Length Definition and 1000 Threads

klotza submitted a new PF Insights post A Hand-Wavy Discussion of the Planck Length Continue reading the Original PF Insights Post.

Count the number of strings of length $8$ over $A = \{w, x, y, z\}$ that begins with either $w$ or $y$ and have at least one $x$ I don't understand this question at all. First of all, this is a set A that contains 4 elements $w,x,y,z$ correct? They are asking me to count the number of strings...

I get that Planck length is derived from h, G and c. But as a theoretical measure of length how is it affected or not affected by cosmological expansion?

Homework Statement Coaxial cable has double layered dielectric. a=2mm, b=4mm, c=8mm, εr1=3, εr2=4.5, Uab=1000V 1. Calculate capacitance per unit length of a cable. 2. Calculate inner and outer charge densities of a cable. 2. Homework Equations Gauss law C'=Q'/U σ = nD σp = nP 3. The Attempt...

Homework Statement Two cylindrical conductors, of distance between them d and radius a (a<<d), have dielectric layer of relative permitivitty εr and thickness a. Calculate capacitance per unit length of this system. Homework Equations Capacitance per unit length, C'=Q'/U Gauss law, cylindrical...

In general I read that: R_m =\frac{l}{\mu A} But considering for example the following transformer: I don't understand why the lengths taken from the sketch by the solution's procedure are the following: For the right and left part resistance: R_r = R_l = \frac{(\frac{1}{2} + \frac{1}{2}...

Hello! So in looking at black hole thermodynamics, I came across the equation ## l_p = \sqrt{G\hbar} ## But in doing a dimensional analysis of ## \sqrt{G\hbar} ## I get ## [\sqrt{G \hbar}] = \sqrt{ \frac{Nm^2}{kg^2} \frac{m^3}{kgs} } ## This obviously doesn't amount to a length. What...

Taken from 'Concise Inorganic Chemistry - J.D.Lee': "According to Bent's rule, more electronegative atom not only prefers to stay in the orbital having more p-character but can also increase the p-character in its attached orbital of the central atom depending on the circumstance... With an...

So i was watching this video : And it got me thinking... i began wondering why, when space contracts from someones frame of reference (In the video, this would be the frame of reference of the cat), why is it that the protons don't become black-holes when the space contracts? If the density...

Hi All, Is there any experimental evidence that photons may have attached to itself a coherence length? Best Regards, DaTario

Hi everyone, I have an exercise I haven't solved yet, please help me. Find the length of the curve: $$y = \frac{{x}^{5}}{6} - \frac{lnx}{4}, 2 \le x \le 4$$.

Hi all, I post a question about the dimension of wave function in position space before and people help me to identify that the unit of wave function should be in the unit of ##\text{m}^{-1/2}##. I am verifying that by doing the dimension analysis on Schrodinger equation...

Homework Statement Hello. This should be rather easy. I am trying to figure out what the Characteristic length I should use in calculating the grashof number for a greenhouse. The dimensions given for the greenhouse are 1.5 m wide x 2 m long and 2 m high. What characteristic length should I...

Homework Statement http://i.imgur.com/lnk7e0D.png CDE is an equilateral triangle inside a circle, with side length 16. FGH is also an equilateral triangle and F is the mid point of DE. Find the length of the side FGH. Should be expressed as Asqrt(B)-C. Where A B and C are positive integers...

Hi the standard focal distance seems to be 45mm for vr headsets such as google cardboard. In other words there's a pair of convex lenses in front of your eyes with the screen being 45mm away from the lenses ... I am not sure why you can't use different lenses to reduce the focal distance to the...

Hey PF, I'm currently double majoring in engineering and physics. I want to be a licensed engineer and go on to grad school to study molecular engineering or something similar. However, I love my physics department. It's smaller so students get more funding and attention and way more...

Hi all, I need to find base length x which would support the pillar and wouldn't topple over (weight of 2.1kg on right hand side of pillar) Thanks in advance

Homework Statement We conducted an investigation into wire length, current and resistance but kept track of the voltage rather than relying on the power pack setting. We noticed the voltmeter (measuring across the power pack) reading increased as the length of the wire increased though by only...

Just wondering if someone could check that I am understating this aspect of length contraction correctly... I am in a spaceship moving at say a speed of 0.6c relative to some imaginary ruler in space which has increments set 1 meter apart. (1 meter in the ruler's rest frame.) I am moving along...

Homework Statement $AB = 20 cm$, $m∠A = 30°$ , and $m∠C = 45°$ . Express the number of centimeters in the length of $BC$ in simplest radical form. Homework Equations $sin A = sin C$ The Attempt at a Solution $AB = 20, BC = x$ D is the point where this obtuse triangle separates into 2 right...

Homework Statement Assume a particle is in the ground state of an infinite square well of length L. If the walls of the well increase symmetrically such that the length of the well is now 2L WITHOUT disturbing the state of the system, what is the probability that a measurement would yield the...

Homework Statement general question: if I give a ball velocity (He is tied to a wire (tension)) and consider that the wire has no mass. Does the length of the wire affects the angle? If I solve this with energy tools then I get that the longer the wire the smaller the angle. it does not settle...

I have been coding a speed of light simulator and I am having a bit of trouble with a few aspects of the project. My first question is: Are the length contraction and relativistic aberration formulas BOTH needed in my calculations or does the relativistic aberration formula already account for...

I'm reading about Line Integrals, so I thought I'd review the proof for the arc length formula. However, there's something I don't quite understand about the proof that I either overlooked or understood before. From what I see, the arc length formula holds because the MVT guarantees that there...

Hi Everyone, Kind of a tough question here. How do I determine the length of a spring if we don't have any visual information about it? All we have is the spring rate & change of object position from when the spring is uncoiled, to fully coiled. Anyone have any ideas on this? I tried the...

Please see the picture. Red dots are stars, lines are the path that light takes, our observer is at center. Assuming that stars are somewhat uniformly spread around us, I suppose that stationary observer (left picture) sees about as many stars in every direction, but an observer moving in...

If a frame is moving at constant velocity relative to an observer, this observer perceives a time dilation and a length contraction. But in this case how the velocity (length/time) can appear constant ? It is expected to be contracted.. Thank you in advance for the explanation

What is the correct value for the vacuum Debye screening length?

I hope to lay to rest two of the misconceptions about special relativity that are evident in the many questions asked here. 1) Why is the speed of light a constant ? Everybody believes Pythagoras's theorem that the length of the hypotenuse of a right angle triangle is ##\sqrt{s_1^2+s_2^2}##...

Homework Statement How fast must a meter stick be moving of its length is measured to shrink to 0.500 meters? Homework Equations v/c = sqrt(1 - (1/L)^2) = sqrt(1 - 1/4) = sqrt(3/4) = sqrt(3)/2 or use v = sqrt(3)c/2 The Attempt at a Solution (squrt 3c/2) = squrt 450000000 = 21213.203 =...

Hi all, I want to make sure of a particular information. Length is contracted only in direction of motion. If I am on a spacecraft moving with high speed, I shall see the universe is contracted just in front of me that I am going to, but there would be no contraction If I look to regions that...

Dear PF Forum I want to know about these questions that are still bothering me, Does the universe have preferred frame of refference? Why there's twins paradox? Motion is relative, why 1 clock experiences time dilation while the other doesn't? V = \sqrt\frac{3}{4} ≈ 86.6\% If V define ratio of...

Muon created by fast cosmic ray has speed 2.99X10^8 m/s and life time 2.2 micro sec. According to this numbers muon should travel only 0.66Km with respect to Earth in his life time. however it travels more than 10 km (10.4km) due to time dilation. in muon frame of reference, Earth travels only...

Hi, I'm looking for the momentum so that the decay length of a tau (mean lifetime ##t_{lft}=2.9 \times 10^{-13}s##) can be ##2mm##. I was wondering whether someone can use the formula I got: l_{lab}= t_{lab} u = \gamma u t_{lft} \Rightarrow pc= m \gamma u = m \frac{l_{lab}}{t_{lft}}? (Looking...

A florist delivers single stemmed flowers in a sealed plastic container that is cylindrical in shape. Each container has a bade radius of 4cm and a height of 45cm. the florist wished to decorate each container with a very thin coloured ribbon. The ribbon will wind around the body of the...

Hello. I am trying to wrap my head around where from did he got the x = sin of theta equation at the 32:44 mark of the video: . Isn't sine of theta x over the hypotenuse in the diagram ? Thanks in advance!

Homework Statement I'm trying to find Arc Length of F(x) = (e^x + e^-x)/2 0< x < 2]Homework Equations L = integrate sqrt ( 1 + (dy/dx))^2)The Attempt at a Solution (dy/dx)^2 + 1 = 1/4e^2x + 1/4e^-2x + 1/2] I don't know how to take the square root of the above function so I can be able...

Homework Statement Two pipes, Identical in length and closed at one end are producing notes. You are very, very annoyed because the notes are creating an audible beat frequency of 20Hz. If one pipe is producing a note at 10Hz and the temperature is 15C (which correlates to a speed of sound of...

Hi, I tried to calculate the distance resulting from Na iron atoms contained in 1 g. scaled in meters and by juxtaposing them in a single thread (segment). I did the following calculation with: Atomic radius : 140 E-10 meters Na : 6 E23 atoms in 56 g. of iron => ( 2 x 140 E-10 x 6 E23 )/56...

Hi, My question concerns the following problem from chapter 4 of Special Relativity by A.P. French. A statement of the problem: 4-15 A flash of light is emitted at point O and is later reabsorbed at point P. In frame S, the line OP has a length l and makes an angle θ with the x axis. In a...

Homework Statement If I have a column, fixed at both ends, i am aiming to work out the minimum length where buckling is likely to occur. I know this is a similar question to that asked before, however please bear with me. Column outer diameter 100mm, inner diameter 60mm Youngs modulus...

Hi, I tried to find design regulations/codes that specify relations between bolt diameter/bolt length against connected plate thicknesses. I couldn't find that in Eurocodes 3. Can someone help me with info where to find those regulations ? Example: can we connect 5 mm plates using M24 ? or...

I was reading a closed thread here about the length contraction being real or not. The best I could understand my self is that space is the one that contracts, the final post by an experienced forum member saying something like its the space-time that changes, it rotates. But I still have to...

Homework Statement Hi.I need an experiment to study and present it.the subject is how to measure coherence length of a monochromatic laser ? lm also search on google.However,is there any advice from you ? Homework EquationsThe Attempt at a Solution

Could anyone tell me or direct me to a source with an answer or way to calculate the neutron aborbtion/interaction length of lithium-6 deutride? I would have expected this answer to be readily available from the government experiments leading up to castle bravo, but I cannot seem to find it. Any...

Homework Statement Say if I had a system with 3 springs on the left, 1 spring in the middle, and another 3 springs on the right. I add masses to the central spring and calculate the extension. After all my measurements, I plot a graph of spring against mass. If I then repeat the experiment...

Wabbit had an interesting comment in the "Aeon to Zeon" cosmology thread. Here's an excerpt, for more follow the link. I replied saying I'd start a separate thread.

Hi, I'm wondering about the effect of the shaft flex on the impact velocity between the club and the ball. I understand that as I swing down the golf club, the shaft flexes and the club head lags behind. Near the end of the point of impact, the shaft bends forward. Intuitively, I would think...

Hi guys, I need to figure out the length of the side of a roof on a scaled down model. The picture below shows what I’m trying to calculate. The real house has a central support pole and it is 10 metres high, with length of the side of the roof at 14.67… metres. If I was to make a scaled...

I never could understand this: the lens focuses light onto the retina so shouldn't the distance between the lens and the retina be the focal distance? It does not seem to be the case while I was trying to look around for the answer on the internet. And since light is focused on the retina, the...