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. okandrea

    Wavelengths: Length between 2nd-order fringes

    Homework Statement Light of wavelenghs 4.80x10^2 nm and 632nm passes through two slits 0.52 mm apart. How far apart are the second-order fringes on a screen 1.6m away? λ₁ = 4.80x10^2 nm = 4.80x10^-7m λ₂ = 6.32x10^-7m d = 0.52mm = 5.2x10^-4m n = 2 L = 1.6 Homework Equations (Maxima/Bright)...
  2. W

    Length of Curve Homework: Find Integral Solution

    Homework Statement Find the length of the curve: ##x=\frac{t}{1+t}## ##y=\ln(1+t)## where ##0 \leq t \leq 2## Length of curve integral ##\int^a_b \sqrt{(\frac{dx}{dt})^2+(\frac{dy}{dt})^2} dt## Homework Equations ##(\frac{dx}{dt})^2 = \frac{1}{(1+t)^4}## ##(\frac{dy}{dt})^2 =...
  3. R

    A Free bar fundamental vibration relationship length to width

    When finding the fundamental for thin bars, the approximate equation (http://hyperphysics.phy-astr.gsu.edu/hbase/Music/barres.html) only refers to the length and thickness when calculating. I'm trying to figure out the frequency and node location along the length and width of the fundamental...
  4. G

    MHB Calculate Length of Median on Trapeze (48 cm)

    The two non-parallel sides of the trapeze are 15 cm and 13 cm, the perimeter is 48 cm. Find the length of the median. I don't know anything about trapezes can someone expain how to do this?
  5. D

    MHB Find side length, cirumference and area of octagon

    Square-shaped piece of paper is intended to make a regular octagon through the cutting of the vertices of a square. The length of the piece of paper is 29 cm. How long triangle cathetus have to be cut off from the vertices of the square? Calculate the octagonal side length, circumference, and...
  6. C

    Length Contraction/Relativistic mass question

    Homework Statement The proper length of spaceship A is 60.0m and the proper length of spaceship B is 120.0m. The proper mass of spaceship A is 15000 kg. An observer on Earth watches the two spaceships fly past at a constant speed and determines that they have the same length. If the speed of...
  7. Alyssa Eiger

    Length a Block on Pulley Moves - (Basic Energy Question)

    Homework Statement Two masses are connected by a string that is passed over a massless pulley. At t=0, the 6-kg mass is moving upwards at 2m/s, while the 4-kg mass is descending at the same speed. How far will the 6-kg mass rise before it stops? Homework Equations KE= 1/2*m*v^2 PEg: m*g*h...
  8. C

    MHB Secant and Tangent Angles in Circles, finding an arc length.

    I got 138.17, but that isn't correct. I don't know how to do it, since the only way I thought, gave me the wrong answer. Can anyone help?
  9. L

    B Finding Radius from chord length and tangent distance

    Ok, i have a question. First, i am an engineering student and have done all math requirements up to linear alg. HOWEVER, my geometry is terrible, oh so terrible and i need some spoon feeding right now because i am stuck on a problem. Ok, i saw a really cool tool the other day called a radius...
  10. Borek

    Minimum length of the Pitot tube?

    I have a thin tube (4 mm diameter) sticking out of a small box (a bit larger than a matchbox). I want to use this tube to measure the dynamic pressure. How long must the tube be for the results to be reasonably accurate? Intuition tells me the working end of the tube should be kept in the...
  11. C

    Using dy/dx to find arc length of a parametric equation

    Homework Statement I have attached a picture of the problem in the attachments I need help on the last section, (part d) Homework Equations (1)##∫√( (dx/dt)^2+(dy/dt)^2)dt## (2)##∫√( 1+(dy/dx)^2)dx##[/B] The Attempt at a Solution In order to get the answer we just need to find the...
  12. mr_sparxx

    Three equal charges held by equal length strings

    Homework Statement Three particles with the same charge q are hold together by three strings of the same length l forming an equilateral triangle. The tension in each string is: a) ## \frac {K q^2 cos 60º}{l^2}## b)## \frac {K q^2 cos 30º}{l^2}## c)## \frac {K q^2 sin 60º}{l^2}## or d)##...
  13. F

    Find the new resistance if its length and D are doubled

    Homework Statement Homework Equations ρl = RA A = π r2 The Attempt at a Solution l = RA (ρ is constant) A1 = π (D/2)2 = (πD2)/4 A2 =π (2D/2)2 = πD2 = A1 /4 l2 = 2*l1 ##R=\frac{l}{A}## R2 = (2l1)/(A1/4) = 8 l /A = 8R1 Could someone tell me where is my mistake ?
  14. J

    Blocks connected by a spring

    Homework Statement [/B] There are two blocks that have equal mass m, they are connected by a spring (with a coefficient of elasticity k) that has length l0. Instantly on the left block a force F begins to act. What will be the min. and max. length of this spring during this movement. There...
  15. lc99

    How Do Spring Length Calculations Relate to Frequency and Harmonics?

    Homework Statement Homework Equations v = sqrt(F/(m/L)) The Attempt at a Solution Trying to find the length of the spring. But i can find the tension of the wire at all. I'm not sure what i can do with the frequencies? Maybe I'm forgetting a concept cause i thought the equation v^2/F = L...
  16. hm_tested

    B How to find a length of a "radius" not centered in a circle?

    Generally in a circle, the radius of the circle is uniform around the circle due to it being at the center, this is the obvious part. However, let's say the the radius was shifted away from the center so that it is somewhere in the circle, in this case called r'. Given that the original radius...
  17. T

    Calculting the length of a solenoid

    Homework Statement Q2 A Cu wire of circular section and diameter 0.2 mm is used to form a one-turn coil and also to form a solenoid. Both have a radius of 2 cm. In both cases, a 10 mA current flows through the wire. a)Work out the magnetic field H in the centre of the one-turn circular coil...
  18. B

    A rod of length L and mass M has a nonuniform mass distribut

    Homework Statement A rod of length L and mass M has a nonuniform mass distribution. The linear mass density (mass per length) is λ=cx2, where x is measured from the center of the rod and c is a constant. Find the expression for c.Find the expression for the moment of inertia of the rod for...
  19. M

    MHB What is the smallest side length BC of triangle ABC with fixed angle and area?

    Calculate what is the smallest side length BC of the triangle ABC if the angle BAC is equal alpha and area of the triangle ABC equals S.
  20. M

    MHB What is the formula for determining the length of a confidence interval?

    Hey! :o A research institute wants to establish a confidence interval for the quota of working people in a city. Let $\hat{p}_n $ be the estimated quota, based on a sample of size $n$. It is assumed that $n> 30$. How can one determine the length of the confidence interval? Generally this is...
  21. M

    MHB Probabilities about length of songs

    Hey! :o We have a playlist with $2000$ songs. The length of the songs on the playlist are on average $3.5$ minutes (i.e. $3$ minutes and $30$ seconds) with a standard deviation of $1.7$ minutes. 1) Can we find the probability that a randomly chosen song is longer than $4.5$ minutes...
  22. D

    MHB Length of sides of right triangle with 1 angle and 1 side

    Hello so I'm a high school student and I came up with this question and I wanted to know if this was possible to do? So I tried to research and find a way to find the length of DC and I couldn't find anything, so I am here to ask for help, is this possible? I figured it would go in the...
  23. J

    MHB How do you calculate the area and arc length of region ABCD using given values?

  24. H

    Calculating Arc Length and Area of Cylinder Side

    Homework Statement Let r be a positive constant. [/B] Consider the cylinder x2 + y2 ≤ r2, and let C be the part of the cylinder that satisfies 0 ≤ z ≤ y. (3) Let a be the length of the arc along the base circle of C from the point (r, 0, 0) to the point (r cos θ, r sin θ, 0) (0 ≤ θ ≤ π). Let...
  25. F

    B Length contraction applet - have they got it wrong?

    Hi, I was browsing the internet for interactive simulations illustrating special relativity concepts. It seems to me that those in this http://kcvs.ca/concrete/visualizations/special-relativity are mostly nice and clear, although not very "chrome-friendly" (I have to use firefox to play their...
  26. T

    Heat Transfer & Combustion: Estimate Pipe Heat Loss/m

    << Mentor Note -- poster reminded to use the standard Template >> Question Three A pipe of outside diameter 200 mm is lagged with an insulating material of thermal conductivity 0.06 W m-1 K-1 and thickness 75 mm. The pipe carries a process fluid at a temperature of 300 °C and the average...
  27. Poetria

    Length of the curve - parametric

    Homework Statement [/B] Find the definite integral formula for the length of the curve for $$0 \leq t \leq \frac \pi 2$$ $$x = 2*cos^k(t)$$ $$y = 2*sin^k(t)$$ for general $$k \gt 0$$2. The attempt at a solution I don't understand why this is wrong: $$\int_0^\frac \pi 2\...
  28. TheSodesa

    The focal length of a microscope eyepiece

    The question: -------------------- The length of a microscope pipe is $L=160\,\rm mm$, the transverse magnification of its objective $M_o = 40\times$ and the diameter $d_o = 5\,\rm mm$. As for the ocular/eyepiece, its magnification is $M_e = 10\times$. 1. Find out the focal length of the...
  29. Physiona

    General Mathematics Grade 9 -- Find the length of a diagonal of the cuboid

    Homework Statement A solid cuboid has a volume of 40cm3. The cuboid has a total surface area of 100cm^3. One edge of the cuboid has length 2cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 significant figures. This question recently came up on my maths exam today...
  30. B

    Relationship between interference and arm length in MZI

    A question about the Mach-Zehnder interferometer. My understanding is: If its two arms are equally long, there is destructive interference in one output and constructive interference in the other output. So, the intensity of light detected at the first output should be 0% and at the second...
  31. M

    MHB Find s, the arc length of a circle

    The question is asking me to find s, the arc length of a circle. How do I convert my answer in radians to the book's answer 7.54 meters? Theta = 4pi/5 radius = 3 meters See picture.
  32. lbwet

    Calculate Height of Light Pole from Shadow Length

    Homework Statement At the outside, there is a vertical stick with a length of 1.1 meter and its shadow on the surface of an Earth is 1.3 meter, there also is light pole and its shadow length is 5.2 meters, what is the height of that light pole? Homework Equations Trigonometry equations to...
  33. A

    Propagation length of the surface plasma wave (SPW)

    Hello, Many Researchers talked about the following parameters: 1. Propagation length of the surface plasma wave(spw). 2. penetration depth of surface plasma wave(spw). 3. concentration of the (spw). 4. the equation of the interface in vacuum - plasma interface. I feel confused regarding such...
  34. Richie Smash

    Find the maximum length of x that will maintain equilibrium

    https://www.physicsforums.com/attachments/220647 Homework Statement Two uniform planks each of mass 10Kg and length 2m, are arranged as shown in the picture. Find the maximum value of x for which the top plank will remain in equlibrium. Homework Equations F= (mgl)/hThe Attempt at a Solution I...
  35. A

    Inertial frame where rods have same length

    Homework Statement I was re-reading my old Relativity book (by Rindler) and taking a look at some of the problems. He asks: Using a Minkowski diagram to establish the following result: Given two rods of rest lengths ##l_1## and ##l_2 (l_2 < l_1)##, moving along a common line with relativity...
  36. Destroxia

    Special Relativity - Length Contraction

    1. Homework Statement Why does the non-relative simultaneous frame have an additional term of ##v \Delta t## along with the contracted length ## L ## for ## \Delta x ##? 2. Homework Equations ## L + v \Delta t = \Delta x ## ---- (1) ## \Delta x = \gamma \Delta x' = \gamma L_{\star} ## ----...
  37. Perodamh

    Relationship between thickness, width and length

    1.A rectangular steelbar of length subjected to tensile force of 80kN. Calculate the change in length if the width and thickness are (40 & 25)mm respectively. (E = 207 GN/m2). Homework Equations E= stress/strain stress = F/A; F =80kN strain = dL/L 3. I just want to know what to use for the...
  38. Phil123

    [LENS] Given focal length and height, find object distance

    Homework Statement An object is in front of a convex mirror. We then obtain an erect image whose height is equal to 25% of the height of the object. What is the distance between the object and the mirror if we know that the focal distance is equal to 0.2m? Homework Equations M = Yi/Yo = q/p...
  39. Richie Smash

    Find the length of PR and the bearing of P from R

    Homework Statement A ship sails 3 nautical miles from Port P on a course of 64° to Port Q, then changes course to 285° and sails a further 7 nautical miles to Port R. (i) Draw a carefully labelled diagram of the entire route taken. Show the north direction where necessary. (ii)Calculate the...
  40. T

    Wave Physics - Optics - Effective Focal Length

    So we have the focal lengths: f1, f2, ..., f7 = 25mm And the distance between the lenses: d1-2, d2-3, ..., d6-7 = 50mm I have figured out that if the system would be afocal if it had an even number of these lenses. This is because the focal length of two adjacent lenses is the same as the...
  41. J

    Satellite and length of liquid column in a barometer

    Homework Statement Homework EquationsThe Attempt at a Solution Mercury will be in a state of weightlessness in the satellite . The air pressure pushes down on the mercury in the cup as a result of which it rises in the barometer tube . But since it is apparently weightless , it tries to...
  42. L

    How to find the length of the wire?

    Homework Statement For a 150 MHz (1 MHz=1 million cycles per second) radio signal, the wavelength is 2 m long. If each wire is about 0.5 m long, a half wavelength of radiation will span the two wires taken as one. The result is that electromagnetic waves are generated in the direction of the...
  43. B

    Angled Length Contraction (Relativity)

    Homework Statement Find the length of a meter stick if in the laboratory frame it is angled at 60 degrees relative to the direction of motion, and it is traveling at .8 c. I have calculated gamma to be 1.667 Homework Equations Lorentz transformations The Attempt at a Solution a' = l' cos(x)...
  44. A

    What Focal Length Eyepiece Provides a -125 Magnification?

    Homework Statement The medium-power objective lens in a laboratory microscope has a focal length fobjective = 3.75 mm. What is the focal length of an eyepiece lens that will provide an overall magnification of -125? Assume student's near-point distance is N=25cm. Homework Equations...
  45. Ranku

    I Length Contraction & Mass Increase in GR | General Relativity

    In special relativity, an object moving at higher speed experiences time dilation, length contraction, and mass increase, compared to an object moving at slower speed. In general relativity, for an object in stronger gravitational field (i.e., with higher acceleration due to gravity), time runs...
  46. I

    Hydrostatics, Length of a mercury column

    Homework Statement What will be the length of mercury column in a barometer tube, when the atmospheric pressure is 75 cm of mercury and the tube is inclined at an angle of 60° with the horizontal direction? Homework Equations Pascal's Law The Attempt at a Solution l ⋅ sinϑ = h l = h / sinϑ l...
  47. I

    Hydrostatics, find length of kerosene column in U tube

    Homework Statement A glass tube is bent into a U shape. Water is poured into the tube until it sands 12 cm high on each side. Kerosene (density = 870 kg/m3) is added slowly to one side until water on the other side raises 5 cm. What is the length of kerosene column? Homework Equations (ρhg)1 =...
  48. N

    About a concave mirror with a large focal length (1000mm)

    I have a Cassini PM-160 spherical mirror used in telescopes as the primary mirror. The mirror is concave with a radius of curvature of 2600mm and focal length of 1300mm. I have a very basic question. If an on object is located beyond the focal length of a concave mirror then the virtual image...
  49. H

    I Gravitational Force between two Rods of Mass M and Length L

    Find the Force of Gravitation between two Uniform Rods of Mass M and Length L. I heard my prof say that we have to do double integration to solve this. Please explain the above step and step with Diagram
  50. Pushoam

    Dimension of length using h,G,c

    Homework Statement Homework EquationsThe Attempt at a Solution Dimension of length using h,G,c [h] = [F r] ##[G] =[ \frac { Fr^2}{m^2} ] \\ [\frac { hG}c] = [L] ## So, the answer is option (b). Is this correct?
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