Length Definition and 1000 Threads

The apparent length of a rod is determined to be$$\tilde{L}(x_0) = \gamma L + \beta \gamma \sqrt{D^2 + (\gamma x_0 - \frac{L}{2})^2} - \beta \gamma \sqrt{D^2 + (\gamma x_0 + \frac{L}{2})^2}$$I am trying to determine expressions for ##\tilde{L}(x_0)## when ##x_0 \rightarrow -\infty## and ##x_0...

Hi, I want to ask how to calculate the length of pipeline..From what i have searched, one of the way to calculate it is from the equation of pressure drop. However, it seems i don't have info about the pipe length and pressure drop (it means i need to calculate it). Is it possible to calculate...

My textbook says ##\vec r (\theta) = r \hat r (\theta)##, where ##\hat r (\theta)## is the terminal arm (a position vector in some sense). It can be seen that both ##\vec r (\theta)## and ##\hat r (\theta) ## are function of ##\theta##; whereas, the length of the vector ##r## is not. I...

Suppose I'm traveling inside a spaceship at speed comparable to light between two points A and B. According to me the distance between the two points will be shortened due to length contraction. But actually my spaceship passes through every point between A and B so the distance measured by...

A unit vector, ##\frac{\vec{v}}{|\vec{v}|}##, has dimensions of ##\frac{L}{L} = 1##, i.e. it is dimensionless. It has magnitude of 1, no units. For a physical coordinate system, the coordinate functions ##x^i## have some units of length, e.g. ##\vec{x} = (3\text{cm})\hat{x}_1 +...

Hi, I'm not sure if I should be asking this but I couldn't make sense of the following Matlab command: length max([2+3-1,2,3]). The result is "16". I couldn't the operation of this command and why it produces the result of "16". Could you please help me with?

I was absent for a while due to personal constraints but I did keep myself busy with the Time dilation equation some member sent me a while back. I decided to set a time limit for myself to learn and understand time Dilation and length contraction, which must be before December 2020, or I will...

A trapezoid with a base of 100m and 160m is divided into 2 equal parts by a line parallel to the base. Find the length of dividing line.

In detail, I came up with 424m for the stretched length of a spring in order to change the mass of an object by 10^-9kg which originally was 1 kg. Problem said, "is it feasible?" In my opinion, there is no spring that can be stretched for this long, so it is not feasible. However, I'm not sure...

If $a,\,b$ and $c$ are the sides of a triangle $ABC$, prove that if $a^2+b^2>5c^2$, then $c$ is the length of the shortest side.

If I make two rods with 1 meter length here on the surface of earth, and send one of them near a black hole that is at rest relative to earth, placing it there with its length alligned in the radial direction of the black hole, would I see the rod close to the black hole with a length shorter...

Alice travels in a spaceship, which she measures to be L. The spaceship is moving with velocity v relatively to Bob. Alice makes a light beam traveling along the spaceship and measures the time interval it takes to go from one end to another, ΔtA. So, equation (1): L = c × ΔtA From Bob's...

Hi there! This is my first post here - glad to be involved with what seems like a great community! I'm trying to understand the acoustics of a finite plane-wave tube terminated by arbitrary impedances at both ends. So far all of the treatments I've managed seem only to address a different...

The velocity of a particle below is expressed in polar coordinates, with bases e r and e theta. I know that the length of a vector expressed in i,j,k is the square of its components. But here er and e theta are not i,j,k. Plus they are changing as well. Can someone help convince me that the...

If Planck length is 10^-35 of a meter and Planck time is 10^-43 of a second, doesn't that mean that as the relative speed gets closer to the speed of light and time acceleration and length contraction are happening, they are happening at a different rate, since length contraction has to reach...

Summary:: We have a rotating arm, offset from the centre of rotation by a certain length, which is controlled by varying the length of a control rod. Need the angle of the rotating arm in terms of length of the rod. The blue line is a fixed column structure. CE and BD form the rotational...

Sean Carroll gives the Planck's set of four dimensioned quantities: Planck's mass, length, time and energy. I wanted to compare them with actual things.\begin{align} m_p=\sqrt{\frac{\hbar c}{G}}&=2.18\times{10}^{-8}\rm{kg}&\rm{{10}^{7}\ E. coli}\phantom {100000000000000000000}&\phantom...

I have read a short story by the Grimm Brothers, named "The Sheperd Boy" and there is a riddle that sounds like this: So we have a mountain made of pure diamond, and it takes 1 hour to climb it, 1 hour to go around it and 1 hour to go down into it (I assume from its peak to its base). And...

I'm trying to evaluate the arc length between two points on a 2-sphere. The geodesic equation of a 2-sphere is: $$\cot(\theta)=\sqrt{\frac{1-K^2}{K^2}}\cdot \sin(\phi-\phi_{0})$$ According to this article:http://vixra.org/pdf/1404.0016v1.pdfthe arc length parameterization of the 2-sphere...

Hey Physics Forum I am currently doing my bachelor project in geophysics, with focus on the evolution of glaciers in Greenland. My project consists partly of programming, because I want to get better at it. I have, however, hit a wall. I can't seem to figure out what is wrong with my code and I...

Here is the question itself Here is my attempt at it Does 4cm look right? Any help would be great, thanks!

Option (B) is wrong because energy should be received by rubber band when it is being stretched Option (D) is wrong because energy should be released by rubber band when it goes back to natural length The area between graph of stretching and contracting represents energy dissipated in rubber...

I have the STRESS , YOUNG S MODULUS ,and the LENGTH . How can you discover the CHANGE IN LENGTH when you don t have the FORCE and AREA unit ?

Strain and change in length what is the difference ?

A steel bar 6.00 m long and with rectangular cross section of 5.00 cm x 2.50 cm supports a mass of 2000 kg. How much is the bar stretched ? (the young s modulus of steel is 20 x 10 n\m squared)

My question is going to be rather specific. I am trying to understand how Gauss's law applies to this scenario. I know if a cylindrical shell is infinitely long, and there is an external electric field, the inside of the shell will have an electric field of zero everywhere. I am wondering...

Having made/modified my own distributors for years, I was surprised to see MSD (Multiple Spark Discharge) company show their graph using Points, HEI, and Performance HEI comparisons, with little difference in Horse Power made, up to about 6000 RPM. I know a points mechanical system makes a...

After seeing a discussion about graphs of the relationship ##x^x + y^y = r^r##, it got me interested in attempting to see what the graphical appearance of ##{^{\infty}x}+{^{\infty}y}={^{\infty}r}## would look like. The first step I did was use the relationship of...

Hi there :smile: Anybody out there able to explain to me how to calculate what the true length of a sidereal year was about 6000 years ago ? Kind Regards Edwin.

I have to admit that my "best" math days are long gone. That said, I wonder if anyone can help me? I'm stuck in part 1 of Einstein's book on 'Relativity, The Special & General Theory: The behaviour of measuring rods & clocks in motion', specifically on the second equation : √(1-v^2/c^2) used to...

Hi, I really need your help. Suppose I have a Raman spectra of a hydroxyapatite, how do I calculate the bond length from the spectra? I've been trying to understand the concept of Badger's rule but I really cannot understand. Please help.

Since Planck length is a distance unit of space-time which cannot be further subdivided, would that not imply that an electron, or singularity, or any other point particle cannot actually be a “point”, but must rather be a spherical volume with a Planck length diameter? i realize this may well...

The three lateral edges of a pyramid based on a square are 6016, 2370 and 4350 long. Calculate the length of the fourth lateral edge. We assume that edges 6016 and 2370 extend from the opposite tops of the base.

1/f = 1/dₒ + 1/dᵢ = 1/1.0 + 1/0.33 = 4.03 m (focal length) Power: 1/4.03 m or 0.248 (0.25) *around to the2 decimal points? or leave it as a fraction? ((Did I do this correctly? I am not sure if this is correct and is it okay to be in meters not centimeters?)) Please let me know!

Suppose one light up with a laser on a grid with grid constant g. The grating is followed by a focusing lens with a focal length of f. In the focus (or immediately in front of it) the maxima have a distance d. How large was the distance of the maxima immediately after the grating? scheme: Laser...

Hi, my try: Do you agree with me? Thanks

Hello all, I am working on a lab report for physics, and am a bit stuck on one aspect. The basic layout of the pulley system is attached. (This is a diagram I made, so if there are any inaccuracies in this one either, I am happy to fix it. So, I mostly understand the lab. My TA said, though...

The radiaton length for air is about $$X_0 = 30420cm$$. This is the length at which the electron has decreased to 1/e of it´ s initially value. I also know that the maximal value of interactions for a specific energy is given by $$ n_{max} = \frac{ln(\frac{E_0}{E_c})}{ln(2)} $$, where E_c is...

The rule for length contraction seems to be inconsistent with the lorentz transformations for distance. The rule for length contraction is: ## x = \gamma x ^\prime ## and ## x ^\prime = \frac {1} {\gamma} x ## But the lorentz transformations for distance are ## x = \gamma x ^\prime + \gamma vt...

Homework Statement: Propagation of Error for Focal Length Homework Equations: f = (s'*s) / (s' + s) In my lab, we had to calculate the focal length of a lens based on object distances (s) and image distances (s') that we measured. The object distances were measured with an uncertainty of...

For instance, if a stream of muons were released from a box near a massive object and traveled on a straight path slowly (at a non-relativistic velocity) away from that object, a faraway observer would notice that the particles would take longer to decay than a muon typically would in empty...

I was wondering, would there be a length contraction (or expansion) in the z and y axis' if an object was accelerating in x axis? I know that in special relativity there is no deformation in the y and z axis' if the object is moving in the x axis. I was looking a this paper for clarification.

Why is it that the smaller the gate length, the higher the max operating frequency becomes? In particular, I think I saw somewhere that a 6 um gate length, seems to limit ICs to 100kHz, where as 1 um is around 1MHz (all rough ball bark numbers, and can be persuaded otherwise). Was wondering if...

Comparing high precision atomic clocks, one flying in a airplane and one on the ground had demonstrated permanent time dilation presumably due to special relativity (speed) and/or general relativity (gravity) . While similar experiment with a ruler would demonstrate length contraction only...

I had this idea when some people said that LHC can produce black hole. Based on the calculation of Schwarzschild Radius, any mass than 9.375×10^7 kg have a Schwarzschild radius smaller than the plank length. Particles inside LHC or other particle accelerator have clearly radii smaller than that...

I tried to think why Ampere's law seems to fail in this case. For me it was clear that there is no symmetry in the z direction, there is no translational symmetry because of the finiteness of the wire. On the other hand, I know that Ampere's law is independent of the loop we take. This also...

15. What is the minimum length of a plane mirror in order for you to see a full view of yourself? A 1/2 your height B 1/4 your height C 3/4 your height D your full height Q Why is answer of A given is the correct one, I understand pictorially how it is, since visually if you were to draw a...

According to this article https://physics.stackexchange.com/questions/321229/why-dont-we-have-proton-neutron-microscopes, they seem to hint that heavier objects have a shorter wavelengths and give better resolution. If I kept increasing the mass of a particle and kept it's speed at .9c would I...

Hi All, When I teach the basic structure of a laser setup, stimulated emission appears as a fundamental phenomenon. But in no reference I found a description that could account for the increase of coherent length of the EM laser field. According to my knowledge, one photon typically doesn't...