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. R

    What is the wavelength of radio waves at 1250 kHz?

    Homework Statement Radio waves travel at the speed of light waves (3.00 *10^8 m/s). If your radio is tuned to a station broadcasting at 1250 kHz, what is the length of the waves arriving at the radio antenna? Homework EquationsThe Attempt at a Solution i can find the wavelength but i don't...
  2. O

    Is mass*acceleration =BIL (magnetic force *current *length )

    As we know force =mass*acceleration & force =BIL. Can we make this equation as ma=BIL?
  3. S

    Focal length to get clear image

    Homework Statement Harris stands at point A and wants to take a picture of bird located at point B. Because there is wall, he has to direct his camera to mirror located 3.7 m to the north from his position. What is the focal length of his camera so that he can take a clear picture of the...
  4. C

    Arc length of a stadium billiard

    I've been trying to figure out the most straightforward way of doing this for a while, and would like to get some advice on new approaches, as the one I was using didn't work out at all. So here it is: The stadium billiard is defined as two semicircles joined by two tangent lines, as shown in...
  5. Calpalned

    Deriving the formula for arc length of a polar function

    Homework Statement Derive ∫(dr/dθ)^2 + R^2 )^0.5 dθ Homework Equations x = Rcosθ y = Rsinθ The Attempt at a Solution Arc length is the change in rise over run, which can be found using Pythagorean's Theorem. Rise is dy/dθ while run is dx/dθ. The arc length is [(dy/dθ)^2 + (dx/dθ)^2 ]^1/2...
  6. J

    Find the arc length (using hyperbolic trig)

    1. The problem statement, all variables and given/known Find the length of the curve $$y=ln(x),\frac{1}{2}<=x<=2$$ Homework Equations Using hyperbolic trig isn't necessary, but it's how my text (Serge Lang's A First Course in Calculus) approaches most square roots, and as a result, it's what...
  7. B

    Signal processing in matlab, what is signal length ?

    Homework Statement Use Matlab to construct a signal of length 2^13 = 8192 that contains only three frequencies: x=0.5*sin(2*pi*200*t)+0.2*sin(2*pi*455*t)-0.3*sin(2*pi*672*t) Compute and plot the absolute value of the DFT. What does the question mean by signal length and why is it expressed...
  8. T

    Need explanation on Chracteristic Length in heat convection

    Hi, I am working on constructing a thermal circuit where I am using the concept of natural convection from a vertical hot plate in the shape of a DVD. In order to calculate the Grashoff number, I have to use the characteristic length. What should I take as my characteristic length? The disc OD...
  9. P

    Exciton Diffusion Length in P3HT:PCBM BHJ Cells

    Hi, I understand that an exciton must reach the D/A interface within the Exciton diffusion length to prevent recombination, however, what are the factors during device fabrication that can affect the Exciton diffusion length of a P3HT:PCBM BHJ OSC?
  10. A

    MHB How to Solve for r and θ in a Circle's Minor Arc and Sector Area Problem?

    The length of the minor arc of a circle is 10cm, while the area of the sector AOB is 150cm2. a) Form two equations involving r and θ, where θ is measured in radians. b) Solve these equations simultaneously to find r and θ. Help to solve? Cant understand the question very well. I think the...
  11. A

    Precalc Trig Arc Length Question

    Homework Statement http://education.Alberta.ca/media/9451970/07_math30-1_released_2014-15.pdf question #7 Homework Equations a=theta*r The Attempt at a Solution I did a=(5pi/6)*20 but the answer is not A
  12. Sivasakthi

    Choosing appropriate length scale in condensed matter

    Hi.. I was reading some papers on continuum dynamics and its application to various material dynamics. The determination of macroscopic behavior is being studied , considering phononic interactions. As a material consists of phonons of various wavelengths, it is necessary to account for various...
  13. Euler2718

    Trigonometry Arc Length Problem

    First I'd just like to point out that I'm taking calculus and advance pre-calculus simultaneously (kind of a stupid system) and this is a problem in the pre-calc. 1. Homework Statement 2. Homework Equations Let 'a' be arc length. a=\theta r a = \int_{a}^{b} \sqrt{1+[f'(x)]^{2}} dx...
  14. P

    Arc Length: Definite and Indefinite Integration

    Several authors state the formula for finding the arc length of a curve defined by ##y = f(x)## from ##x=a## to ##x=b## as: $$\int ds = \int_a^b \sqrt{1+(\frac{dy}{dx})^2}dx$$ Isn't this notation technically wrong, since the RHS is a definite integral, and the LHS is an indefinite integral...
  15. Nathanael

    Length of a spring constantly accelerating through space?

    Imagine if I were to apply a constant force, F, to a spring of length L, spring constant K, mass m, and uniform density. The force causes the spring to accelerate with acceleration a. For the sake of imagination, I will say I'm applying the force with my hand (which is pushing one end of the...
  16. E

    Find total length of cylinder (springs, natural frequency)

    Homework Statement A simple pressure relief device is shown in Figure Q6.1 below. It consists of a piston of mass 0.5 kg and thickness 3 cm sliding without leakage or friction into a cylinder of diameter 5 cm. The bottom section of the cylinder can be exposed to a varying source of pressure...
  17. G

    How can it be deduced general relativity from planck length

    How can it be deduced general relativity from Planck length?
  18. L

    Are force fields deformed by length contraction?

    Imagine you have an electron traveling at high speeds... would you expect it´s EM field to be contracted following the Lorentz transformations?? If the answer is no, please explain why fields and their shape don´t deform when space-time does. How they retain their shape in a space that is not...
  19. J

    Proper Distance, Rest Length: What to Know

    Hello, Could someone check my following statement: The proper distance between two spacelike separated events can be thought of as the rest length of a rod that connects both events in an inertial frame in which both events happen simultaneous. Thanks in advance!
  20. Ganesh Ujwal

    Why isn't length contraction permanent even though time dilation is?

    Why isn't length contraction permanent even though time dilation is? It's my understanding that when something is going near the speed of light in reference to an observer, time dilation occurs and time goes slower for that fast-moving object. However, when that object goes back to "rest", it...
  21. D

    Hydrodynamic Entry Length of Flow Through Circular Annulus

    I might be going crazy or searching at the wrong places. Is there an empirical formula for solving the hydrodynamic entry length of laminar flow through a circular annulus? Thanks!
  22. M

    Focal length from thin lens to object distance

    Hello, I've come across an problem that requires the lens to be at least about 350 mm away from the object. Object to be examined is 80 mm tall and imaging plane is either 11 mm or 25 mm tall. I've tried to calculate required focal length, but have not succeeded. Distance from lens to imaging...
  23. ubergewehr273

    Length Contraction in Special Relativity

    Could somebody explain the logical reasoning behind lorentz contraction when an object travels faster and faster ?
  24. S

    Guitar string tension: effect of total length

    I suspect my question will be somewhat unique, please forgive me if it's entirely out of place. (Please also forgive my ignorance when it shows, my knowledge of physics is extremely limited.) You might wonder why I'm asking it here, rather than on a guitar forum. Let me simply say that the...
  25. Z

    MHB How to Calculate Arc Length for a 124° Angle in a Circle?

    A circle has a radius of 10cm. Find the length s of the arc intercepted by a central angle of 124° . Do not round any intermediate computations, and round your answer to the nearest tenth. How do I do this?
  26. B

    Time Dilation/Length Contraction Qs: Exploring SR Basics

    It pains me to even type these out. I realize how many threads there are with very similar questions and to someone well versed in these topics, these questions probably all seem the same. But after reading what seems like all the questions, I feel I'm still confused. 1) In regards to the light...
  27. M

    Length contracting between objects

    If two objects start moving near the speed of light at the same speed, is the length between the two objects contracted?
  28. F

    Does Length Contraction Imply Superluminal Speeds?

    Assume a rocket sets off from Earth accelerating to 0.8c within 1 second. The distance to a star originally 1000 light years away contracts thus to 600 lightyears within 1 second. This means the star moves 400 lightyears in one second in the travelers frame. I make this an average speed of more...
  29. ArcanaNoir

    Arc length of intersecting circles

    Homework Statement My class is working through chapter 2 of Newman's Analytic Number Theory text (on partitions). We have come to a part where he states that "elementary geometry gives the formula" (for the length of arc A) 4r\text{arcsin}\frac{\sqrt(2)(1-r)}{\sqrt(r)} We are attempting to...
  30. B

    How does eye strain affect the length of the eyeball?

    Ever since I learned that short-sightedness is due to the eyeball being too long, and far-sightedness is due to the eyeball being too short, I've wondered what the point of avoiding eye strain is. How could straining the eyes possibly have the effect of changing the length of the eyeball? By...
  31. M

    Length contraction of particles

    As an object moves, it is contracted in the direction of it's motion. Why wouldn't each individual subatomic particle be contracted rather than the object as a whole?
  32. E

    Calculating Length of Line cf: A Math Problem Explained

    In the problem attached, why is the integral become just the length of line cf?
  33. A

    Slip Length: u - u_wall = β ∂u/∂n

    Wondering if someone could link me to a derivation of this formula? It's on the Wikipedia page for the no-slip condition. u - u_wall = β ∂u/∂n β = slip length n = coordinate normal to the wall
  34. C

    Focal Length Problem: -30cm Converging/Diverging Lens

    Homework Statement A lens made of glass has one concave side with a radius of curvature of 5 cm, and one convex side with a raduis of curvature of 7.5 cm. What is the focal length of the lens? Is this a converging or diverging lens? Homework Equations nglass=1.5 nair=1.0...
  35. P

    Length of a plate after roll forging?

    Hello, I'm new here. so I hope I posted this question in the right section. For this problem, I have to compute a couple of parameters: An Aluminum plate (7075-O) (length 10 [m], thickness 10 [mm], width 40 [cm]) is reduced in thickness from 10 to 9,5 [mm]. The radius of the rolls is 25 [cm]...
  36. E

    Projectile angle that considers canon length

    Greetings, Most projectile problems are presented from the muzzle of a cannon; however, how do we solve the problem if the velocity is known at the muzzle; but the angle is controlled at the base of the canon. The issue is that, when the canon angle changes, so does the muzzle location! The...
  37. N

    How Can You Calculate the Length of a Ramp Based on Sliding Time and Friction?

    Homework Statement You are passing a construction site on the way to physics class, and stop to watch for a while. The construction workers appear to be going on a coffee break, and have left a large concrete block resting at the top of a wooden ramp connecting one of the building's upper...
  38. Ookke

    Light reflection in length contracted system

    Light beam hits the mirror perpendicularly and returns to the source (left picture). The same system in horizontal motion (right picture) is skewed due to length contraction so that both beam and mirror are at higher angle. Because the beam returns to source in the system's rest frame, it must...
  39. snowwhite

    Work problem -- Steam piston volume and work length

    Homework Statement Steam is raised as saturated steam at 6 bar (g) and supplied to the first ( high pressure ) piston. The steam then exhausts from piston 1 at 3 bar (g). The steam is thought to expand adiabatically in accordance with PV^( 135 .1)= Constant Given the initial volume is...
  40. M

    Gravitational Time and Length Change, Looking for mass formula

    Hi, Just curious if anyone knows of a formula that would show how mass changes in a gravitational field? I have seen the formulas for gravitational time dilation and length contraction (which are rather similar) and was wondering is mass changes the same way. Thanks
  41. M

    Length Contraction of Electrons

    If you have a still wire with electrons moving through it, to an outside observer at rest relative to the wire, would the space between the electrons contract? I would think that special relativity causes the electrons to contract, (not the space between them) but the contracting of the...
  42. 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
  43. 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...
  44. 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 -...
  45. 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...
  46. 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...
  47. 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...
  48. 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})##...
  49. 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...
  50. 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...
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