Natural Definition and 1000 Threads

I read that if a beam of unpolarized light goes through a polarizer, the intensity of the polarized beam is equal to half the intensity of the original beam. Can someone explain me why? I thought the intensity would be the same.

Find all values of $x$ such that $f(x)=x^2-19x+99$ is a perfect square for all $x\in N$.

Hi there, I've just been having a little trouble with this short question from a past exam paper... Homework Statement "An atomic state has a dominant decay mode which produces an emission line of wavelength 6 \times 10^{-7} m and natural width 10^{-13} m . Estimate it's natural lifetime...

HelloI am trying to prove that $\lim\left((2n)^{1/n}\right) = 1$. Here $n\in \mathbb{N}$. I have already proven that $(2n)^{1/n} > 1$ for $n > 1$. So we can write $(2n)^{1/n} = 1 + k$ for some $k > 0$ when $n>1$. Hence $2n = (1+k)^n$ for $n>1$. By the Binomial theorem, if $n>1$, we have, \[ 2n...

Why is e^-1 the inverse of natural log e? Thank you

shaft -- find natural frequency of horizontal shaft with bearings how to find natural frequency of horizontal shaft with bearings at either sides, using (Ansys-classic). Please reply, Thank you.

Is the set of the natural Nos complete?

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

Can I find out the natural extension of a spring if I am only given the mass of a block that can be put on it and the value of the spring constant? I have found x ( from the formula F = -kx ) when the block is on it but I now need to find the extension of the spring with no mass on the end. It...

Homework Statement I am having issues with some problems relating to a plant theoretically shut down on natural circulation, and calculating the core ΔT and natural circulation flow rate.. Can anyone provide some equations or theory I could use to assist me? I'm not familiar with this...

The March 2014 issue of Physics Today has an article by Lee Smolin in which he argues that natural laws must change over time. As examples of such theories, he gives Penrose's CCC and his own cosmological natural selection (CNS): http://arxiv.org/abs/hep-th/0612185 My understanding was that...

how does U 238 change to U 235 in nature earth or how does uranium enrichment in nature

Pure hypotetical question about cinemascope light source. As we know cinescope uses artificial light source to project it on cinema screen. Question, its possible to use natural daylight to project it on screen ?

Hello, all. My whole life, I've had a passion for physics and understanding the universe in general. For years since I was younger I've read layman's books on the subject, reading articles and journals, etc. I have deeply thought about physics (theoretical physics in particular) as being my...

So apparently the natural frequency is zero for uniform column with axial load when P is equal to the critical buckling load. Could anyone please explain theoretically why this is the case.

Find natural numbers a and b such that $2^a-3^b = 7$

Hi, I just want some explications about the nature of "Natural Selection" in term of physical laws acting on molecules. In other words, how exactly "Natural Selection" acts on molecules and atoms.

A Cantilever beam of SiO2 of length 100μm, width 20μm and thickness of 5μm. How to calculate the resonant frequency? I know f=1/2∏√(k/m) where k=3EI/L^3 and mass = l*w*h *ρ (density) and I = w*t^3/12, but i don't get the desired answer. pl correct me. What changes are to be considered for...

Many books give bad answers or no answers at all to why we work with base $e$ and measure angles according to radians in calculus. Here is what I tell my students, as far as I know, this is the best explanation I seen because it is essentially a one line explanation that is short and to the...

How would you think natural human flight would be possible?

In math, we have axioms that we assume to be true. We don't have proofs for it. Similarly english or any other natural language attempts to describe the world using words, alphabets etc. So there must be some axioms, right? Everything cannot be described / defined. But obviously, we can...

Homework Statement A natural-gas fuel contains 85 mol-% methane, 10 mol-% ethane, and 5 mol-% nitrogen. a) What is the standard heat of combustion (kJ mol-1) of the fuel at 25°C with H2O(g) as a product? b) The fuel is supplied to a furnace with 50% excess air, both entering at 25°C. The...

I have googled it but couldn't find a simple, easy to understand answer answer. Why does a body have a particular natural frequency. Can it be changed by any way?

Homework Statement It is often stated that heat sinks, radiators, and the like require proper spacing of fins/pins/etc., especially when relying on natural convection. There is a formula from Rohsenow and Bar-Cohen that allows one to calculate the proper spacing between rectangular fins in...

I am an international student from Pakistan doing A levels. I applied to St John's College of Cambridge uni for Natural Sciences and have luckily got an offer from there as well. I have also got a full scholarship which includes tuition and living expenses. But I have also applied to MIT...

Why is natural log abbreviated as "ln" and not "nl"? I've been taking calculus for a while now and I was just wondering why natural logarithm is abbreviated as "ln" and not "nl". I'm just curious!

An easy question. All "odd" number can be expressed as a sum of consecutive natural numbers. Example: 35=17+18 35=5+6+7+8+9 35=2+3+4+5+6+7+8Question: Demonstrate that prime numbers (except for the "2"), can only be expressed as the sum of two consecutive natural numbers.

A professor in Cambridge University has showed his proof that the sum of natural number was equal to -1/12. The video can be found on the internet.Well, although the way to proof I think is really ridiculous, it could be a good way to building a new math model. Since we think the sum of natural...

Hi lovely people, I recently came across a video http://www.youtube.com/watch?v=w-I6XTVZXww that said if you add all of the natural numbers from 1 to infinity, the answer is... What do you think it is? Infinity or something like that? They said it was -1/12. I watched the proof but I don't...

So I have been going through a book on physics-based mathematics. I have seen the author using natural units (h = c = 1) in formulae. Why is this done? Most importantly, doesn't it mess up the true calculation? For example, take e = mc^2. If I set c = 1, it becomes e = m. So if I am given a mass...

My father told me that when he was a child in the 1950s, his parents owned a natural gas powered refrigerator. He said that the refrigerator made no noise when it was running. I can't fathom how a natural gas powered refrigerator would work. I mean, it would make no sense for natural gas to...

Hello, I am interested in estimating/modelling the behavior of a rubber stud mount (http://image.made-in-china.com/2f0j00nemTaJBgEcbE/Anti-Vibration-Mounting.jpg) when a moment is applied about its radial axis. In my application, I am using it primarily as a spring alternative where it supports...

Anyone have an idea to find a first and second natural frequency from time domain and frequency domain plot resulting from an accelerometer measuring the vibration in cantilever beam ? Thanks very much :)

This is a closed loop system. My teacher showed me that one of the methods to find the natural frequency of this system is by finding the frequency at phase -90 degrees. Why must it be -90 degrees? Please explain. From the phase graph, the frequency at -90 degrees is 32 [rad/s], so that's the...

I have posted this on other forums, and I have discussed this with my professors, but I thought I would share it here for those interested. Essentially, I have a function that efficiently approximates arctangent on [-1,1] and ln(1+x) on [0,1]. For some background about me, I am a Z80...

Question 1) Write ⊆ or ⊄: {x/(x+1) : x∈N} ________ QNOTE: ⊆ means SUBSET ⊄ means NOT A SUBSET ∈ means ELEMENT N means Natural Numbers Q means Rational Numbers Question 2) Which of the following sets are infinite and uncountable? R - Q {n∈N: gcd(n,15) = 3} (-2,2) N*N {1,2,9,16,...} i.e...

Homework Statement ∫(ln(√x))/(x)dx Homework Equations The Attempt at a Solution I am really not sure where to start. All of the other integration problems were relatively simple, sticking with the ∫u'/udu = ln(u).

I am giving a presentation on the principle of induction. I'll be showing how acoustic energy (sound) is converted into an electrical signal (via mic) & thus converted back into acoustic energy (via loudspeaker). Now I need to address the following, How & Why? How doesn't bother me. I can...

Given the definition: A^{n+1}=A^n\cup A then prove that: (A\cup B)^n =(A\cup B)\cup(A\cap B) for all natural N0s n

Few days ago, I was thinking about why we need to define V*=Hom(V,K) for a K-vector space when the dimension of V is finite because then V* and V both will have the same dimension and will be isomorphic. So, I couldn't understand why such a thing would be even called a dual vector space if it's...

Homework Statement Hey everyone! So to elaborate the title a bit more: basically I have to show that the natural representation of S_{3} is a direct sum of the one-dimensional irreducible representation and the two-dimensional irreducible representation of S_{3}. Homework Equations Im...

My question is: Show the limit of x_{n}=\frac{ln(1+\sqrt{n}+\sqrt[3]{n})}{ln(1+\sqrt[3]{n}+\sqrt[4]{n})} as n approaches infinity Solution: {x_n} = \frac{{\ln (1 + {n^{\frac{1}{2}}} + {n^{\frac{1}{3}}})}}{{\ln (1 + {n^{\frac{1}{3}}} + {n^{\frac{1}{4}}})}} = \frac{{\ln \left(...

Often there's these stories on TV about someone accidentally damaging a large diameter natural gas pipeline while digging a ditch etc. and then a huge raging fire. What I'm wondering about is how frequently are shutoff valves installed on these lines. My intuition says ~30 miles apart at most...

is there a straight formula for finding one of the natural (preferably fundamental) frequency of a steel flat with dimension say, L=1000 mm, B=100 mm and Thickness T=10 mm ? The flat is fixed at both ends by bolts and two weights of equal magnitude are suspended at 1/4 and 3/4 (i.e. 250 mm and...

is black hole a theoretical concept or a natural phenomenon?

Hi I am working on a problem that ends up having the natural log of a negative e which I'm confused on how to find the explicit solution. The Problem: Find an explicit solution with C. y'-e^{-y}cos(x)=0 My Conclusion: First of all, I'm confused how I should solve this explicitly if I'm...

Hello, everybody: I was wondering if you knew if there is a book, journal, webpage or a compendium of some sort in which different and diverse curious common and uncommon natural phenomena are explained with physics (preferably with math involved). For example, a place where to look if I'm...

Hi! I am trying to compute the natural frequency of a system and I also need to add the added mass term to my equation. The object I have is a torus and is basically in heaving motion. I found a good paper, which gives a formula for 3d added mass and 2d added mass. I would figure that I...

Which do you think would be more lucrative in the long run? I am in computer engineering, and I would like to do my own startup, but I am exploring other options as well.

$a,b,c,d,e,f,g \in N$ $a<b<c<d<e<f<g$ $\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}+\dfrac{1}{d}+\dfrac{1}{e}+\dfrac{1}{f}+\dfrac{1}{g}=1$ please find one possible solution of a,b,c,d,e,f,g (you should find it using mathematical analysis,and show your logic,don't use any program)