Equivalent Definition and 1000 Threads

1. The problems: The questions are to find the x, y and z components of the equivalent MOMENT at point A in both diagrams. For the green block, I found the y and z components of the equivalent force at point A are -39.04kN and 15.48kN respectively. The Attempt at a Solution For the first...

Homework Statement Homework EquationsThe Attempt at a Solution In the attached image the outer circular wire is represented as N . We have to find the equivalent resistance between O and N . Consider a battery of voltage V between O and N . From O there are six similar paths OA...

1. The Problem Statement Calculate the equivalent resistance between O and the circumference. Each wire has 24 ohm resistance and the circumference has zero resistance. 2. Homework Equations Not needed.3. Attempt at solution I tried to use symmetry to solve this problem. I understand that...

Homework Statement Determine the Thévenin equivalent of the following circuit with respect to terminals A-B Homework Equations $$U=RI$$ The sum of the currents in a node is zero. The sum of voltages in a mesh is zero. I'm always considering the currents in the resistors directed downwards...

Homework Statement I will post a photo of the question in the thread once I've created it. I have found the magnitude and angle of the resultant force, but I am unsure of how to proceed. I find moments and couples confusing. Homework Equations $$\vec M = \vec r \times \vec F$$ The Attempt at...

Homework Statement [/B]Homework EquationsThe Attempt at a Solution I really have no idea how to proceed. Applying Kirchoff's laws to this would be quite lengthy. This circuit is supposed to be a wheatstone bridge but I can't see it.

Hello! Recently I was going through some old exams and upon encountering this problem (which seemed pretty easy) I got stuck. Exams at my university are composed of individual tasks, each having three subquestions with four plausible answers respectively. Solution sheet gives results only, so...

I know that one can easily prove the result that a function is injective if and only if that function has a left inverse. But is there intuitive reason for this? Same goes for the fact that having a right inverse is equivalent to being surjective. Why are the properties of injectivity and...

Is there a precise definition for the statement that two differently worded probability problems are "equivalent"? One technique of (purportedly) solving a controversial probability problem is to propose an "equivalent" problem whose solution is not controversial. (e.g. The Sleeping Beauty...

Homework Statement A lot of people are familiar with equivalent inertia problems, where you have a drive train and inertia on different axis and you calculate the equivalent inertia on whichever shaft you want. This time I (try to) bring something new, trying to associate the output power to...

Homework Statement The minimum resistance obtained by connecting 50 resistances of 0.25 ohm each is A)50/4ohm B)4/50 ohm C)200 ohm D)1/200 ohm 2.Relevant equations 1.When resistances are connected in series, ▪R(equivalent)=summation of all individual resistances 2.When resistances are...

Homework Statement Homework EquationsThe Attempt at a Solution [/B] All the resistors are connected in parallel across A and B .The equivalent resistance is 1/Req= (1/R) +(1/2R) + (1/6R) + (1/12R) + ... I tried to work with few terms and it seems the effective resistance tends to zero as...

Homework Statement From Introduction to Set Theory Chapter 8.1 exercise 1.4 Prove that Zorn's Lemma is equivalent to the following statement: For all ##(A,\leq)##, the set of all chains of ##(A,\leq)## has an ##\subseteq##-maximal element.[/B]Homework Equations N/A The Attempt at a Solution...

$\textrm{write an equivalent polar equation}$ \begin{align*}\displaystyle x^2+(y-1)^2&=1 \end{align*} $\textrm{expand and rearrange}$ $$x^2+y^2=2y$$ $\textrm{substitute $r^2$ for $x^2+y^2$ and $r \cos(\theta)$ for $y$}$ $\textrm{then}$ $$r^2=2r\cos(\theta)$$ $\textrm{or}$ $$r=2...

Homework Statement : [/B]Two conducting spheres of radii R1 and R2 are kept widely separated from each other. what are their individual capacitances? If the spheres are connected by a metal wire, what will be the capacitance of the combiation?Homework Equations Capacitance of a sphere of radius...

Why is the dot product equivalent to the matrix multiplication of its components? I've seen some proofs using Pythagorean and cosine law but they don't give you an intuitive feel as to why matrix multiplication works. The geometric definition (##ab cosθ##) is very easy to understand. To a...

Homework Statement Steam runs through a pipe, and the state of the steam is required to be found. To do this, some of the steam was condensed inside a container filled with water. The container weighs 850g, and has 8kg of liquid water inside it initially. The whole system was measured to be...

Suppose one starts with the standard Klein-Gordon (KG) Lagrangian for a free scalar field: $$\mathcal{L}=\frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi-\frac{1}{2}m^{2}\phi^{2}$$ Integrating by parts one can obtain an equivalent (i.e. gives the same equations of motion) Lagrangian...

The focal of the lens equivalent of two thin lens at distance h is $$1/f=1/f_1+1/f_2+h/(f_1 f_2)$$ Therefore, supposing that ##f_1>0## and ##f_2>0## (both lenses are convergent), if ##f_1+f_2 <h## then the equivalent lens should be divergent. Nevertheless consider the example in picture...

Homework Statement I'm going through the derivation here starting on page 16. This image adds some context: . Generalizing their result to the i'th particle they find the extended distance between two masses being ##\Delta l= \frac{(y_i-y_{i-1})^2}{2a}## Then since the potential energy is...

Hi, Silly little question about the transformer short circuit test. When I perform it with the secondary shorted and I get Req = Power / current2 is this Req = Rpri + Rsec? If I measured Rpri and Rsec with a multimeter? Thanks

1. The problem A very simple question on a quiz given to me states that, "A 63 kg diver is standing on a diving board waiting to commence her dive. The diving board has compressed 0.08 m. Determine the elastic potential energy of the diver." 2. The attempt at a solution I thought this question...

Homework Statement Homework Equations / 3. The Attempt at a Solution Here is my attempt from the homework assignment. It doesn't appear that I got any points for this question and was hoping to get a little help in correcting my issues or pointed in the right direction to start over. [/B]

Could I combine the two resistors together in parallel to make an equivalent resistor, and then use that equivalent resistor in series with the capacitor? It would be great if there was some rule of thumb that I can use to know what I can make into an equivalent resistor/capacitor down the line...

Homework Statement Find the equivalent capacitance between points A & B Homework Equations Ceq1 = C + C 1/Ceq2 = 1/2C + 1/2C + ... The Attempt at a Solution [/B] It is my understanding that each capacitor top and bottom are connected in parallel, so their equivalent is 2C. Now, they...

Homework Statement There are four (sub)problems in the attached PDF file, but I don’t see the common pattern that the solutions to these kinds of problems have; see “3. The Attempt at a Solution ”. Homework Equations Logical equivalence The Attempt at a Solution I am trying to find the...

Hi, I was just looking at an example for a certain problem and noticed that in the second step they went to arctan(epsilon). I know there's a form that is equal to arctan but am a little unsure. I've come across formulas on the web such as arctan(x) = ∫(dt)/(a2+t2) but nothing else that would...

【Mod Note: thread moved from technical forum, so homework template is missing】 Hi every one! I am encountering difficulties on finding the Req. in the sense that i can't really see which is in parallel end which is not, especially on the diamond shape. I haven't really understood how to treat...

Homework Statement Homework Equations Finding the Thevenin equivalent? The Attempt at a Solution I found the thevenin resistance to be 185/47 ohms, which came out to be correct. I've been struggling with this question all day. I ended up attempting to find the norton equivalent and then...

Homework Statement Integrate x2(2+x3)4dx. Show that Wolfram Alpha's answer is equivalent to your answer. Homework Equations No equations besides knowing that the integral of xpower is 1/power+1 * xpower + 1 The Attempt at a Solution So I have the answer to the integral by hand as (2+x3)5)/15...

Hello. Please looks at the attached image first. The left image is LCC impedance matching network (one of T-type impedance matching networks) and the right is the corresponding equivalent circuit when CT and CL are adjusted such that an equivalent impedance of the sub-circuit surrounded by...

Hello. I was browsing online to answer the question to why RMS voltage is used as opposed to the average voltage (and by average I mean over half a period, roughly 0.64V_peak), and the explanation I found was that the RMS voltage would produce the same heat as equivalent DC through a resistor...

Hello. Please look at the attached image first. There are two circuits A and B which have individual electrical components a and b. Components a and b are electrically and directly connected by the red lines. Impedances of individual components a and b are not matched, however, equivalent...

Hey! :o Let $V$ be a finite dimensional vector space and $\Phi \in \text{End}(V)$. I want to show that the following statements are equivalent: $V=\ker (\Phi)\oplus \text{im} (\Phi )$ $\ker (\Phi )=\ker (\Phi^2)$ $\text{im} (\Phi )=\text{im} (\Phi^2)$ I have done the following...

Homework Statement Find the Thevenin's equivalent with respect to points A and B Homework Equations 3. The Attempt at a Solution [/B] The resistance i found to be ##R_t=(R_2+R_1)||R_3+R_4## and that is the correct expression but for the voltage source the book gives...

Homework Statement Hello gentlemen! I came across a real challeging problem about static, which states the following: assume a force system is equivalent to a force \vec{F}_{1} and a couple M_{1}\vec{k} acting at a point \vec{r}_{1}. Find some point \vec{r}_{2} and a force \vec{F}_{2} so that...

Hello, According to the Wikipedia article on random variables: If the above statement is true, then, instead of defining a (real) random variable as a function from a sample space of some probability space to the reals, could we equivalently define it as a subset of ℝ associated with a CDF?

Homework Statement Homework Equations Thevenin Equivalents V = IR The Attempt at a Solution To try to find R_th, I replaced all the voltages with short circuits but I do not what to do next. Then I believe V_th would just be the same as the voltage of the rightmost resistor.

1.Prove f(A⋂B) ⊂ f(A) ⋂ f(B) 2.Prove f(A) ⋂ f(B) ⊂ f(A⋂B) ⟺ f is an injection I've solved the first question , as for the second I started with f(A) ⋂ f(B) ⊂ f(A⋂B) ⇒ f is an injection this way : Let's suppose f(a) = f(b) = p If we consider A = {a} and B = {b} then f(A) = f(B) = p then f(A) ⋂...

Hello! I am a university student working on a project regarding a piezoelectric patch transducer, and RLC modelling of said transducer. Edit: After reading the rule post i think i should clarify this is not coursework homework, this is a thesis project. The short version of my question is how...

Homework Statement I have a suspension mount (square tube with unknown thickness) with a bolt going through it that undergoes an 800 lb load laterally into the bracket in an on/off fashion (NOT fully reversed) at a rate of 50 Hz. Ultimately we are trying to calculate the dimensions of the bolt...

Homework Statement See attached image Homework Equations Thevenin EquivalentThe Attempt at a Solution a) Find the total resistance between A and B by short circuiting the voltage sources: Rt = 100Ω in parallel with the two 150Ω Two 150Ω in series: R = 300Ω 1/Rt = 1/100 + 1/300 Rt = 75Ω I...

Homework Statement Show that ##\forall x(P(x) \land Q(x)) \equiv \forall xP(x) \land \forall xQ(x)## Homework EquationsThe Attempt at a Solution Based on my work from propositional logic, to show that two expressions are logically equivalent, then we have to show that ##\forall x(P(x) \land...

I imagine there's no simple answer to this, but I'm wondering what tier graduate schools I would be applying to next year. I am in third year so I still have over a year before applications, but I'm curious. My overall grade is 90% at UBC. I'll have about a year and a half of research experience...

Homework Statement [/B] All voltages and impedances are in per unit values. After all the source transformations, why is the voltage source still 1 ? Homework EquationsThe Attempt at a Solution [/B]

Homework Statement Homework Equations See if you can show that L##_1## and L##_2## as in (a) can be replaced by the equivalent inductor L##_{eq}## as in (b): $$L_{eq} = \frac {L_1 L_2 - M^2 } {L_1 + L_2 - 2M } $$ The Attempt at a Solution Um, I don't really know where to start because I...

Homework Statement Hello everyone, I have a problem to solve, which I found hard and so looked for help on the web. Finally found this...

Homework Statement State an equivalent expression in terms of the related acute angle? (A) cot(-π/4) Homework EquationsThe Attempt at a Solution (A) I made the the unit circle and since its negative I went clockwise and made it into the fourth quadrant. I ended up getting -cotπ/4. However...

Homework Statement Calculate the equivalent capacity of the capacitor system between points ##x## and ##y## Homework Equations ##C=q/V## The Attempt at a Solution I'm asking about this problem because I know how to calculate ##V_x-V_y##, but I don't know how can I extract the equivalent...

I just heard something that made me realize I was taking the equivalence principle way too literally. If I were in a windowless room, and was standing on its floor, then there is, in principle, a performable experiment by which I could determine whether I was moving upward at 1 g of...