Length Definition and 1000 Threads

In this solution, aren't we assuming the power or inverse of focal length of these 3 lens when they are kept with respect to air?? Is that obvious in the question?

If length contraction occurs due to relativistic effects, the atomic spacing becomes shorter. This should also increase the repulsive force between atoms. Then how can the stable bonding length remain short in such a scenario?

Taking B as origin, the boundary condition provided was ##v(x=0)= 0 , v(x=L)=0 , v'(x=0)= \theta B## ##v'(x=L)=0## , and also ##v'' (x=0) = M_B/ EI## However, I had problem of expressing the equation in terms of ## \omega L## Can anyone help ?

I noticed that the three seed articles about space-time quantisation are aligned in 1994. https://inspirehep.net/literature/371960 Garay https://inspirehep.net/literature/386329 Doplicher et al https://inspirehep.net/literature/379391 Rovelly-Smolin I wonder, does anybody remember why this...

I was asked if the balancing length at which the galvanometer shows no deflection be affected by the internal resistance of the dc source. I am not sure why my answers incorrect my reasoning was yes if I had put a higher resistance then the voltage drop across the metre bridge would decrease...

I'm having a hard time since the angle is being measured in frame ##S##. What I have put together so far is ## l_y = l_{y0} = 1m(sin(\theta_\circ)) ## And ## l_x = l_{x0}/\gamma ## Where ## l_{y0} ## and ## l_{x0} ## are the respective x and y values of the meter stick in the proper lengths...

So I found the location of the image of the object produced by the mirror to be -58.2628 cmi^ and the length of the image of the object produced by the mirror to be -9.40012 cm. (these are correct values). To find the location of the final image of the object as produced by the lens I used 1/f...

Hi All, We often read that the gravitational field acts by slowing down clocks. Is there any statement that, with the same simplicity, reports on the action of the gravitational field on lengths measured by observers which are close or far from Earth, for example? Best wishes, DaTario

I know gravity needs to be taken into account and that I can find the stiffness but generally I'm pretty lost

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...

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

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...

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...

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...

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...

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.

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 %...

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!

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...

For this problem, How do we tell when the buzzer vibrates during the cycle to provide the driving force? Many thanks!

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...

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.

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...

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...

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)...

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...

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...

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...

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...

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...

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...

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...

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...

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!

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...

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...

My attempt: m=-v/u=-f/(-f-u) -1/0.5= -f/-f-0.10 -> -f-0.10=0.5f -> f=0.20 m

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...

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...

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?

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...

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.

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...

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...

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...

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...

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...

AB=3, DC=5, ∠ CAD=$45^o$, AB ⊥ BC. Find the length of AC.

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?

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...