Extension Definition and 294 Threads

For P, the force will be 2F and the spring constant will be ##\frac{k}{2}## so the extension will be 4 times, and the energy will be 8E but there are no options showing 8E What is my mistake? Thanks

The English Wikipedia page seemingly changed from using "displaystyle" to "$" with the consequence that I can't use it anymore on Chrome. It is simply unreadable. Does anyone know a good browser extension to solve the problem?

TL;DR Summary: Have a university project where we are calculating the speed of the arm at the end. I need some help on where to start on the calculations. We have tried to determine instantaneous center of rotation for the device. We want to find the linear velocioty of point B. There is a...

Torque limiting extensions act as a torsion device by flexing once a certain amount of torque is applied onto the fastener that they are tightening down. This helps prevent from over tightening the fastener when using an impact wrench. Seems like a great tool that can speed up the process of...

Proof of 84i): We assume that ##E/F## is a field extension. For each ##i##, ##F(\alpha_i)## is the smallest subfield of ##E## containing ##F## and ##\alpha_i##. Let ##F'## be a subfield of ##E## containing ##F## and ##\alpha_1, \dots, \alpha_n##. Then ##F'## containing ##F(\alpha_i)## for all...

I'm learning about Fourier theory from my lecture notes and I have a few questions that I wasn't able to concretely find answers to: 1. What's the definition of periodic extension? I think the definition is as follows ( Correct me if I'm wrong please ): for ## f: [ a,b) \to \mathbb{R} ## its...

Below shows the generic V-N diagram for most of the civil aircrafts. Now, I have the CFD results available for multiple combinations of angles of attack of the aircraft, with the deflection angle of the flap. I have to choose a couple, to input into my structural analysis of the flaps. How to...

Wikipedia says that a general projective representation cannot be lifted to a linear representation and the obstruction to this lifting can be understood via group cohomology. For example, I see that a spin group is a central extension of SO(3) by Z/2. More generally I can follow the reasoning...

Are you aware of the 3-article series of Wiesendanger's quantized extension of GR? This is open access: C Wiesendanger 2019 Class. Quantum Grav. 36 065015 and the two sequels linked to in the PDF. The question is if this work counts as a quantization of a reasonable extension or reformulation...

I'm studying elasticity from classical Gurtin's book, and my professor gave us the following example, during lecture. Unfortunately, this is not present in our references, so I'm posting it here the beginning of the solution, and I will highlight at the end my questions. First I need to state...

I found the ratio between the weight exerted by the 70kg man to the weight exerted by the 20kg load, and equated it to the ratio of maximum extension by the 70kg man to the extension by the load Is this a right step to use, because the book didn’t give any answer nor solution which can help me...

Hi everyone, We've been looking at Fourier series and related topics in online class, touching upon odd and even periodic extensions. However, we haven't looked at what this translates to for sine and cosine functions - only sawtooth and line examples. So, I'm trying to do my own investigation...

I have attached the homework with some of the solution. I have ciuple of questions about it. For part b, what else I can say? I think the copper wite is ductile . Elastic and plastic behaviour have already been mentioned. I need to add another word to describe it. Can say it's hard ? Or...

You may have watched this interview of Nobel prize winner, Roger Penrose. Now with Zoom-Clude®, the amazing nobel prize winning Firefox extension, you can block out the left person on a video of a 2 person zoom meeting. The extensions works on both PF and YouTube. Different occlusion...

the acceleration of the center of mass is ##a_{cm} = F/(M+m)## I considered the forces on the block of mass m(when the system is at maximum extension) I got the equation $$kx - \frac {mF}{(M+m)} = ma_{cm}$$ and from that I got the value of the maximum extension $$x = \frac {2mF} {k(M+m)}$$ which...

It's just think that if we measure 1 second with a clock we should be able to "see" a 300'000km long piece of something in space or not ? Or does the time extension only has to be understood as a set of numbers indicating timelaps, so that there is no "geometry" of time ?

From what I understand, the force between two current-carrying wires can be calculated as: $$\dfrac {F}{L}=\dfrac {\mu _{0}I_{1}I_{2}}{2\pi R} $$ Doesn't this mean: $$\dfrac {F}{L}=\dfrac {\mu _{0}I_{1}I_{2}}{2\pi 1^{2}}=\dfrac {1}{2}kx^{2} $$ ? $$\dfrac {\left( 4\pi \times 10^{-7}\right)...

I have a home appliance that should be plugged into one single wall socket because it's energy consuming, and shouldn't share with other appliances by common sense. However, due to some practical problems, I can't plug it directly into the wall socket. If I use a power extension board (i.e...

Hey guys, I think that the answer to this question is to solve for the amount of kinetic energy that the ball exerts on the spring, and the substitute that value to solve for x. However, I am not sure and quite stuck on how to start

Homework Statement f Homework Equations Hooke's Law: F = -kx Series spring combinations: ##\frac{1}{k_{eq}} = \frac{1}{k_1}+\frac{1}{k_2}## Parallel spring combinations: ##k_{eq} = k_1+k_2## The Attempt at a Solution The slope of 1 is ##\frac{4}{5}## and the slope of 2 is ##\frac{3}{2}## I...

All, I have been going back and forth in my head on if I should shorten my extension or increase it and I need a second opinion to straighten me out. PN: 5T-I-SET https://snaponindustrialbrands.com/DSN/wwwsnaponindustrialbrandscom/Content/PDF/Snap-on%20Industrial%20Brands%20CAT4%20113.pdf Its...

I am reading Kaplansky's text on metric spaces and this part seems redundant to me. It was stated below (purple highlight) that we need to show that the convergence of ##(f(a_n))## to ##c## is independent of what sequence ##(a_n)## converges to ##b##, when trying to prove the claim ##f(b)=c##...

When we define a limit of a function at point c, we talk about an open interval. The question is, can it occur that function has a limit on a certain interval, but it's extension does not? To me it seems obvious that an extension will have the same limit at c, since there is already infinitely...

I have been stuck several days with the following problem. Suppose M and N are smooth manifolds, U an open subset of M , and F: U → N is smooth. Show that there exists a neighborhood V of any p in U, V contained in U, such that F can be extended to a smooth mapping F*: M → N with...

Let us look at short segment of a rod with its length dx. Due to longitudinal wave, left endpoint moves for s in the direction of x-axis and the right endpoint moves in the same direction for s+ds. Because I want to calculate the elastic energy of the wave motion, I need the extension of dx so...

Homework Statement Ans) F/k Homework EquationsThe Attempt at a Solution Consider only figure a) . I believe the given answer is wrong . The maximum extension should be 2F/k . F/k is the extension in the spring in the equilibrium position . Maximum extension should be double of that . Work...

a) dimension the moving-coil movement so that it indicates full deflection at 25 V given Values: Voltage Source: U2Max = 25V; moving-coil movement: IM = 100µA; UM = 270mV Rv = ( U2Max - UM ) / IM = (25V - 270mV) / 100 µA = 247,3kΩ b) the internal resistance is increased by 20 %...

The short version: If you had an infinite amount of time, would the standard proof for the insolubility of the halting problem still work? The longer version: A simple proof that there are non-computable functions can be easily seen by the fact that there are only countable number of Turing...

Homework Statement Two blocks of masses m, and m2 are connected by a spring of spring constant k. Suppose each of the blocks is pulled by a constant force F Find the maximum elongation spring will suffer and the distances moved by the two Homework EquationsThe Attempt at a Solution the two...

Can I extend the function $f(x,y)=(x^2+y^2)\arctan\dfrac{1}{|xy|}$ to a continuous function? If I consider the restriction of $f$ along the line $x=k$ i find $\lim_{(x,y)\rightarrow(k,0)}(x^2+y^2)\arctan\dfrac{1}{|xy|}=k^2\dfrac{\pi}{2}$ how can i prove that?

I am trying to make a browser extension. Tutorial (https://developer.mozilla.org/en-US/Add-ons) from mozilla webpage teaches to make these in javascript, but is it possible to make browser extension in some other programming language? How can I get URL of the tab user is watching. I tried...

Hi, I was wondering if anyone has any links or documents of some challenging projectile motion and circular motion questions. Also, if you have any regarding 'Energy' and roller coasters and pendulums and Hooke's law they would be great too. I am in year 11 and am looking to do some extra study...

Hi, So I am currently working on a rather simple problem of a projectile being launched by a spring at a certain angle. Ignoring friction, from conservation of energy we know that the velocity of the launched projectile would be ##v = \sqrt{\frac{kx^2}{m}}## (with ##m## being the mass of the...

I am a little confused about terminology when it comes to extension fields. In my textbook, E is a field extension of F if F is a subfield of E. This is understandable. However, in proving that all polynomials have a zero in an extension field, ##F[x] / \langle p(x) \rangle##, where ##p(x)## is...

Homework Statement Let ##K = \mathbb{Q} (1, a_1, a_2, \dots, a_n)##, which is the smallest field containing ##\mathbb{Q}## and ##a_1, a_2, \dots, a_n##, where each ##a_i## is the square root of a rational number. Show that the cube root of 2 is not an element of K. Homework EquationsThe...

Hello! (Wave) According to my notes: For the solution of problems with differential equations it is often useful to expand to a Fourier series with period $2L$ a function $f$ that is initially only defined on the interval $[0,L]$. We could define a function $g$ with period $2L$ such that...

I know the seesaw mechanism is a model used to explain both neutrinos having mass and why their dirac mass/yukawa coupling is so much smaller than for the other fermions. The seesaw mechanism needs the right handed neutrino to exist. How does the seesaw mechanism for the vMSM differ from that...

Hello. Im trying to learn more about different extensions of the standard model. Are the Left Right Symmetric Extension of the Standard model and the Neutrino Minimal Standard Model different extensions? I know both add 3 right handed neutrinos. Do these neutrinos differ in any way, also are...

Homework Statement Scenario: a block of mass 5 kg is hanging from a spring from an ideal pulley from one side, the other side supporting a mass of 10 kg through a STRING. Now, the 10 kg block replaced with a 5 kg block. In which case would the extension in spring be greater, assuming constant...

Homework Statement An ideal spring of relaxed length l and spring constant k is attached to two blocks, A and B of mass M and m respectively. A velocity u is imparted to block B. Find the length of the spring when B comes to rest. Homework Equations ∆K + ∆U = 0 U = \frac {kx^2}{2} ∆p = 0...

Hey! Let $C$ be an algebraic closure of $F$ and let $f\in F[x]$ be separable. Let $K\leq C$ be the splitting field of $f$ over $F$ and let $E\leq C$ be a finite and separable extension of $F$. I want to show that the extension $KE/F$ is finite and separable. We have that $KE$ is the smallest...

Hey! :oI want to calculate the degree $[\mathbb{Q}[\sqrt{3}, \rho] :\mathbb{Q}]$. It holds that $$[\mathbb{Q}[\sqrt{3}, \rho] :\mathbb{Q}]=[\mathbb{Q}[\sqrt{3}, \rho] :\mathbb{Q}[\sqrt{3}][\mathbb{Q}[\sqrt{3}] :\mathbb{Q}]=[\mathbb{Q}[\sqrt{3}, \rho] :\mathbb{Q}[\sqrt{3}]]\cdot 2$$ and...

Hey! :o We have that $E/F$ is an extension Kummer of degree $n$ and that $F$ contains a $n$-th unit root $\omega$ with $\text{ord} (\omega)=n$. I want to show that $E/F$ is an extension with radicals of order $n$. I have found the following theorem: Could we maybe use that theorem in...

Hey there, i guess i just need to ventilate some and see what people think about my situation and about the choices i have. First of all i must say that i am from Sweden and therefore i have conditions that few other people have. I get my education for free and i am free to chose whatever field...

Homework Statement I'm following the solutions to a homework tutorial and I'm having trouble understanding why what they're saying is true. Question: Let f be a polynomial in K[x] and let S be the splitting field of f over K. decide whether the extension S:K is galois and describe the...

Homework Statement Let S= {e^2*i*pi/n for all n in the natural numbers} and let F=Q Is F:Q 1) algebraic? 2) finite? 3) simple? 4)separable? Homework EquationsThe Attempt at a Solution 1) Every element in S is a root of x^n-1 and every element of a in Q is a root of x-a, and thus I think...

Homework Statement Let c be a primitive 3rd root of unity and b be the third real root of four. Now consider the extension Q(c,b):Q. Find the degree of this extension, show that it is Galois, and calculate Gal(Q(c,b):Q) and then use the Galois group to calculate all intermediate fields...

Homework Statement If Char(K) = 0 and [L:K]=2, is L:K a galois extension? Homework EquationsThe Attempt at a Solution My gut is saying yes because if [L:K]=2 then it seems that any polynomial in K[x] with a root in L should split in L[x]. Something about how some hypothetical minimal...

Homework Statement Hey PF, I'm trying to find fields K<M<L such that K:L is Galois but K:M is not. Homework EquationsThe Attempt at a Solution My first idea was let K=Q the field of rational numbers and c be a primitive 6th root of unity, so then Q<Q(c^4)<Q(c). Q:Q(c) Is galois, and I'm...

Homework Statement Let Q < L < Q(c) where c is a primitive nth root of unity over Q. Is [L:Q] a Galois extension? Homework EquationsThe Attempt at a Solution L must be equal to Q(d) where d is a non primitive nth root of unity. [Q(d):Q] is not a galois extension because the minimal polynomial...