3 ## GeV , what is V in meters ? My solution : The equation becomes ## V = 10^{30}## GeV , but ## 1 m \sim 10^{15} ~...
  36. karush

    MHB :Calculating $k$ to Find Wire Length

    $\tiny{2.5.1}$ Electrical Resistance of a Wire 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 432 feet long and 4 mm in diameter has a resistance of 1.24 $\Omega$ find the length of a wire of...
  37. S

    B Planck Length 1 Detector? Emitter?

    Do we have the ability to detect the gamma ray of Planck Length 1? Is there any known phenomenon, natural or man-made, that could emit on Channel 1? How dangerous to man and machine would Channel 1 be / at what density (is that the right term?) would it become dangerous? Would there be any...
  38. kimiko333

    Measuring the length of a moving Beam in two different directions

    v_g+v_e=15/t_1 v_g-v_e=10/t_2 v_g=s/(t_1-t_2) But there are too many unknowns. What am I missing?
  39. thegroundhog

    I LIGO: Detecting Differences Less Than a Proton Length - How is It Possible?

    I read that the LIGO detector in the US was able to detect a difference of less that the length of a proton, or maybe even less than this. How is this possible? The perpendicular arms won't be the same length down to the nearest proton length. Also, at such small lengths the microclimate on each...
  40. S

    MHB Calculate the Length & Potential Energy of a Sliding Box on a Ramp

    A ramp rises 10cm for every 80cm along the sloping surface. A box of mass 50 kg slides down the ramp starting from rest at the top of the ramp. The coefficient of friction between the ramp and the box is 0.03 and no other resistance acts. The box is traveling at 2 m/s when it reaches the bottom...
  41. G

    MHB Find the length x if the shaded area is 1200 cm^2

    Find the length x if the shaded area is 1200 cm^2
  42. N

    Find the Length of a Pass of a Soccer Ball

    A soccer player passes the ball from a pointthat is 18 yards from the endline and 12 yards from the sideline. A teammate who is 42 yards from the same endline and 50 yards from the same sideline receives the pass. How long is the pass? I am suppose to use the distance formula for points. I will...
  43. The Baron

    What Happens to the Wavelength of Light as it Passes Through Water?

    I have a question, say a wave of light is emitted, and it passes through water, changing it's wave length to 380nm inside the water, once it comes out of the water, to vacuum will the wavelength remain at 380nm or will it change?
  44. F

    Relativity of Length: Understanding Length Contraction & Time Dilation

    a) We use the definition of speed: v = delta_L/delta_t delta_t = delta_L/v = 45000 m/(0.99540*3*10^8 m/s) = 1.55*10^-4 s b) We use the length contraction equation: delta_L = L_0*sqrt(1-v^2/c^2) L_0 = delta_L/sqrt(1-v^2/c^2) = 45000 m/sqrt(1-0.99540^2) = 469698 m However, the solution shows...
  45. O

    I Compute Length Contraction: Is ##l=1## a Possible Model?

    Sorry, I accidentally posted this while typing it up, then when I finished typing it I found the mistake that made me come here to make this thread. I'll still write it up just to make the thread somewhat useful, and then ask my follow-up question at the end I'm picking units so the speed of...
  46. B

    I How to calculate the focal length and focal point of collimator?

    I wanted to calculate the focal length and focal point of the collimator. The collimator diameter is 3mm, and I wanted to focus on the 100-micrometre active area of the detector.
  47. R

    I Length contraction and time dilation

    A long time ago, I was very impressed by a lecture on elementary special relativity which showed in simple math how the correct conclusion to the null results of the Michelson-Morley experiment were obtained by concluding a constant c but then adding a length contraction and time dilation. I...
  48. M

    MHB Uniform convergence - Length of graph

    Hey! :giggle: We define the sequence of functions $f_n:[0,1]\rightarrow \mathbb{R}$ by $$f_{n+1}(x)=\begin{cases}0 & \text{ if } x\in \left[ 0, \frac{1}{2n+3}\right ]\\ |2(n+1)x-1| & \text{ if } x\in \left [\frac{1}{2n+3}, \frac{1}{2n+1}\right ] \\ f_n(x) & \text{ if } x\in \left...
  49. MisterH

    A Fitness function for window length of filter

    Fitness function for window length of filter On a sinusoidal signal with amplitude 1, and period P, an exponential moving average (EMA) (with alpha = 1/n), and a linear weighted moving average (LWMA) (with window length n) are calculated; when you subtract the EMA from the LWMA, it can be seen...
  50. Kaguro

    Deriving length contraction using spacetime

    Deriving time dilation was easy: Imagine two events in frame O' at the same location. ##ds^2 = -c^2 dt'^2## The same viewed in O frame is: ##ds^2 = dx^2+dy^2 + dz^2 - c^2 dt^2## ##\Rightarrow dx^2+dy^2 + dz^2 - c^2 dt^2 = -c^2 dt'^2## ##\Rightarrow (\frac{dx}{dt})^2+(\frac{dy}{dt})^2+...
Back
Top