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).

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  1. D

    Finding the Length of a Small Square

    Homework Statement 2. Homework Equations [/B] The Attempt at a Solution I can find the length of the large square. The small square is where the trouble starts. If I look at the part of the circle where the small square is and put a center of a coordinate system at the bottom part of the...
  2. K

    I Inconsistency in Length contraction

    Let there be 2 astronauts A and B in uniform relative motion and they are moving towards each other. Let A be moving in a spaceship of length L and there are 2 clocks ca1 and ca2 attached to the front and back of the spaceship respectively and let clock of B be cb. The moment when the front of...
  3. J

    I Is the Planck length a proper length?

    The reciprocal of the Planck length, ##\Lambda=1/l_P##, is used as a high-frequency cutoff in the particle-physics estimation of the vacuum energy. For example in "the cosmological constant problem" Steven Weinberg says that summing the zero-point energies of all normal modes of some field of...
  4. F

    Relation between s=d/t and length contraction ?

    Homework Statement A 16m long vessel moved passed you at a relative speed of 0.86c. What was the length of the vessel recorded by your measuring device? Homework Equations Speed = distance/time t=to/√1-v2/c2 L=Lo⋅√1-v2/c2 The Attempt at a Solution Ok, so I can just sub the 16m and 0.86c in...
  5. H

    I Length-contraction time-dilation fallacy & length measurement

    Suppose an observer in the Earth frame set out to measure the length AB by measuring the time interval between the event "B coincides with D" (event BD) and the event "A coincides with D" (event AD), and then multiplying the time with ##v##. This observer argues that an observer in the train...
  6. Z

    Length of diagonal from bottom to top

    1. Homework Statement I have to find the length of a diagonal from bottom to top. I don't know which formula i would be using? Please see the attachment for more information. Homework Equations May be pythagorous theorem. But i don't know which sides i have to select The Attempt at a Solution...
  7. J

    A Is the Plank length the same in every direction?

    while i understand what plank length is... Has it ever been measured on multiple axis? As an indicator of the granularity has the plank length (or second) been thus measured?
  8. J

    I Planck length and space expansion/contraction

    Imagine a cubic volume of space, defined today, with edges of the order of the Planck length. As cosmological time goes forward this volume expands so that the edges of the cube expand with the scale factor. This seems ok. However, as physics is time-reversible, it should be valid to imagine...
  9. DoobleD

    I Why is inflation initial patch length ~ 1 Hubble length ?

    I'm asking many questions on inflation, I hope this is the last one... If inflation is correct, our observable Universe would have been a tiny homogeneous patch before inflation started (if it started at all). The length of that initial patch is estimated to be of the order of 1 Hubble length...
  10. A

    I The length of the visible horizon

    How much is the length of horizon that human's eye can see at sea level? How much is the length of horizon that human's eye can see at higher level? any formula? I am not sure i should use wide or length. i mean the rightest point of horizon to the leftest point of it for human' eye angles.
  11. N

    What fraction has the length of the rectangle been reduced?

    Homework Statement The width of a rectangle is increased by one tenth, but the area remains the same. By what fraction has the length of the rectangle been reduced? The Attempt at a Solution Length = x Width = x + 1/10 Set equation: L * W x *(10x + x) 10x^2 + x^2 I am stuck... Please help...
  12. ibkev

    B Length Contraction: Real Compressive Forces?

    I'd like to get some conceptual clarification on whether or not length contraction is only apparent to an observer or if it's physically real in the sense that the object under contraction would experience compressive forces? My thinking on this has been along the lines of: I know that time...
  13. Pushoam

    Length contraction -- numerical problem

    Homework Statement Homework EquationsThe Attempt at a Solution a) t' = l0/c b) ct1 = l0 /ϒ - vt1 t1 = l0 /ϒ(c + v) c) t2 = l0 / (ϒ v) Is this correct?
  14. Pushoam

    Length contraction numerical problem

    Homework Statement Homework Equations 1) k.e. = (1/2)mv2, non- relatvistic 2)K.E. = m0 c2 (ϒ -1), relativistic 3) L=L0/ϒ , Length contraction The Attempt at a Solution (A) Taking 1019 eV to be the kinetic energy of the proton, Non- relativistic calculation (1/2)mv2 = 1019 eV = 1.6 v =...
  15. R

    Length of a 60/40 soldering lead that is 1lb and 0.8mm dia?

    what is the Length of a 60/40 soldering lead that is 0.453kg and 0.8mm in diameter? i could not find the volume of the thing so is there any other way to go around this? i could also not find the density of the 60/40 solder. so yeah I am asking here if anybody knows thank you
  16. Q

    Creating a two lens system of tunable focal length

    Hello, I would like to reduce the beam size of a laser by a factor of 10, with the purpose of replacing a long (750 mm) lens with a more compact design. Ideally I'd make a Galilean lens pair where the ratio of the focal lengths are 10:1 to produce a small collimated beam. However, I think I...
  17. A

    B Reporting length with error limits

    Hello all, I am in a total state of confusion with regard to this. Here is question. The length of a rod is [11.05 (+/-) 0.2]cm. What is the length of two rods? I want to know should the answer be reported like [22.1(+/-) 0.2] or [22.1(+/-) 0.4]. Regards:)
  18. A

    What's the shortest length here?

    Homework Statement Question: An ant starts at one vertex of a solid cube with side of unity length. Calculate the distance of the shortest route the ant can take to the furthest vertex from the starting point. Now, in the answer, the cuboid is unfolded and a rectangle of side 1 and 2 is...
  19. aatari

    Adding Vectors: Understanding Direction and Length

    Homework Statement Hi Guys, I am a bit unclear regarding adding vectors and hoping someone can clear up the confusion for me. In the image below, we are adding two vectors and we used the vector components to find find x and y. Finally we then used x and y to get the resultant and the angle...
  20. Pushoam

    I Derivation of length contraction

    Problem : To measure length of a scale Rest frame : The frame w.r.t. which scale is at rest Moving frame : The frame w.r.t. which the scale is moving with speed v along +ve x-axis In rest frame ,the positions of the two ends of the scale are (measured simultaneously ) x1 and x2. So length L =...
  21. H

    A circle is circumscribed around triangle ABC, find length?

    some formula related I tried to draw the problem can anyone give me clue how to solve it?
  22. Lunct

    B What is the significance of the Planck length in physics?

    The definition of the Planck length I have found is that it is the shortest length that has meaning. What is meant by that? Can someone give be a better definition of what it is?
  23. J

    I Does the Planck length expand in a FRW universe?

    By using particle physics natural units with ##\hbar=c=1## so that Planck's length ##l_P=(8\pi G)^{1/2}## we can express Einstein's field equations as $$G_{\mu\nu}=l_P^2\ T_{\mu\nu},$$ where ##G_{\mu\nu}## has dimension ##[\hbox{proper length}]^{-2}##, ##l_P## has dimension ##[\hbox{proper...
  24. AdrianMachin

    Multiplying epsilon naught by a length quantity

    Homework Statement Note that this formula (##C=4 \pi \epsilon_0 R##) and the others we have derived for capacitance involve the constant multiplied by a quantity that has the dimensions of a length. Homework Equations ##\epsilon_0## has the following units in SI: $$\frac {C^2} {N \cdot m^2}$$...
  25. Bunny-chan

    Conservation of the string length in pulleys

    Homework Statement This is a common massless string and pulleys problem. I'd just like to understand why, according to the solution, l_2 + 2l_1 = constant. It doesn't seem to me that two times the l_1 length is equivalent to l_2. Can somebody explain? Homework EquationsThe Attempt at a Solution
  26. G

    What is the estimated path length traveled by a deuteron in a cyclotron?

    Homework Statement Estimate the total path length traveled by a deuteron in a cyclotron of radius 53 cm and operating frequency 12 MHz during the entire acceleration process. Accelerating potential between dees is 80 kV. mass m = 3.2e-27 kg charge q = 1.6e-19 C radius r = 0.53 m frequency f =...
  27. T

    What is the length of Chromatosomal DNA?

    I see various sources: 1. Karp- Cell biology 2. some papers 3. Michael M. Cox -...
  28. H

    MHB Finding the Length of the Right Angle Bisector

    Hello I would need help to continue. calculation problem: Given a right angled triangle with catheter lengths a and b length units, determine and indicate the length of the bisectris to the right angle. find: Xa^2 + b^2 = (y+z)^2X^2 + y^2 = a ^2X^2 + z^2 = b ^2
  29. R

    Help me find the arc length of a parametric equation....

    1. The problem statement, all variables and given/k nown data x = (sin(t))^2 y = (cos(t))^2 t goes from 0 to 3 pi Homework Equations ∫ \sqrt{ {(dx/dt)}^2 + {(dy/dt)}^2 } dt The Attempt at a Solution ∫ \sqrt{ {(2sin(t)cost)}^2 + {(-2cos(t)sin(t))}^2 } dt ∫ \sqrt{ 4(sin(t)cos(t))^2 +...
  30. M

    I Determining Appropriate Focal Length

    So I'm working on a project where we're deciding a new lens to use for our laser diode. I need to determine the appropriate focal length based on the equation: 1/ƒ = 1/μ + 1/σ where ƒ is our focal length, μ is the distance from the lens to image and σ is distance from lens to object. For the...
  31. peroAlex

    Special Relativity: Length Contraction Problem

    Hello! I have a small problem with a task professor gave us. I tried many options (you will see below) but I cannot seem to get the right solution. Any advice or guideline how to solve this would be really helpful. In advance I thank you for helping me. Homework Statement Our professor of...
  32. DevonZA

    Calculate the total change in length of a brass bar

    Homework Statement Homework Equations Stress = force/ cross sectional area elongation = force x length / modulus of elasticity x cross sectional area The Attempt at a Solution The given solution is 0.149mm I assumed that the bar needs to be solved in two sections because of the hole...
  33. S

    B Length Contraction & Time Dilation: Relative Velocity Impact?

    So an object moving close to the speed of light will be length contracted. Does that mean the distance it covers also contracts in length? From the traveling object's point of view it's surrounding's would contract as he sees them moving along. In these scenarios wouldn't velocity be a...
  34. R

    Chemistry Correct order of bond length in two organic molecules

    Homework Statement : [/B]The correct relation is: A. x=y B. x>y C. x<y D. None. Please refer to picture attached.Homework Equations : [/B]As stability increases, bond length decreases. When a Π bond is delocalised i.e it takes part in resonance, stability increases.The Attempt at a Solution I...
  35. V

    Length of sinusoid on a sphere

    Homework Statement Originally the statement: Find a length of two points on sphere. It was easy. ##\int \sqrt{g_{\phi\phi}}d\phi## I hope you agree :-) But I have idea, how to find a length of path which is NOT a part of arc (circle). For example sinusoid. Is possible to find length of sinusoid...
  36. T

    B Confused About the Length of Time Between Ticks in Time Dilation

    I am confused about time dilation. I understand that a common pedagogical device used is a light clock, in which a pulse of light flashes back and forth between two objects. I understand that when an observer in a vehicle carrying such a contraption is moving, to an external observer, as the...
  37. M

    MHB Length of Wire and Area of Squares: Solving for the Length of Each Piece

    A piece of wire is cut into two pieces. Each piece is then bent to form a square. If the sum of the areas of the two squares is 5L^2/128, how long is each piece of the wire? My Reasoning: I see the words square and sum of the squares. A = s^2, where s is side of the square. Sum of the areas...
  38. Superman123

    Calculating Angle to Shoot Sword Over Wall for UT - 65 Characters

    Homework Statement UT has jumped over a wall and unfortunately for her, she forgot to bring her sword. Her friend SS decided to shoot the sword to her with a bow. He can bend a bow and arrow so that it gets a potential energy of 179 Nm. It seemed that Ut landed 9 meters behind the wall; a...
  39. A

    I Length of lunar month immediately after moon's formation?

    Does anyone know how long the lunar month was when the moon was formed? I can't get the equation to work. I'm looking for speed of the moon when it was created at about 1/10th the current distance from the earth. Thanks.
  40. P

    Plano convex lenses and focal length

    Does the orientation of a plan convex lens affect it's focal lenght? If I put il like in the first example in the photo and makeep the calculation using the lens maker equation I get f positive What happens if I turn the curved face on the right? Using the lens maker equation now the radius...
  41. P

    B Measuring Length: Accurately Calculate Coastline Length

    How would you approach a most accurate measurement of the "length" of a coastline?
  42. Vitani11

    Difference b/t equilibrium and unstretched length of spring?

    Homework Statement Consider a mass attached to four identical springs, as shown in the figure. Each spring has a force constant k and an unstretched length lo, and the length of each spring when the mass is at equilibrium at the origin is a (not necessarily the same as lo). When the mass is...
  43. R

    I Arc Length Parameterization for Unit Circle: Cos(s) & Sin(s)

    (cos(s), sin(s)) gives an arc-length parameterization of the unit circle so that the speed is constantly 1, but the second derivative doesn't give zero acceleration which should be the case with constant speed?
  44. T

    Number of turns vs. wire length affecting voltage in coil

    When winding a coil around a magnetic core, if you wanted to tap the coil such that each half has the same AC voltage output, would you: A) wind each part at the same RPM for the same amount of time, to get the same number of turns for each, or B) wind the second part proportionally less, to...
  45. F

    Half life - Calculate the length of time

    Homework Statement A source having a half life of 5.27 years is calibrated and found to have an activity of 3.5*10^5 Bq.The uncertainty in the calibration is +- 2% Calculate the length of time in days after the calibration has been made for the stated activity to have a maximum possible error...
  46. I

    MHB This gives us the length of each train as 500 meters.

    Two trains of equal length are on parallel tracks. One train is traveling at 40 km/h and the other at 20 km/h. It takes two minutes longer for the trains to completely pass one another when going in the same direction, than when going in opposite directions. Determine the length of each train...
  47. M

    I Has Planck length been derived rigorously?

    ħello. Here is my question: Has the so-called "planck length" (~1.61622837 * 10^(-35) meters) been derived with mathematical rigor within standard quantum field theory? If so, I need help finding this proof. Any literature would be appreciated. Also: If it has, then doesn't this imply a...
  48. R

    Length and Area of Cylindrical Nichrome Resistor

    Homework Statement You must complete the circuit of (Figure 1) in such a way that it draws a current of 0.450 A from the battery. The battery maintains a potential difference of 10.0 V with no load, but has an internal resistance of Rbatt = 15.0 Ω . The only material you have is 20.0 mm^3 of...
  49. V

    Integrated track length in electromagnetic shower

    Homework Statement Show that integrated track length in EM-shower is proportional to ##E_0##. Homework Equations ##E(t)=\frac{E_0}{2^t}##, with radiation length, ##x_0##. Knowledge that shower terminates at ##E_c##. The Attempt at a Solution The total track length is naturally the total...
  50. D

    What is the Method for Finding the Magnitude of a Complex Vector?

    Homework Statement Let a is a complex vector given by a = 2π K - i ρ / α^2 , where ρ is a two dimensional position vector and K is the corresponding two dimensional vector in the Fourier space. In order to find magnitude of this vector, i found that it is 4π^2 K^2 + ρ^2 / α^4 . The logic...
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