Length Definition and 1000 Threads

If you guys haven’t noticed through my posts so far is that I am interested in the Big Bang. I am considering the concept of the Planck length, but I may have some confusion. How did Space time start? Did the universe start from nothing and created units of spacetime? Could the original size...

This is not a school problem, just my own mucking about, but since it has the form of a problem, I am willing to shift it to the "homework problems" rubric. If there is a theoretical string (no thickness, etc.) that is non-stretchable tied to two endpoints and is long enough to be able to form a...

Homework Statement Prove that if ##\sigma## is the m-cycle ##(a_1 ~a_2~ \dots ~ a_m)##, then for all ##i \in \{1,2, \dots , m \}##, ##\sigma^i (a_k) = a_{k+i}##. Deduce that ##\sigma^m (a_k) = a_k## Homework EquationsThe Attempt at a Solution I will try to do this by induction. Clearly...

1. Charge is distributed through an infinitely long cylinder of radius R in such a way that the charge density is proportional to the distance from the central axis: ß = A r, where A is a constant and ß is the density. (a) Calculate the total charge contained in a segment of the cylinder of...

The electric field of an infinite conductor of net charge Q along the x-y plane is easily found using Gauss's Law: $$ \vec E(x, y) = \frac {\lambda} {2\pi \epsilon}\frac {[(x-x_c)\hat x + (y-y_c)\hat y]} {[(x - x_c)^2 + (y - y_c)^2]^3}, $$ where ##x_c## and ##y_c## mark the location of the...

On a piece of equipment, I purchased new, the digital clock ran slow. The second digital clock that was installed ran slow---it lost approximately 4.1 minutes in one month. Below is what I sent the Service Manager who I understand thinks it is possible to test the newly installed clock...

Hi this is my first question and love these Forums. I have a Independent research task due next term. My idea was: Seeing the change of wave length of light as it passes through different substances. My question is: How do i measure the wave length? Because I could use a spectrometer but my...

Homework Statement Light of wavelenghs 4.80x10^2 nm and 632nm passes through two slits 0.52 mm apart. How far apart are the second-order fringes on a screen 1.6m away? λ₁ = 4.80x10^2 nm = 4.80x10^-7m λ₂ = 6.32x10^-7m d = 0.52mm = 5.2x10^-4m n = 2 L = 1.6 Homework Equations (Maxima/Bright)...

Homework Statement Find the length of the curve: ##x=\frac{t}{1+t}## ##y=\ln(1+t)## where ##0 \leq t \leq 2## Length of curve integral ##\int^a_b \sqrt{(\frac{dx}{dt})^2+(\frac{dy}{dt})^2} dt## Homework Equations ##(\frac{dx}{dt})^2 = \frac{1}{(1+t)^4}## ##(\frac{dy}{dt})^2 =...

When finding the fundamental for thin bars, the approximate equation (http://hyperphysics.phy-astr.gsu.edu/hbase/Music/barres.html) only refers to the length and thickness when calculating. I'm trying to figure out the frequency and node location along the length and width of the fundamental...

The two non-parallel sides of the trapeze are 15 cm and 13 cm, the perimeter is 48 cm. Find the length of the median. I don't know anything about trapezes can someone expain how to do this?

Square-shaped piece of paper is intended to make a regular octagon through the cutting of the vertices of a square. The length of the piece of paper is 29 cm. How long triangle cathetus have to be cut off from the vertices of the square? Calculate the octagonal side length, circumference, and...

Homework Statement The proper length of spaceship A is 60.0m and the proper length of spaceship B is 120.0m. The proper mass of spaceship A is 15000 kg. An observer on Earth watches the two spaceships fly past at a constant speed and determines that they have the same length. If the speed of...

Homework Statement Two masses are connected by a string that is passed over a massless pulley. At t=0, the 6-kg mass is moving upwards at 2m/s, while the 4-kg mass is descending at the same speed. How far will the 6-kg mass rise before it stops? Homework Equations KE= 1/2*m*v^2 PEg: m*g*h...

I got 138.17, but that isn't correct. I don't know how to do it, since the only way I thought, gave me the wrong answer. Can anyone help?

Ok, i have a question. First, i am an engineering student and have done all math requirements up to linear alg. HOWEVER, my geometry is terrible, oh so terrible and i need some spoon feeding right now because i am stuck on a problem. Ok, i saw a really cool tool the other day called a radius...

I have a thin tube (4 mm diameter) sticking out of a small box (a bit larger than a matchbox). I want to use this tube to measure the dynamic pressure. How long must the tube be for the results to be reasonably accurate? Intuition tells me the working end of the tube should be kept in the...

Homework Statement I have attached a picture of the problem in the attachments I need help on the last section, (part d) Homework Equations (1)##∫√( (dx/dt)^2+(dy/dt)^2)dt## (2)##∫√( 1+(dy/dx)^2)dx##[/B] The Attempt at a Solution In order to get the answer we just need to find the...

Homework Statement Three particles with the same charge q are hold together by three strings of the same length l forming an equilateral triangle. The tension in each string is: a) ## \frac {K q^2 cos 60º}{l^2}## b)## \frac {K q^2 cos 30º}{l^2}## c)## \frac {K q^2 sin 60º}{l^2}## or d)##...

Homework Statement Homework Equations ρl = RA A = π r2 The Attempt at a Solution l = RA (ρ is constant) A1 = π (D/2)2 = (πD2)/4 A2 =π (2D/2)2 = πD2 = A1 /4 l2 = 2*l1 ##R=\frac{l}{A}## R2 = (2l1)/(A1/4) = 8 l /A = 8R1 Could someone tell me where is my mistake ?

Homework Statement [/B] There are two blocks that have equal mass m, they are connected by a spring (with a coefficient of elasticity k) that has length l0. Instantly on the left block a force F begins to act. What will be the min. and max. length of this spring during this movement. There...

Homework Statement Homework Equations v = sqrt(F/(m/L)) The Attempt at a Solution Trying to find the length of the spring. But i can find the tension of the wire at all. I'm not sure what i can do with the frequencies? Maybe I'm forgetting a concept cause i thought the equation v^2/F = L...

Generally in a circle, the radius of the circle is uniform around the circle due to it being at the center, this is the obvious part. However, let's say the the radius was shifted away from the center so that it is somewhere in the circle, in this case called r'. Given that the original radius...

Homework Statement Q2 A Cu wire of circular section and diameter 0.2 mm is used to form a one-turn coil and also to form a solenoid. Both have a radius of 2 cm. In both cases, a 10 mA current flows through the wire. a)Work out the magnetic field H in the centre of the one-turn circular coil...

Homework Statement A rod of length L and mass M has a nonuniform mass distribution. The linear mass density (mass per length) is λ=cx2, where x is measured from the center of the rod and c is a constant. Find the expression for c.Find the expression for the moment of inertia of the rod for...

Calculate what is the smallest side length BC of the triangle ABC if the angle BAC is equal alpha and area of the triangle ABC equals S.

Hey! :o A research institute wants to establish a confidence interval for the quota of working people in a city. Let $\hat{p}_n $ be the estimated quota, based on a sample of size $n$. It is assumed that $n> 30$. How can one determine the length of the confidence interval? Generally this is...

Hey! :o We have a playlist with $2000$ songs. The length of the songs on the playlist are on average $3.5$ minutes (i.e. $3$ minutes and $30$ seconds) with a standard deviation of $1.7$ minutes. 1) Can we find the probability that a randomly chosen song is longer than $4.5$ minutes...

Hello so I'm a high school student and I came up with this question and I wanted to know if this was possible to do? So I tried to research and find a way to find the length of DC and I couldn't find anything, so I am here to ask for help, is this possible? I figured it would go in the...

Homework Statement Let r be a positive constant. [/B] Consider the cylinder x2 + y2 ≤ r2, and let C be the part of the cylinder that satisfies 0 ≤ z ≤ y. (3) Let a be the length of the arc along the base circle of C from the point (r, 0, 0) to the point (r cos θ, r sin θ, 0) (0 ≤ θ ≤ π). Let...

Hi, I was browsing the internet for interactive simulations illustrating special relativity concepts. It seems to me that those in this http://kcvs.ca/concrete/visualizations/special-relativity are mostly nice and clear, although not very "chrome-friendly" (I have to use firefox to play their...

<< Mentor Note -- poster reminded to use the standard Template >> Question Three A pipe of outside diameter 200 mm is lagged with an insulating material of thermal conductivity 0.06 W m-1 K-1 and thickness 75 mm. The pipe carries a process fluid at a temperature of 300 °C and the average...

Homework Statement [/B] Find the definite integral formula for the length of the curve for $$0 \leq t \leq \frac \pi 2$$ $$x = 2*cos^k(t)$$ $$y = 2*sin^k(t)$$ for general $$k \gt 0$$2. The attempt at a solution I don't understand why this is wrong: $$\int_0^\frac \pi 2\...

The question: -------------------- The length of a microscope pipe is $L=160\,\rm mm$, the transverse magnification of its objective $M_o = 40\times$ and the diameter $d_o = 5\,\rm mm$. As for the ocular/eyepiece, its magnification is $M_e = 10\times$. 1. Find out the focal length of the...

Homework Statement A solid cuboid has a volume of 40cm3. The cuboid has a total surface area of 100cm^3. One edge of the cuboid has length 2cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 significant figures. This question recently came up on my maths exam today...

A question about the Mach-Zehnder interferometer. My understanding is: If its two arms are equally long, there is destructive interference in one output and constructive interference in the other output. So, the intensity of light detected at the first output should be 0% and at the second...

The question is asking me to find s, the arc length of a circle. How do I convert my answer in radians to the book's answer 7.54 meters? Theta = 4pi/5 radius = 3 meters See picture.

Homework Statement At the outside, there is a vertical stick with a length of 1.1 meter and its shadow on the surface of an Earth is 1.3 meter, there also is light pole and its shadow length is 5.2 meters, what is the height of that light pole? Homework Equations Trigonometry equations to...

Hello, Many Researchers talked about the following parameters: 1. Propagation length of the surface plasma wave(spw). 2. penetration depth of surface plasma wave(spw). 3. concentration of the (spw). 4. the equation of the interface in vacuum - plasma interface. I feel confused regarding such...

https://www.physicsforums.com/attachments/220647 Homework Statement Two uniform planks each of mass 10Kg and length 2m, are arranged as shown in the picture. Find the maximum value of x for which the top plank will remain in equlibrium. Homework Equations F= (mgl)/hThe Attempt at a Solution I...

Homework Statement I was re-reading my old Relativity book (by Rindler) and taking a look at some of the problems. He asks: Using a Minkowski diagram to establish the following result: Given two rods of rest lengths ##l_1## and ##l_2 (l_2 < l_1)##, moving along a common line with relativity...

1. Homework Statement Why does the non-relative simultaneous frame have an additional term of ##v \Delta t## along with the contracted length ## L ## for ## \Delta x ##? 2. Homework Equations ## L + v \Delta t = \Delta x ## ---- (1) ## \Delta x = \gamma \Delta x' = \gamma L_{\star} ## ----...

1.A rectangular steelbar of length subjected to tensile force of 80kN. Calculate the change in length if the width and thickness are (40 & 25)mm respectively. (E = 207 GN/m2). Homework Equations E= stress/strain stress = F/A; F =80kN strain = dL/L 3. I just want to know what to use for the...

Homework Statement An object is in front of a convex mirror. We then obtain an erect image whose height is equal to 25% of the height of the object. What is the distance between the object and the mirror if we know that the focal distance is equal to 0.2m? Homework Equations M = Yi/Yo = q/p...

Homework Statement A ship sails 3 nautical miles from Port P on a course of 64° to Port Q, then changes course to 285° and sails a further 7 nautical miles to Port R. (i) Draw a carefully labelled diagram of the entire route taken. Show the north direction where necessary. (ii)Calculate the...

So we have the focal lengths: f1, f2, ..., f7 = 25mm And the distance between the lenses: d1-2, d2-3, ..., d6-7 = 50mm I have figured out that if the system would be afocal if it had an even number of these lenses. This is because the focal length of two adjacent lenses is the same as the...

Homework Statement Homework EquationsThe Attempt at a Solution Mercury will be in a state of weightlessness in the satellite . The air pressure pushes down on the mercury in the cup as a result of which it rises in the barometer tube . But since it is apparently weightless , it tries to...

Homework Statement For a 150 MHz (1 MHz=1 million cycles per second) radio signal, the wavelength is 2 m long. If each wire is about 0.5 m long, a half wavelength of radiation will span the two wires taken as one. The result is that electromagnetic waves are generated in the direction of the...

Homework Statement Find the length of a meter stick if in the laboratory frame it is angled at 60 degrees relative to the direction of motion, and it is traveling at .8 c. I have calculated gamma to be 1.667 Homework Equations Lorentz transformations The Attempt at a Solution a' = l' cos(x)...