# 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. ### Spaceship length contraction problem

For this problem, Does someone please know that won't the cabin, the person, and the clothing all shrink by the same proportion in the direction of travel so if you brought smaller cloths or a smaller cabin than you normally would then you may not be able to fit in? So you should not buy a...
2. ### How long is the longest piece of the given Rope?

I do not seem to understand why the ms answer is (C) 45 m unless i am missing something, In my working i have the longest piece being; ##x+0.5x+0.25x= 95## ##x=\dfrac{380}{7}= 54.28 ##m
3. ### I Relativity of Simultaneity and Length Contraction

This has probably been discussed/explained many times before so I apologize in advance. Please just direct me to the relevant thread if it has. In Morin, "Special Relativity For the Enthusiastic Beginner", he explains the loss of simultaneity and specifically the "rear clock ahead" effect. If...
4. ### I Perceive Length Contraction VS Terrell Penrose

This is a more of a "can you confirm" what I am thinking here; I think I understand what is going on, but just want to make sure. At the end of this post, I reference the two selected websites at the times mentioned that compare "Length Contraction" verses "Terrell Penrose Rotation." My...
5. ### Finding the power loss in a wire of varying cross-sectional area

TL;DR Summary: Finding the power loss in a wire of varying area - my problem is I don't know how to set up the integral Hopefully you can see in the diagram below that the area of the wire varies linearly with length. I know the equations for resistance and power loss and I can express the...
6. ### Calculate Max Resistance for 2 Parallel Wires

Hi, I am not sure if I have calculated the task here correctly: Based on the drawing, I now assumed that the two resistors are connected in parallel. The total resistance can then be calculated as follows ##\frac{1}{R_T}=\frac{1}{R_1}+\frac{1}{R_2}##. Since the two wires are made of the same...
7. ### Do different length ramps violate conservation of energy?

mgh=(1/2)(m)(v^2) gh=(1/2)v^2 sqrt(2gh)=v Should have the same v, but this is not the case based on the answer and real-life experiments.
8. ### I Surface area and length (percent increase relationship)

Hi all, While calculating the surface area for an object, I was told the below statement. However, I am not sure is this correct, please can someone help me to explain this with an example? Is the below statement always true? The surface area % increase should be in line or less than the %...
9. ### Speed of sound from resonant length of tube vs tuning fork wavelengths

The graph is, I do not understand why how it is possible to find the speed of sound from the gradient for this graph. Can someone please help? Many thanks!
10. ### A Boundary conditions for variable length bar

Suppose I'm looking at a bar of length L(t) in 1D and I have the conservation of mass: \frac{\partial\rho}{\partial t}+\frac{\partial}{\partial x}(\rho u)=0 In order to make things easier, I make the change of variable x'=x/L(t) so that in this frame of reference, the length remains constant...
11. ### Driving force from buzzer for jacket of length L

For this problem, How do we tell when the buzzer vibrates during the cycle to provide the driving force? Many thanks!
12. ### Electrical Load Cell Wiring Length Question

I would like to weigh our pet parakeets. They are rather skittish, so the idea I came up with was to hack a digital scale so as to put the controls and display some distance from the scale. Then I would add a perch to the scale. When one of our birds lands on the scale, I could turn on the...
13. ### Length element in Ampere's law

Why is the length element (vector ds) perpendicular to the current? I though length element should be parallel to current. Would anybody be kind enough to help.
14. ### I Let a standing wave of length L go, get traveling wave of length 2L?

Consider a very long string between fixed supports of mass density rho and tension T. At a distance 1 meter from one support pinch the string. The pinching does not change the tension. Adjust the mass density or tension so that when we add energy to this section of string we produce the first...
15. ### I Calculate Length Contraction for Accelerated Motion to Proxima Centauri

Let's assume a spaceship traveling from the Earth to the Proxima Centauri with constant acceleration g = 9.81 m/s2. The ship is accelerating the first half of the trajectory and decelerating the second half. I calculated the velocity profile from the Earth reference: The travel time on...
16. ### B Length Contraction: Exploring the Possibility of Black Holes at High Speeds

If I am traveling in my spacecraft at .99999999 percent the speed of light past a star, then according to the equation of length contraction a star with 4x or more solar mass would contract along the line of motion according to my frame of reference by an amount of over Length naught (8*10-E)...
17. ### I How to calculate focal length?

Hello, I am new to this forum and know very little about it. But perhaps somebody can help me. I have an Epson 2040 projector. The beam it projects fits into the screen at a distance of about 4.5 meters. But logistically I need to put it at 8 meters from the screen, so the projected images are...
18. ### Physics project confusion (effects of length on a pendulum)

We are seeking to design a project where we use a simple pendulum and a motion sensor (that will give us velocity) in order to study centripetal acceleration by essentially changing the length of the pendulum for each trial. This felt simple enough, however our professor insists that we would...
19. ### I Time Dilation & Length Contraction: Graphically Explained

The thread "twin paradox without math" inspired me try to find fully graphical solution of length contraction. Here is the result: Graph is 3D as I think that is ilustrative to make all in one graph, but I am sure that it is possible to do it in 2 or 3 2D slices. X and Y are spatial axes, T is...
20. M

### C/C++ Max length of substring-palindrome

Hi PF! I'm trying to find the max length of a sub-string palindrome. My logic is to have a left-most index called start that starts from string loc 0 and traverses to the end of the string via a for loop. Next I was thinking a while loop as long as L < R: I'd have a left index L=start and a...
21. ### What is the length of an infinite potential well for an electron?

I have a nanoparticle of cadmium selenide with a diameter d. When it emits a photon with a wavelenght lambda, it happens because an electron jumps from the conduction band to the occupied band across a forbidden band. I can suppose that jump as a jump from a higher energy level (the conduction...
22. ### I Why is length considered a fundamental (base) quantity?

Hello all, Textbooks define fundamental or base quantities as those quantities which are not expressed in terms of other quantities and they define derived quantities as those quantities which are expressed in terms of other quantities. I have the basic understanding that the choice of a set of...
23. ### Find the length of the curve C

This question is from a Further Maths paper; Part (a) is pretty straight forward...No issue here...one has to use chain rule... Let ##U=\dfrac{e^x+1}{e^x-1}## to realize ##\dfrac{du}{dx}=\dfrac{-2e^x}{(e^x-1)^2}## and let ##y=\ln u## on taking derivatives, we shall have...
24. ### I Relativistic length contraction

Hello! I have a question. If there is a wooden rod which burns certain time, and an astronaut inside rocket lights two such rods: one oriented along the rocket's length and the other goes across the rocket, and an observer see the rocket passing by with a relativistic speed. Will the observer...
25. ### I An issue with length contraction

I have read that length contraction is real and not just an illusion. However, when I compare an object at rest with an observer and the object in motion relative to another observer, I see that instead of there being a real length contraction, there is simply a difference in the part of the...
26. ### Find the length of PA - deductive Geometry

Text question is here and solution; My approach; ##BP ×AP= PT^2## Let ##AP= x## Therefore, ##(6+x)x=16## ##x^2+6x-16=0## ##x=2## or##x=-8## ##⇒x=2## positive value only. I guess this may be the only approach. Cheers!
27. ### Need to determine best placement and stroke length of a pneumatic cylinder

I'm making a device that will tilt a 500# load 20 degrees. Going to consist of a hinged 24" x 24" platform (that the load sets on). The platform will tilt to the right(clockwise) according to sketch. The upright post that the cylinder is attached to could be any length. The cylinder will...
28. ### I Time difference caused by length contraction

The goal is to calculate the difference in the passage of time between two ends of a cabin which is accelerating upwards due to length contraction. To help in the calculations we can consult: https://arxiv.org/pdf/1807.05338.pdf There is an old problem called the 4/3 problem which has been...
29. ### What is the Focal Length of a Lens for a Perfectly Fitting Image on a Sensor?

My attempt: m=-v/u=-f/(-f-u) -1/0.5= -f/-f-0.10 -> -f-0.10=0.5f -> f=0.20 m
30. ### Comp Sci Run Length Encoding: 20W, 8W5K7W, 9W3K8W, 7W7R6W, 6W4R1Y4R5W

Line Run length encoded sequence 1 20W 2 20W 3 20W 4 8W5K7W 5 8W5K7W 6 8W5K7W 7 8W5K7W 8 9W3K8W 9 7W7R6W 10 6W4R1Y4R5W 11 6W1R1W5R1W1R5W 12 6W1R1W2R1Y2R1W1R5W 13 6W1R1W5R1W1R5W 14 6W1R1W2R1Y2R1W1R5W 15 9W3B8W 16 9W3B8W 17 9W3B8W 18 9W3B8W 19 9W3B8W 20...
31. ### I Total focal length and magnification

I would like to realize an image of the cantilever. The dimensions are (450x50) microns. I would like to use a self-constructed telephoto lens. This consists of two lenses. The image magnification can be 4 to 8. The magnification of the image is nothing more than the ratio between the two focal...
32. ### Misc. Headwater: 2" drop in a 40 foot length culvert

I am trying to figure out the fps of 18 inch culvert with 13.5 inches water over the top on inlet and about 2 inches lower on the outlet and 2 inch drop on the outlet end over 40 foot length, what I need to know what would be the headwater on this type of configuration?
33. ### A Calculate the exact or approximate length of one period of the wave function

The known expression of the wave function is where A is the amplitude, k the wave number and ω the angular velocity. The mathematical definition of arc length for a generical function in an interval [a,b] is where, in our sinusoidal case: For our purpose (calculation of the length in one...
34. ### Is this question doable? Finding triangle side length

Given a triangle ABC, whose area is 5.5 cm square, and length of AB = 2√3 + 1 cm, find the value of length AC. Given triangle has no special properties like isoceles etc. Only 1 length and area of the triangle are given. Is it possible to solve such a question? thanks.
35. ### Focal length of LCD screen as a car's rear view mirror

I noticed on the commute home today a car with a LCD rear view mirror and I wondered whether, if I were driving it, I'd be able to focus on it the same as I focus on my car's glass review view mirror? I need glasses to read, and that includes a computer, so figured a LCD screen that close, even...
36. ### I What is the Formula for Calculating the Length of a Hanging Spring?

Trying to derive the length of a spring hanging under its own weight. I was trying to approach it like a series of small springs free length ##l## connected in series, in hope to use a limit as ##l \to 0 ## to get the final result, but either I'm bungling it, or it just doesn't work. I'm...
37. ### A Range of Difference: Bounds for Length of Stay

Ok, so I'm given hotel data :{Arrival Date, Departure Date}, each in terms of nth day of the year , and I want to estimate whether the range/difference, aka, the length of stay is below a bound. Say a week ( 7 days) for definiteness. I'm thinking of using either the distribution of the range...
38. ### Centre of mass (composite rod) - length and densities provided

I feel like I'm missing something fundamental here. Given only the lengths and the densities, how am I supposed to find a numerical centre of mass?Thought process so far: Are we supposed to use the ratio of the densities to find this answer? like ##\frac{8g/cm^3}{2.7g/cm^3}##? and then use that...
39. ### Minimum Length of Cuts for Unfolding Box Into Flat Sheet?

Hi everyone I got 36 cm as the answer for the following problem, but it's supposed to be 32cm. These are the cuts I have 4 x 5cm = 20cm 2 x 3cm = 6 cm 1 x 10cm = 10cm which adds up to 36cm. I can get 32cm with 4x3=12 2x5=10 1x10=10 But I don't think that would be the correct net. Is...
40. ### MHB How to Find the Length of the Hypotenuse of a Right Triangle?

AB=3, DC=5, ∠ CAD=$45^o$, AB ⊥ BC. Find the length of AC.
41. ### I The Length of World Line: Prerequisite for Proper Time

What is the prerequisite of "the length of world line equals proper time"?C=i?orC=1?If metric is-+++: ##ds^2=-c^2d\tau^2\Rightarrow whenC=i,s=\tau## If metric is +---: ##ds^2=c^2d\tau^2\Rightarrow whenC=1,s=\tau## So,which one?
42. ### I The Theoretical Minimum: Length Contraction and Time Dilation

Hello, My name is Dave and I'm a physics major at UIUC. It looks like I will be taking the special relativity course (phys 225) this fall. I've always been fascinated by the theory so I decided to get a head start with Lenny and Art's perspective on it. My first head-scratching moment came in...

44. ### MHB Why do we need "total length" field in ipv4 datagram?

TBH I don't really understand the question that I am asking myself. I was inspired asking this from my textbook "Do you know". Can you make me understand why would not we require total length field? Here's a similar question-...
45. ### Comp Sci Total length IP header and 65535 bytes relation-:

So IPV4 header has a topic called "total header length" and it is of 16 bits. That means it can count from 0-65535. Book says it means IP datagram is limited to 65535 bytes. how do we get to idea of 65535 bytes? is it 1 memory location=1 byte idea? It doesn't make any sense to me(I have studied...
46. ### Length of AD inside a triangle ABC

I get the answer but my working is really long: 1) Find all the length of sides of the triangle 2) Let DB = x, so CD = CB - x 3) Compare the area of triangle ADC and ABD using formula 1/2 . a . b sin θ then find x 4) Find cosine of angle B by using cosine rule on triangle ABC 5) Use cosine rule...
47. ### The length of the line in the MCNP cell card MCNP

Homework Statement:: I go back to the line to finish the previous line in MCNP cell card but I had the error message shown in the photo. Please make a solution to my problem Relevant Equations:: c ********************* BLOCK 1: cartes des cellules **************** 1 2 -1.184 -40 #3 #19 #18...
48. M

### Stick is broken randomly EDIT TWICE, what is expected length of small side?

Cut the stick twice, at locations ##x## and ##y##. Assume ##y>x##. The lengths of the stick are ##x,y-x,1-y##. Assume ##x < y-x \implies y> 2x## and ##x<1-y \implies y < 1-x##. These two boundaries intersect at ##x = 1/3##. Thus the following integral should yield the expected value for ##x##...
49. ### How do you know if the focal length is positive or negative?

In this problem, it doesn't tell you where is the focal length. So how do you know if it is in front or behind the object?
50. ### How can an event which has length and time have L = 0?

I apologize if this is a stupid question I just always thought length involves 2 points to have a length at different locations.