Length Definition and 1000 Threads

Homework Statement A polymer consits of ##10^{20}## monomers, each 2 nm long. One end of the polymer is hanged at the ceiling on the other end, we have a load of ##4\cdot 10^{-10}g##. Calculate the average potential energy!Homework Equations The Attempt at a Solution Well... I don't know...

Hi I have a problem understanding a figure in my lecture notes. The figure is the following one It shows the deformation of a triangular element from time t to time t+dt: So at t it is a isosceles triangle and at t+dt it is deformed. According to my lecture notes (page 16, eq. 28), the...

Why is it that the maximum sound coming from a Rijke tube happens only when heated wire gauze is placed at 1/4th the length of the tube from the bottom. According to Rayleighs criterion(copy pasted) "If heat be periodically communicated to, and abstracted from, a mass of air vibrating in a...

I have just learned from nice article http://motls.blogspot.com/2013/12/edward-witten-what-every-quantum.html that the propagator of a massive particle can be rewritten as an integral over the so-called Schwinger parameter t as $$ \frac{1}{p^2 + m^2} = \int\limits_0^\infty dt...

Homework Statement S = {1, x, x^2} Find ||1||, ||x||, and ||x^2||.Homework Equations ##\sqrt{v \cdot v}##The Attempt at a Solution I don't know the components of each vector, so how can I perform the dot product?

Homework Statement I am currently reviewing the physics of 'standing waves on a string'. I know that for the nth harmonic, the length of the 'string' is \frac{n\lambda}{2}. Instead of just memorizing these, I have been trying to apply my knowledge of Calculus to figure out why these numbers...

Hello, I am having trouble understanding why the equivalent length in buckling problems, as well as the moment of inertia, change depending on what plane of buckling you are looking for, and how to calculate the moment of inertia in a particular plane

Hey, so I am trying to figure out the optical path length change of an optical fiber due to absorption. I'll post what I have so far and let me know if I have done anything wrong or if you have suggestions. so the optical path length is L' = nL (L' is optical path length, n is refractive...

Length Contraction:Does the object or travel distance shrink? I had always thought that length contraction meant that the object itself shrunk but I stumbled across an article where they said "Because of length contraction the photon doesn't travel any distance at all. Which is it? Any help...

Homework Statement (a) What would have to be the self-inductance of a solenoid for it to store 9.3 J of energy when a 1.56-A current runs throught it? (b) If this solenoid's cross-sectional diameter is 3.85 cm, and if you could wrap its coils to a density of 10 coils/mm, how long would...

Consider two iron rods of about 10 metres separated by 10 metre. They are in series position and not connected in anyway. If the rods are passing nearby an observe with a velocity of 90% speed of light, then what would he observe? 1) does the separation between the rods (ie 10m) undergo length...

Homework Statement px+qy=40 is a chord of minimum length of the circle (x-10)^2 + (y-20)^2 = 729 . If the chord passes through (5,15), then p^{2013}+q^{2013} is equal to Homework Equations The Attempt at a Solution Let chord length be L \frac{L}{2} = 729-...

Suppose I'm standing on Earth and i see an iron rod accelerating through space with a rate of 1m/s^2. Will it undergo length contraction after reaching a speed nearly to the c? Will there be any deformations to a spinning disk?

Hi, As is well known, Relativity claims that a rod of a given proper length will appear length contracted when measured by a moving observer. Now consider a rod of length L and observer initially at rest relatively to it, with one end of the rod at the observer's coordinate x1(0) and the...

The problem has been shown in the picture. Because of relativity, both the guys on the ground and on the vehicle would observe length contraction. So the destination of the guy on the vehicle---the galaxy, would be more closed to him. If the vehicle is replaced with the light, which means the...

If the bond length of two atoms is the distance where the force of repulsion is equal to the force of attraction, then one could figure out what the bond length of H2 is by setting the net force of attraction to the net force of repulsion and solving for distance. However when I try this ...

Homework Statement (Diagram of problem is given in attachment) m2 is stationary The coefficient of kinetic friction on m2 is 0.2 while the ground below m2 has a coefficient of friction of 0. a) Find the final velocity of both objects if m1 moves at the same v as m2 b)Find the minimum length...

Homework Statement y^2 = x from (0,0) to (1,1) Homework Equations L = ∫√(1+[g'(y)]^2) dy The Attempt at a Solution So this is a problem in my textbook that has been bothering me because I can't seem to come up with the same answer. 1. [bounds 0 to 1] 1/2∫ sec^3θ was obtained...

Hello All, I like to think that I have a decent background in physics and related material, but I confuse myself quite easily on, well, everything. I guess I think about it too much, really. So feel free to give complex answers and I will do my best to follow along accordingly. Anyways, here...

Homework Statement A girl with a mass of 40 kg is swinging from a rope with a length of 2.8 m. What is the frequency of her swinging? Homework Equations I could find the period of the situation and then from there could calculate the frequency. For the period I'm not sure what...

In special relativity, length dilation is defined as follows: X' = X0√(1 - V2/c2), where X' is the apparent/dilated length and X0 is the "proper length" Therefore proper length: X0 = X'/√(1 - V2/c2), where c > V > -c I read a book on the spacetime approach to relativity using the...

The area of a polar curve is given by A=(1/2)∫ r2 d (theta). this can be interpreted as δA= ∏r2δ(theta)/2∏ (treating the area element as the area of a sector of a circle with angle δ(theta).) taking limit of δ(theta)→0, dA= ∏r2 d(theta)/2∏=1/2 (r2d(theta) ) there fore A=1/2∫r2 d(theta)...

Hello, I was wondering if someone knew the equation which describe the exact or statistical relation between the length(# of digits) of a power of 2 based on it's power. I plotted 200 of the powers in mathematica and I get a fairly straightforward staircase plot. I'm just wondering what's the...

Homework Statement Two sources, A and B, emit a sound of a certain wavelength. The sound emitted from both sources is detected at a point away from the sources. The sound from souce A is a distance d from the observation point, whereas the sound from source B has to travel a distance of...

This is a thought experiment that just popped up in my head, please excuse any layman inaccuracies. Imagine the largest, most massive galaxy in the entire universe. Let's hypothesize that it is at a great distance from earth, beyond the edge of the observable universe. Now, since all objects...

Homework Statement Homework Equations The Attempt at a Solution Solution: Graph: For part a, I understand mathematically why the value of c matters. What I don't understand is how it can possibly matter intuitively. I get that ##\overrightarrow { \nabla }...

Homework Statement Find the total length of the curve t --> (cos^3(t), sin^3(t)), and t is between 0 and ∏/2 where t is in radians. Find also the partial arc length s(t) along the curve between 0 and ∏/2 Homework Equations The length is given by: S = ∫\sqrt{xdot^2 + ydot^2} dt...

Homework Statement Find the length of the curve traced by the given vector function on the indicated interval. r(t)=<t, tcost, tsint> ; 0<t<pi Homework Equations s= ∫||r'(t)||dt The Attempt at a Solution r'(t) = <1, -tsint + cost, tcost + sint> s= ∫||r'(t)||dt ||r'(t)|| =...

Homework Statement A particularly beautiful note reaching your ear from a rare Stradivarius violin has a wavelength of 39.1 cm. The room is slightly warm, so the speed of sound is 344 m/s. If the string's linear density is 0.560g/m and the tension is 160N , how long is the vibrating section...

I'm designing an eyepiece for fun and want to be accurate. I just realized my physics book equations are approximated for thin lenses only. Suppose I have a convex convex lens or a plano convex lens, lateral parallel rays coming from one side or the other, and a focal point on the opposite...

EDIT: It seems that just after posting this, my professor decided this problem is too difficult for us to be responsible for. I can't delete this question, so don't feel obligated to answer it. But who knows? Maybe someone else out there has the same question. Homework Statement The Sun...

Homework Statement A person on a unicycle has a total weight of 900N. They need to climb to a height of one meter. If we build the ramp for a minimum pushing force of 50N, how long must the ramp be? m=91.7kg w=900N F1=50N Ry=1m Rx=? Rxy=? θ=? Homework Equations .5mv2=mgh F1=mgsinθ The...

Homework Statement If abscissa and ordinate of vertex of parabola y^2+2ax+2by-1=0 are equal then least possible length of latus rectum is Homework Equations The Attempt at a Solution The give equation can be rewritten as \left( y+b \right) ^2 = -2a\left\{ x-\dfrac{1+b^2}{2a}...

I got asked how the scalar product can be used to find the length of a vector? Could someone please explain

Homework Statement Find the length of the chord which the circle 3x^2+3y^2-29x-19y+56=0 cuts off from the straight line x-y+2+=0. Find the equation of the circle with this chord as diameter Homework Equations x^2+y^2+2gx+2fy+c=0 The Attempt at a Solution I can solve the second part...

Ello every one, i have interesting question. Any one who has james stewert 7th edition calc book I am on secotion 8.1 studying for an exam. number 13 of 8.1 says this y= ln(secx) find arc length from 0-pi/4 here is what i do first in my opinion. y`= 1/sec(sectan) y`= tanx...

The question is: the wavelength of a spectral line on the left edge of Jupiter's equator is 499.98 nm, and the right edge is 500.02 for the same spectral line, what is the length of jupiter's day (in hours)? I know that its 10 hours but I need to show my work. I tried using many different...

Homework Statement The window is held open by the cable AB. Determine the length of the cable and express the 30N acting at A along the cable as a Cartesian vector. http://img802.imageshack.us/img802/9599/ru5y.jpg Homework Equations vector(F) = FuAB The Attempt at a Solution Here's my...

Homework Statement Please refer to the image attached. I don't understand why can they just take 1.8m as the original length, since there is already a load hanging there. My calculations yield the value of strain to be e/L, but in the answer it is e/1.8. Please explain this to me. Homework...

Homework Statement Calculate the arc length of <2t,t^2,lnt> from 1=<t=<e Homework Equations Arc length=∫√{(x')^2 + (y')^2 + (z')^2} The Attempt at a Solution So I have gotten to this point: ∫√{4 + 4t^2 + \frac{1}{t^2}} Am I on the right track, and if so, how do I integrate that?

This is from my course notes http://img28.imageshack.us/img28/2630/ckyl.jpg In line 3, there's the integral \int_0^t ||y'(s)||ds which represents the length of the curve as a function of t (which I am thinking of as time). Here, I think s is a dummy variable for time. The equation in line...

Homework Statement The problem asks us to prove the length of a curve decreases as one of its parameters, t, increases. Here is the full statement http://img94.imageshack.us/img94/6560/yf6j.jpg Homework Equations L_t=\int_0^1 ||\partial_s x(t,s)||ds is the length of the curve as a...

Homework Statement Find the arc length parameterization of r(t) = <(e^t)sin(t),(e^t)cos(t),10e^t>The Attempt at a Solution so I guess i'll start by taking the derivative of r(t)... r'(t) = <e^t*cos(t) + e^t*sin(t), -e^t*sin(t) + e^t*cos(t), 10e^t> ehh... now do I do ds = |r'(t)|dt and...

Homework Statement It's a balanced seesaw but the pivot isn't in the exact middle and two weights are on it. One at the very end of each side. The weight on the left is 4.8 kg.[m1] The weight on the right is 5.5 kg[m2] The length of the entire seesaw is 5m L1 is the distance from the...

Difference between Optical and Geometrical length!? I'm having this question since 2 times now in the theoretical part of the exam & still I couldn't find anything about it in the book neither in google. Can anyone who's more experienced in Optical Physics give me the answer to this please !?

Here is the question: I have posted a link there to this topic so the OP can see my work.

Homework Statement Show that in cylindrical coordinates x = \rho cos \theta y = \rho sin \theta z = z the length element ds is given by ds^{2} = dx^{2} + dy^{2} + dz^{2} = d \rho^{2} + \rho^{2} d \theta ^{2} + dz^{2} Homework Equations -- The Attempt at a Solution...

Math Problem: Find the length of the third side of a triangle if the area of the triangle is 18 and two of its sides have lengths of 5 and 10. Which one of these are correct when I am working them out? If none of these are correct, then can somebody please help me solve this math problem...

Homework Statement Two trains, A and B, are moving towards each other with relative speed 0.8c. The passing of the two trains (from when their fronts align to when their backs align) takes 20% longer as observed from train A as is does as observed from train B. What is the ratio of the length...

Homework Statement We are to assume an infinite transmission line with the following parameters: capacitance: 296 ρF/ft Zc=52Ω inductance: 8.0 × 10-7 H/ft We are told that a 100MHz signal is attenuated 31 dB per 100 feet and asked based on the information, assuming no leakage through...