Point Definition and 1000 Threads

Today I read a book in mechanics and encountered a funny proposition about rigid body with fixed point. Perhaps somebody will be interested to propose it to students as a task. This proposition is almost correct:) Consider a rigid body with a fixed point ##O##. Let ##Oxyz## be a coordinate...

I want to find the email of the authors. The problem is I cannot find hers. How to find it? Any help? Thanks in advance!

For this question the ball is rolling without slipping so that means the velocity of the point of contact is zero. Does that also apply to the acceleration of the point of contact? Because that’s what I assumed and I applied the relative acceleration formula above and use the starting point to...

For this question, I don’t understand the steps for the relative motion part. When I try it I get angular acceleration to be zero which is obviously wrong. The solution doesn’t consider the Y distance between G and A but I don’t understand why. In the relative motion equation it’s suppose to be...

I know how to derive field using ##E = -\nabla V## in polar coordinates and doing so gave me $$E = (kP/r^3)(1 + 3cos^3\theta)^{1/2}$$ now I am trying to derive ##E## at point P using the fields produced by +ve and -ve charge respectively and taking components of each along the radial direction...

My two questions: The author claims that ##T_1=T_2## and ##\alpha = \beta##, and this is supposed to be clear the force triangle. Why is this so? Is it possible to use calculus of variation to find the lowest point C? That is, by maximizing the triangle ABC (Area of ABC = ##\frac{1}{2}(line...

So for this question I got the right angular velocity. But I don’t get the same velocity for point A. I don’t understand why it’s cos30, problem asked for V_a when theta = 45 so I used cos45. I have my work below.

The answer should be (2×sqrt3×k×q^2)/a^2. What did I do wrong?

Could you point me to interesting videos about plasma ball?

I want to use the point reactor kinetics equations to solve for the power as a function time when a reactivity of gamma*t is added to a reactor that is at equilibrium at time 0. I am also asked to consider the case where the transients are long-lived compared to the lifetime of prompt neutrons...

in Finite Difference Method (FDM), the boundary conditions can be implemented by applying the continuity of parallel component of magnetic field intensity. when it comes to the interface of two areas, it is done at ease, but consider this case at the red point: in FDM we exactly require on...

A rail gun exerts an electromagnetic force on a projectile. The only moving object is the projectile, so is the point of application of force moving? Update - For others reading this thread, after a re-think on this, for linear motion (as opposed to angular motion), the point of application of...

Edit: Below is my work but i believe i have chosen the wrong values of the separation vector in the s direction. Any ideas as to what it should be?

I get the first part of B, but why doesn't the transported direction not change as the electric field changes? Does it follow the right-hand rule?

Dear everybody, I am involved with a system of two spins and I ended up with the following Hamiltonian: $$H_c(t) = W\sin(2J_+ t) \big( \mathbb{1} \otimes \sigma_z - \sigma_z \otimes \mathbb{1}\big) + W \cos(2J_+ t) \big( \sigma_y \otimes \sigma_x - \sigma_x \otimes \sigma_y \big) \: ,$$ where...

Hi, starting from this thread I'm a bit confused about the content of the principle of relativity from a mathematical point of view. Basically the "Galilean principle of Relativity" puts requirements on the transformation laws between Inertial Frame of Reference (IFR); thus they have to...

Question: For the following functions, does the fixed point iteration for finding the fixed point in $\left [ 0,1 \right ]$ converge for all first points $ p_{0} \in \left [ 0,1 \right ]$? Justify your answer. a.$ g(x) = e^{\frac{-x}{2}}$ b.$ g(x) = 3x - 1$ Let me attempt for part a first...

So this is more of an intuitive question rather than a mathematical one. I present the problem. Assume I have 2 charges of charge +q at a distance r from each other on the z axis. Position of two charges is (0,0,r/2) and (0,0,-r/2). Assume now that I want to calculate the force these two...

I’m coming at this question with a physics application in mind so apologies if my language is a bit sloppy in places but I think the answer to my question is grounded in math so I’ll post it here. Say I have a function F(z) defined in the complex z plane which has branch points at z=0 and z =...

I traced a spherical X-ray Gaussian (green) where the negative charges were diametrically opposite. My question is this: I can transform the entire charge of the Gaussian sphere into a point charge placed in the center. So, can I analyze only the electrical forces of the two negative charges...

My first question, so be kind (!) Long time since I was at school, and can only remember the basics of beams and fulcrums. In essence, that a 1kg weight 5mtrs from a fulcrum / pivot needs 5kg at 1mtr to counterbalance. But what about the beam itself? Do the two sides cancel each other out? For...

Hey! :giggle: Question 1 : Let $g(x)-=x-x^3$. The point $x=0$ is a fixed point for $g$. Show that if $x^{\star}$ is a fixed point of $g$, $g(x^{\star})=x^{\star}$, then $x^{\star}=0$. If $(x_k)$ the sequence $x_{k+1}=g(x_k)$, $k=0,1,2,\ldots$ show that if $0>x_0>-1$ then $(x_k)$ is...

I can use integral as attached to obtain the answer. However, I wonder why I can not use " V = KQ / r " the get the correct answer. Thanks.

I am parsing data from an excel sheet using pandas ExcelFile class and read_excel function. I noticed that when reading the file, there are floating point errors in the results. For example, a cell that contains 25.15 will be 25.149999999999977 in the pandas data frame. The value 25.15 in Excel...

Can we prove that there is a corespondence 1-1 between a real number with a point of straight line?It seems to me that we can use Dedekin's cut to prove each point of line corresponds a real number. But how about the reverse?

Is there any software/simulator of point charges/conductors? Preferably with features enabling dynamics of charges.

What are the possible ways of solving the operating point of air gapped transformer with nonlinear B-H curve? For example let's consider 3C90 E34 sized core with 0.5 mm airgap. I know that the magnetomotive force over the ferrite part can be formulated as function of the reluctances...

Hi, I'm being asked to determine the tension of a rope only knowing that g = 9.8 m.s-2. I understand that in order to calculate tension, I would need to multiply mass with acceleration. But i don't understand how i would in this case. This is the question for reference. Thanks for your help...

The following proof (in the image below) is from the book Euclid's "Elements" Redux (by Daniel Callahan and John Casey). I did not understand why the point D or the ##\triangle \rm ABD## was necessary. (I mean, what was the "point" of D? :-p) Joking apart, wasn't this sufficient: suppose we have...

Here is my attempt at a solution I don’t know where to go from here, as the equation is a quadratic it will have two solutions which means there will be two stationary points, but I don’t know how to solve for z.

Hi. For some background, I am running molecular dynamics simulations of silica fracture in LAMMPS. Each point represents the location of a broken bond. I would like to find regions where many bonds are breaking, which I speculate would be locations of crack formation. These computations are...

For ##x=-1## to be an *horizontal* inflection point, the first derivative ##y'## in ##-1## must be zero; and this gives the first condition: ##a=\frac{2}{3}b##. Now, I believe I should "use" the second derivative to obtain the second condition to solve the two-variables-system, but how? Since...

Summary:: I'm stuck on a year 2 mechanics question. I have this simplified crankshaft with a load P at the end. The solutions to the exercise have said that point A is in compression due to a bending moment but I don't understand why that is. The solutions and my calculations have both come out...

the idea of time dilatation is that the light should cross 299 792 458 meters each second relative to all point of views , so when there is two observer that one of them is in rest and the other observer is moving , the clock ticking of the moving observer would be slower(by clock ticking i...

How do I distinguish between a point of local maxima or minima, when the second derivative in that point is equal to zero?

So 0=q1q3/r+q2q3/(13.6-r) 0=-8.5/r-3.63/13.6+3.63/r 0.2669=3.63/r-8.5/r r=-18.2465, but the answer is supposed to be 8.24

Moment about X2 to calculate force at X1: x1 * 9 = (250 * 2) Therefore, x1 = 500/9 = 55.5N The book however gives force at x1 as 110N. So I figured I have not understood a concept somewhere

https://www.physicsforums.com/attachments/273785 What are the possible materials (beams, H-profiles) etc that can be used to withstand the pressure of the whole system if there are 12 tonnes of wheat in the pipe at all times? How you would make this system work? There always has to be an angle...

The derivative of a point of maximum must be zero, and since $$y'=3ax^2+2bx+2 \rightarrow y'(-1)=3a-2b+2 \rightarrow 3a-2b+2=0$$ we get the first condition for ##a## and ##b##. Now, since we want ##x=-1## to be a local maximum, the derivative of the function must be positive when tending to...

Hi, I have this scheme, in which there are 3 segments: - I is coaxial to c axis and free to rotate in the origin. Length d1 - II is coaxial with a axis and free to rotate around c axis. There a fixed angle θ between a and c axis. Length d2 - III is welded to II, it's the PM segment. α is fixed...

From my understanding, quantum fluctuations create particle pairs that are usually annihilated. Is it possible to use some kind of force (eg: electromagnetism) to direct and separate antiparticles from normal particles? I believe experiments have proven that it is possible to store positrons...

Suppose there is a 3d plane z=a*x+b*y+c. Suppose there is a point in space near, but not on the plane. (xo, yo, zo). What is the coordinate (x1,y1,z1) on the plane that is nearest the original point? My attempt uses minimization but the result is blowing up into large answer. I wonder if...

I am following a lecture note on the QFT. But am a little confused about some parts related to the vacuum bubbles. We define the Feynman propagator, ##D_{F}(x-y)##, as giving the amplitude for a particle emitted at ##x## to propagate to ##y## (where it can be measured). After following the...

Is there a relationship between the Lagrangian ‘hill diagram’ and the spacetime curvature embedment graphs? The Lagrangian map shows effective potential, which deals with centrifugal force. As centrifugal force is a fictitious force (and gravity is as well), I would assume the underlying...

For this problem (see image), I get the correct answer for the normal force at point E if I: 1) divide the frame into members AB and CB, 2) solve for the x and y components of the reaction force at point B, 3) make a free body diagram with the cut at point E forming member EB and setting the sum...

Data ##E^{0}_{I_2/I-}= 536mV## ##E^{0}_{Cr_2O_7^{2-}/Cr^{3+}}= 1330mV## ##I_{2} + 2e- \Leftrightarrow 2I^{-}## ##Cr_2O_7^{2-} + 14H^+ + 6e^- \Leftrightarrow 2Cr^{3+} + 7H_2O## Total Reaction ##6I^{-} + Cr_2O_7^{2-} + 14H^+ \Leftrightarrow 3I_{2} + 2Cr^{3+} + 7H_2O##...

Could somebody check my solution? I want to know is it correct.

The Attempt at a Solution I know the answer is supposed to be ##(-1,0)##. However when I differentiate the above expression I get. $$ 2x+{\frac 5 2} $$ Then the shortest distance would be when the expression equates to 0. $$ 2x+{\frac 5 2}=0 $$ I should be getting ##x=-1## but solving for ##x##...

Is it the lower the boiling point the better? As room pressure and temperature already can change the phase without working at vacuum? And the higher critical point means it is hard to reach super critical phase? But there is transcritical CO2 cycle, which the critical point is so low, and...