Length Definition and 1000 Threads

Homework Statement The medium-power objective lens in a laboratory microscope has a focal length fobjective = 3.75 mm. What is the focal length of an eyepiece lens that will provide an overall magnification of -125? Assume student's near-point distance is N=25cm. Homework Equations...

In special relativity, an object moving at higher speed experiences time dilation, length contraction, and mass increase, compared to an object moving at slower speed. In general relativity, for an object in stronger gravitational field (i.e., with higher acceleration due to gravity), time runs...

Homework Statement What will be the length of mercury column in a barometer tube, when the atmospheric pressure is 75 cm of mercury and the tube is inclined at an angle of 60° with the horizontal direction? Homework Equations Pascal's Law The Attempt at a Solution l ⋅ sinϑ = h l = h / sinϑ l...

Homework Statement A glass tube is bent into a U shape. Water is poured into the tube until it sands 12 cm high on each side. Kerosene (density = 870 kg/m3) is added slowly to one side until water on the other side raises 5 cm. What is the length of kerosene column? Homework Equations (ρhg)1 =...

I have a Cassini PM-160 spherical mirror used in telescopes as the primary mirror. The mirror is concave with a radius of curvature of 2600mm and focal length of 1300mm. I have a very basic question. If an on object is located beyond the focal length of a concave mirror then the virtual image...

Find the Force of Gravitation between two Uniform Rods of Mass M and Length L. I heard my prof say that we have to do double integration to solve this. Please explain the above step and step with Diagram

Homework Statement Homework EquationsThe Attempt at a Solution Dimension of length using h,G,c [h] = [F r] ##[G] =[ \frac { Fr^2}{m^2} ] \\ [\frac { hG}c] = [L] ## So, the answer is option (b). Is this correct?

Homework Statement A graduate student discovers that an elementary particle produced in his experiment travels 0.250 mm through the lab at a speed of 0.950c before it decays (becomes another particle). What is the lifetime of the particle measured in its rest frame (proper lifetime). A) 8.77 x...

Hello I am new here and I am just Junior college student. So please use simpler terms. I need to know that does relativity work for mediums like air and water. I mean the equations of time dilation and length contraction, do they work for other mediums. If so shall I take C as the speed of light...

Homework Statement A solid sphere is cut in half and a homogeneous hemisphere of radius r and mass M is set upon a table(with its flat side up). The surface of the table is perfectly rough. The hemisphere rocks back and forth with small amplitude excursions from equilibrium. What is the length...

Does the “space twin” benefit from length contraction as well as time dilation? In Einstein’s thought experiment, let one of twins travel to a galaxy known to be 10 light years from Earth at a speed of sixty percent of light speed (0.6c). Were it not for time dilation the one-way trip would...

Homework Statement The following task causes me problems: The science fiction writer R.A. Heinlein describes in the novel "Friday" a satellite ("space elevator"), which consists of a long rope, placed directly above the equator. The rope is aligned along the Earth's radius. It moves so that...

$\begin{align*}\displaystyle f(x)&=\ln(\sin{x})\\ \frac{\pi}{6}& \le x \le \frac{\pi}{2}\\ \end{align*}$ $\begin{align*}\displaystyle f^\prime(x)&=\cot{x} \end{align*}$ so $\begin{align*}\displaystyle L&=\int_{\pi/6}^{\pi/2} \sqrt{1- (\cot{x})^2} \,dx \\ \therefore...

Homework Statement The distance between an object and its upright image is 28.0 cm. If the magnification is 0.550, what is the focal length of the lens that is being used to form the image? Homework Equations 1/f = 1/so + 1/si M= -si/so The Attempt at a Solution See included image...

Homework Statement Part C: Find fundamental frequency. Homework Equations Tension(y) = μgy v(y) = sqrt(gy) Time it takes to travel from bottom to top = t_up = 2srqt(L/g) The Attempt at a Solution I found part A and B, which are tension and velocity. I don't know how to find part C because...

Hey, The question sounds like this: I have 100 fs 400 nm pulse passing through the CaF2 crystal. After passing, it gets twice wider (200 ps). What is the length of the crystal? Can anyone share the equation which would help me to calculate this? Thank you in advance!

$\textsf{12 Find the length of the curve $y=\ln(e^x-1)-\ln( e^x+1 )$ from $x=\ln{4}$ to $x=\ln{5}$}$ ok I thot that curve lengths were done with parametric equations but didn't know how to convert this

Homework Statement In the following problems let ##\alpha## be a cycle of length ##s##, and say ##\alpha = (a_1a_2 . . . a_s)##. 5) If ##s## is odd, ##\alpha## is the square of some cycle of length s. (Find it. Hint: Show ##\alpha = \alpha^{s+1}##) Homework EquationsThe Attempt at a Solution...

As I understand, there are peripheral neurons that stretch for up to a meter or more from the spine to wherever the muscle is. I was curious, does this apply to all the neurons that for example, move my right hand? Are all the neurons in my fingers individually that long, starting at the spine...

Homework Statement Homework Equations Area of triangle=(base x height)/2 The Attempt at a Solution a is the side of the triangle. Area of an equilateral triangle: ##~\displaystyle \frac{a}{2h}=\tan 30^0=\frac{\sqrt{3}}{3}## $$\rightarrow A_t=\frac{\sqrt{3}}{4}a^2$$ Side of the rectangle...

How can I calculate the length L of each side of a cubic simulation box with 500 molecules (in Ångstrøm) when I want molar volumes of V1 = 0.6 l/mol?

When a test charge stands next to a wire, there are coulomb forces between the test charge and the protons of the wire. 1: When the test charge starts to move, the Coulomb forces stays the same, because distances from test charge to protons stay the same. There is no magnetism in this case...

Homework Statement Homework Equations First derivative=maxima/minima/vertical tangent/rising/falling The Attempt at a Solution a are the sides of the base and b is the height $$A=4ab+a^2,~~V=a^2b=a^2\frac{A-a^2}{4a}=...=\frac{1}{4}a(A-a^2)$$...

Hi people, me bother yo again! I understand that relativity theory length contraction is the explanation of magnetics fields. See the image: https://dl.dropboxusercontent.com/s/vuy69jhig3kni3n/densidadcargasencorriente.jpg?dl=0 1) In the S system, if q is moving at the same velocity than the...

Homework Statement Anna and Bob are both born just as Anna's spaceship passes Earth at 0.9c. According to Bob on Earth, Planet Z is a fixed 30 ly away. As Anna passes Planet Z on her continuing outward journey, what will be (a) Bob's age according to Bob, (b) Bob's age according to Anna, (c)...

For the Image given, i have to calculate reluctances of air gap and core which depends on respective mean path lengths. For the left hand core, the mean path length calculated in the solution manual is 1.11 meter . However what I don't understand is that why is the length of the air gap included...

Homework Statement 1) A double convex thin lens has a radius of 25 cm for the first surface and a radius of 40 cm for the second surface. If the glass has a refractive index of 1.55 the focal length is a) 28 cm, b) 9.93 cm, c) 121 cm, or d) 63 cm. 2) An object is placed 16 cm in front of a...

Hi Is this analysis right A spaceship is traveling at a steady speed V in the direction shown. Inside the spaceship is a simple clock of length L and consisting of a light source at “a” and a mirror at “b”. The light leaves “a”, bounces off the mirror at “b” and goes back to “a”, which counts...

I would like to find the average chord length of a circle. And I have 2 methods, which gave different answers... [The chord is defined as the line joining 2 points on the circumference of the circle.] The general formula for a chord length is ##d=2R\sin(\delta/2)=2\sqrt{R^2-u^2}## Method 1...

Homework Statement Hi. I ve got a problem, where I have to show torque by integrating the weight of the rod over the whole it's length. Homework Equations [/B] Result, what I am suppose to get is: ## \tau_{rod} = \frac{mgb}2 ##The Attempt at a Solution [/B] When I try to integrate, I am...

Suppose we have a spinning disk with a very fast spin, an observer in the center, and an observer on the edge. Suppose that the observer on the edge measures the circumference of the spinning disk. (1) Now, the observer on the edge at a given instant will be moving at a faster speed than the...

I haven't touched a physics textbook in a while and need help with something fairly simple. I am staring straight down on a rectangular prism that is tilted on one axis to a known angle, theta. I have a measurement of a vector length in this orientation. I would like to know how much that length...

I've heard that Planck length is the smallest length ever! but if something that his length is equal to Planck length and moving by speed dv which is infinitesimal change in speed or higher than that , then according to special relativity his length must be equal to L'=L \sqrt1-v^2/c^2 which...

Homework Statement A pole BC is supported by the cable AB as is shown in the figure. If the magnitude of the force applied on the point B is 70 lb, and the moment of this force about the x-axis is -763 lb ft, determine the pole lenght. I'LL ATTACH AN IMAGE SO YOU CAN SEE IT. Homework Equations...

What is the surface area ("surface volume") of a 3-sphere having a radius of 2 Planck lengths? Is the product of the Planck's constant, Einstein's proportionality constant and Planck time also equal to this volume? Does this equivalence signify anything? What does it signify?

Hello, I'm self-studying Ta-Pei Cheng's Relativity, Gravitation and Cosmology. Problem 2.8 is the following: Two spaceships traveling in opposite directions pass one another at a relative speed of ##1.25 \times 10^8## m/s. The clock on one spaceship records a time duration of ##9.1 \times...

I have a step index SMS (single-multi-single mode fiber) with an equal lateral splicing offset at both junctions. Refractive indexes, offset and radius of cores are given. This device is fed by a broad-band source and the spectral response collected by an Optical Spectrum Analyzer is given...

Homework Statement This is a question asked in a entrance examination[/B] A spacecraft moves at a speed of 0.900c with respect to the ground. If its length is L, as measured by an observer on the spacecraft , what is the length measured by a ground observer? Homework Equations observed...

Homework Statement The problem states: Racer A and Racer B have the same care length, but from a spectators view Racer A looks (1/2) that of Racer B. Also Racer B is traveling at a speed v = (c/2). I am to find the spedd of Racer A in the spectators frame of reference. Homework Equations...

Is there any experimental proof which shows that the force of gravity works at Planck length? Has it been verified already? Is it verifiable?

http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/muon.html https://newt.phys.unsw.edu.au/einsteinlight/jw/module4_time_dilation.htm#equivalence I was looking at these links and got confused. It seems to me that they are saying the same thing but the UNSW link uses the clock in the other...

find the length of the cardroid \begin{align*}\displaystyle L&=\sqrt{r^2+\left( \frac{dr}{d\theta}\right)^2}\\ r&=8(1-\sin {\theta})\therefore \frac{dr}{d\theta}&=-8\cos\left(\theta\right)\\ r^2+\left( \frac{dr}{d\theta}\right)^2 &=(8(1-\sin {\theta}))^2+((-8)\cos(\theta))^2\\...

The shorter leg of an integer-sided right triangle has length 2001. How short can the other leg be?

Homework Statement How much do you need to increase the pendulums length by to double the pendulums period Homework Equations T = 2PI sqrt(length/gravity) The Attempt at a Solution Answer is 2sqrt(l). But I don't know how to get there. Any help would be greatly appreciated, thanks.

Suppose we have monthly totals of observed data for last 35 years. That data is of inflow of a river in a reservoir and monthly demands from the reservoir. We are interested to check the effect of construction of a dam in the upstream. The effect is, whether the downstream reservoir will have...

The Problem is #16 in the attached picture. Essentially, I need to find the length of BC using information about congruency and the location of the centroid. I've been able to show a whole bunch of things, but nothing that gets me close to actually finding out the missing side length. I began...

Homework Statement Consider the curves: y = x^2 from 1/2 to 2 and y = \sqrt{x} from 1/4 to 4. a. Explain why the lengths should be equal. b. Set up integrals (with respect to x) that give the arc lengths of the curve segments. Use a substitution to show that one integral can be...

Homework Statement The volume of a cube is 'v' cubic yards, and its surface area is 'a' square feet. If 'v' = 'a' what is the length in inches of each edge?Homework Equations volume of a cube = e^3 surface area of cube = 6e^2The Attempt at a Solution volume of a cube = 'v' cubic yards...

Homework Statement 2. Homework Equations [/B] The Attempt at a Solution I can find the length of the large square. The small square is where the trouble starts. If I look at the part of the circle where the small square is and put a center of a coordinate system at the bottom part of the...

Let there be 2 astronauts A and B in uniform relative motion and they are moving towards each other. Let A be moving in a spaceship of length L and there are 2 clocks ca1 and ca2 attached to the front and back of the spaceship respectively and let clock of B be cb. The moment when the front of...