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. L

    What is v×w if v, a, and b have length 1 and w has length 2?

    Homework Statement Let v, a, and b be the vectors (in the plane of the paper), all of which have length 1. (See attached picture). Let w be a vector of length 2 pointing directly out of the paper. Which of the following vectors is v×w? Homework Equations The formula for the cross product of...
  2. pixel

    I Implication of length contraction

    I had posted a similar question on another forum but didn't get much of a discussion. I'm interested to know what people here think. So consider a spaceship midway between stars A and B and initially at rest in the reference frame of the stars. The ship then accelerates away from A to some...
  3. M

    Length Contraction & Time Dilation

    Homework Statement A spaceship of proper length L is moving with respect to the ground with speed v. As measured on the ground, how much time does a light signal need to get from the front to the end of the spaceship. Homework Equations L'=L/γ t'=tγ The Attempt at a Solution The right answer...
  4. M

    Find the area and length of a gold leaf

    Homework Statement Gold, which has a density of 19.32 g/cm3, is the most ductile metal and can be pressed into a thin leaf or drawn out into a long fiber. (a) If a sample of gold with a mass of 3.872 g, is pressed into a leaf of 5.372 μm thickness, what is the area of the leaf? (b) If...
  5. G

    Calculate the focal length of the spectacle lens

    Homework Statement A hyperopic eye has a near point of 1.10 m. Calculate the focal length of the spectacle lens required to correct the hyperopia (assume that the near point of the normal eye is 25.0 cm.) Homework Equations 1/f=1/p+1/q The Attempt at a Solution I just used .25 m as p and...
  6. S

    How many words of length n are there in this regular language?

    Homework Statement I am self studying automata theory and I found a problem set from an old class I took a few years ago, but I have no clue how to solve the following problem, any help would be appreciated.Suppose we have a regular language ##L \subseteq \{0,1\}^*## and the language ##...
  7. U

    MHB Right Isosceles triangle: solve for the length of the unknown legs

    For a right isosceles triangle (45-45-90) of hypotenuse 1, solve for the length of the unknown legs. Give an exact answer and rationalize the denominator in the final answer.
  8. D

    MHB Scale Drawing: What is the real length of the bus

    QS) A model of a bus has a scale of 4cm to 3m. The model is 10cm long. What is the real length of the bus? my workout: 4cm to 3m. 4 cm is length of model and 3m is real length. so we have, mode = 10 cm long so 4 cm to 10 cm: 10/4= 2.5 cm for real length 3 X 2.5= 7.5 m. I am not sure about...
  9. J

    How do I Calculate Maximum Length for a W24 X 94 Beam with Moment Loads?

    I have a W24 X 94 beam (50KSI) that is loaded with a 3,500,000 in-lb moment load at each end. How do i calculate the maximum length of the beam that can support the moment loads?
  10. C

    Calculate the Length of a Circle's Radius

    1. Homework Statement A circle in a x-y coordinate system is given. The equation of the circle is unknown. The circle touches the x axes at (3,0). It also passes through the point B (0,10). Calculate the length of the circle radius? Homework Equations (x-p)^2 + (y-q)^2 = r^2 The Attempt at a...
  11. EEristavi

    Finding Length of a Curve: y2 = (x-1)3

    Homework Statement I have to find length of the curve: y2 = (x-1)3 from (1,0) to (2,1) Homework Equations s = ∫ √(1 + (f '(x) )2 ) dx where we have integral from a to b The Attempt at a Solution I'm bit confused: I'm thinking of writing function regarding x, f(x)...
  12. B

    Relation of laser pulse length and the Output Coupler trasmissivity

    Dear all, I'm within my Ph.D. studies in laser engineering and most of the details are rather new to me. Working on short pulse systems, my advisor told me some times about the relation of the output coupler transmissivity and the outcoupled pulse length, but more as a rule of thumb. According...
  13. H

    Transition energy estimation based on bond length

    I come across this question in a textbook. Somehow my result is way off from the solution answer. I used the energy formula for particle in a box with n(Initial) = 22 and n(End) = 23, the calculated box length is 732 pm. I arrived at an answer of 39.3 nm. The answer from the answer book is but...
  14. E

    MHB Find radius, circumference, area and arc length in circle

    So I've been able to solve A.12 inch B.24 inch C.75.3982 D.452.389 Cant solve e. Arc length can anyone please explain the formula. Thank you
  15. B

    MHB Calculating Triangle Side Length with Known Angles and Radius

    Hi there. Can someone tell me how to calculate the length of "a", shown in these drawings? "r" is the radius of the corner, so these 2 sides have the same length. "C" is 90 deg angle "B" is known (the angle of the corner) Here are the diagrams. First example 45 degree corner, second example 75...
  16. opus

    I Looking for intuition on differentials and arc length

    Please see the attached image. It's a part of a study guide for my final, but I didn't put it in the homework section because I already got the answer, I just don't know what it means. The question has to do with the differential of an arc length. I made some drawings to see if I could make some...
  17. Krushnaraj Pandya

    Relation between vector length and direction ratios

    Homework Statement A vector r has length 21 and direction ratio's 2,-3,6. The direction cosines of r, given that r makes an obtuse angle with x-axis is given by? Homework Equations l/a = m/b =n/c ...(1) (l,m,n are direction cosines, a,b,c are direction ratios l^2 + m^2 + n^2=1...(2) The...
  18. J

    Channel length modulation in a MOSFET

    Hi, I'm struggling to understand how channel length modulation takes place in mosfet. The books n internet said that as drain side is positive, there is less potential difference between positive gate and positive drain, while there is more potential difference between positive gate and zero...
  19. S

    Minimum Wire Length Calculation for Square Pattern in 10cm Square

    Homework Statement A wire pattern is inserted into a ##10##cm square by making a horizontal line in the middle of the square (not all the way across and with length ##x##) and connecting the ends of this line to the closest two corners. What is the minimum value of ##x##? Homework EquationsThe...
  20. S

    B Take on Length Contraction at relativistic speeds

    Hello everyone and apologize if my questions seem a bit off, please have patience with me. I want to have the following, rather simple, thought experiment. Let's say that we have a moving object O with the proper length L, when at rest. Let's say that object O starts moving at 0.9c (90% the...
  21. Krushnaraj Pandya

    Ratio of the length of resistive wires in a square

    Homework Statement In a given square ABCD each side is of 1 m and resistance of wire is 1 ohm/m. A resistance of 1 m is connected from A to E (which lies on side CD). A constant potential difference is applied across A and C, if potentials of B and E are same then find CE/ED. Homework...
  22. K

    MHB How Can the Sine Rule Help Determine Lengths in Irregular Shapes?

    Hello, What is the value of x in the attached? obviously angle EAD = EDA but then what? the shape is irregular.
  23. K

    MHB Find Length X in Triangle: Learn How to Calculate It

    what is the length x? (FH and HC perpendicular too, which I missed to write) I am totally stuck can not make any progress on this question. Answer should be 5. I don't know how to obtain it
  24. Charlie Cheap

    Automotive Points ignition output voltage and length?

    As the go-to-guy for first generation 6-cylinder Mustangs, I have an unusual question. With a carburetor type engine, operation at 1000 to 5000 rpm, is a modern electronic ignition truly better than a hot points system? After studying both types it seems newer ignitions make a hotter spark but...
  25. K

    MHB What is the minimum value for x in this triangle with angle bisectors AD and BD?

    Hello, In the attached, what is the minimum integer value x can take? AD and BD are angle bisectors the answer is 16 - but i do not know how they did it I am totally stuck, could not think of anything here. The angle bisector formula I know does not fit here
  26. YoungPhysicist

    I Wavelength approaching the Planck length

    If I heat up an object,the object emits a electromagnetic wave with a shorter and shorter wavelength. But if I heat an object up to Planck temperature, and making the EM wave that it emits has a wavelength of Planck distance,what will happen when I heat it up even more? Will the wavelength...
  27. YMMMA

    Path length differences/ interference problem

    Homework Statement In the figure below, Two wave sources, M and N, are vibrating in phase on the surface of water and generate waves of wavelength λ. Which of the following values for the distances MP and NP will result in minimum disturbance at a particular point P on the surface of the water...
  28. DracoMalfoy

    Shear modulus, finding length of board

    Homework Statement A diver stands (80kg) at the end of a diving board, causing the board to dip 10cm. The board has a width of 34cm and a height of 6cm. If the shear modulus of the board is 2x10^6pa, what is the length of the board? (Ans: 5.2m) Homework Equations [/B] F/A=S⋅Δx/h The...
  29. DracoMalfoy

    Young's modulus of a steel post, finding change in length

    Homework Statement Superman pulls on a steel post to trap a supervillian. The post has a cross-sectional area of 30cm^2 and a length of 2m. If Superman applies a force of 6X10^6N by how much is the length of the post increased? A) 2mm B) 7mm C) 1.2cm D) 1.7cm E) 2cm Homework Equations...
  30. zox00

    I Deriving Lorentz from time dilation and length contraction

    Is it possible to derive the Lorentz transformation from time dilation and length contraction? If so, how should I start? I know how to derive it while considering 4 scenarios finding values of A, B,D,E in x'=Ax+Bt t'=Dx+Et and the transformation is: x'=(x-vt)/sqrt(1-v^2/c^2)...
  31. E

    How to calculate the required length of an axial pump piston

    Based on other parameters how do you calculate the required length of a piston inside the cylinder block of an axial piston pump? What are the relevant equations? I've found many for the required diameter but not the length.
  32. T

    How is the horizon length related to the power law spectrum

    Homework Statement For a power spectrum density fluctuations ##P(k) \propto k^n##, I need to find the scaling (with respect to ##a##) of the horizon wavenumber ##\frac{2\pi}{\chi_H}## in a matter dominated universe in terms of ##n##. ##\chi_H(a)## is the evolving particle horizon, in a flat...
  33. W

    I Does the Planck Length Experience Length Contraction at High Speeds?

    Imagine I had a ruler 1 Planck length long, I then send it on a rocket close to the speed of light, does its length contract? It seems to my simple intuition, relativity would say yes and Qm would say no. Is there a simple solution to this ?
  34. J

    Should I use time dilation or length contraction?

    1. Homework Statement [/B] This is a problem that was in my Physics HW. Two powerless rockets are on a collision course. The rockets are moving with speeds of 0.800c and 0.600c and are initially ## 2.52 × 10^{12} ## m apart as measured by Liz, an Earth observer, as shown in Figure P1.59. Both...
  35. M

    Python How to drop rows when there is a length mismatch?

    I am trying to drop the series size so that it matches the size of the dataframe as I need to copy the index value of the series into the df but I am getting mismatch errors. df has a size of 100 but time has a size of 200 so I want to remove the extra rows in time to match df. how can i handle...
  36. K

    Max. acceleration of a pendulum changes with its length and mass?

    Hi, If I find out the tangential force on the bob at position 1, it turns out to be m*g*sinθ. From this if I find out acceleration by dividing this equation by m, I get only g*sinθ. Does it mean the max acceleration of pendulum has got nothing to do with its length or mass but theta?
  37. Umaxo

    Find Length of Median in Triangle via Cosine Law

    <Moderator's note: Moved from a technical forum and thus no template.> Hi, i am quite embarrassed to ask this question, but i am really stuck. i want to derive length of median of triangle from cosine law and i am getting wrong results. I cannot spot the mistake. So let's have a triange with...
  38. DoobleD

    I Why is the number of wavelets in a slit = slit length / lambda

    Hi folks, Huygens principle is not really new to me but I just realized there is something I don't understand with it. Take a single 1D slit with a coherent incident plane wave. It seems that the number of wavelets in the slits is ##n = l/\lambda##, where ##l## is the length of the slit, and...
  39. S

    Decay length of the evanescent wave

    Homework Statement A beam of light of vacuum wavelength λ = 550nm passes from water (refractive index 1.33) into air (refractive index 1.00). (a) What is the critical angle? (b) Suppose the beam is totally internally reflected. At what angle of incidence would the decay length of the...
  40. N

    I Length Expansion Opposite Direction: SR Simultaneity Explained

    SR says that there is length contraction in the direction of movement. This works nicely for light going from the back of the ship to the front. From my perspective, the ship is moving away but that is offset by the ship's contraction. But things get tricky for light going from the front of the...
  41. N

    I Question about length contraction

    I have seen in SR that regular time and regular distance is equal to slower time and less distance because of length contraction. Say a person on Earth sees a ship moving towards it. This reference frame has regular time and regular length and it views the ship's reference frame as having slower...
  42. DracoMalfoy

    Measurement and Graphing. Dependence of a Pendulum on length

    For the experiment, we were to determine the relationship between two quantities through linearization after collecting measurements. To verify that P~L^1/2. and determine proportionality constant, C. P=C√L/g= (Cg^-1/2)(L^1/2) Materials used were a timer, string(The pendulum on length), and a...
  43. babaliaris

    I Is the universe actually just mass and length?

    After reading some classical physics I learned that the entire physics is actually studying the combination of 3 quantities mass, length and time. Anything in the universe is just the combination of mass and length and time. And why i say that? Because if you notice the formulas that the...
  44. DracoMalfoy

    Dimensional Analysis: Period of a Pendulum to the length

    Homework Statement Use unit analysis to show that the constant, 2π, is unitless. Homework Equations T=2π√L/g[/B] The Attempt at a Solution T= [T] L= [L] g= a= [L]/[T]^2= [L T^-2] [T]= 2π√[L]/[L T^-2] [/B] Is this correct? I wasn't really sure how to do this. I'm using book examples to...
  45. K

    Min max problem: length of pipe from 2 towns to the river

    Homework Statement Homework Equations Minimum/Maximum occurs when the first derivative=0 The Attempt at a Solution $$l_1^2+l_2^2=(a^2+x^2)+[b^2+(d-x)^2]=a^2+b^2+x^2+\left[ \sqrt{c^2-(b-a)^2}-x \right]^2$$ $$(l_1^2+l_2^2)'=2x+2\left[ \sqrt{c^2-(b-a)^2}-x \right](-1)$$...
  46. H

    B Why does a Moebius strip twist unevenly along its length?

    A recent article in Smithsonian magazine about knitting geometric forms stimulated the following question: In the above, knitted Moebius strip, there are areas where the material is twisted (seen in front) and areas where the material is flatter/less twisted (seen in back). So far as I can...
  47. N

    I Length Contraction of Protons in the LHC

    What affect does the phenomenon of "length contraction" have on the shape (e.g. spherical, rugby ball, barbell, donut) of protons accelerated to 0.999999991 c in the LHC?
  48. S

    I Extreme Length Contraction: Classical to Quantum?

    Hello! If we have a 1m stick (as measured in its stationary reference frame, call it S) and we (S') move with a high enough velocity, we can make the length of the stick in our frame as small as we want. So for high enough velocities, the stick will appear so small in our frame, S', that it will...
  49. Brilli

    Dependence of extention on length

    Homework Statement A light uniform spring is tied between the ceiling and the floor keeping the spring vertical as shown in the figure. A bead of finite mass is glued at a distance l from the upper end and then allowed to go slowly down. The bead shifts a distance y.How does the y depend on...
  50. E

    Find the length of a roll of GI steel sheet given its weight

    Homework Statement I have a roll of galvanized iron sheet steel. Its width is 19mm and thickness 0.25mm Density 7850 kg/m^3 Weight of the roll is 75kg I want to find how long would be the roll if its unwound. Homework Equations Density D = M / V Length L = V / A Area A = Width * Thickness The...
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