Curve Definition and 1000 Threads

This is the explanation in the section of DC motor Based on the above explanation i have drawn the torque curve. Can you please confirm if it is correct? In the initial position the torque is maximum and when it reaches the diagram 2 the torque is 0 and then it is maximum.

The motional EMF is$$\mathcal{E}_{\text{motional}} = \oint_{\partial \Sigma} (\vec{v} \times \vec{B}) \cdot d\vec{x} = \int_{\Sigma} \frac{\partial \vec{B}}{\partial t} \cdot d\vec{S} - \frac{d}{dt} \int_{\Sigma} \vec{B} \cdot d\vec{S}$$(that's because Maxwell III integrates to...

I have attached a photograph of my workings. I do not know if I have arrived at the right solution, nor whether this is the gradient of f(x) at point P. I think I seem to overcomplicate these problems when thinking about them which makes me lose confidence in my answers. Thank you to anyone who...

My attempt is below. Could somebody please check if everything is correct? Thanks in advance!

I was watching a lecture that made the conclusion about the torsion being equal to zero necessitated that the path was planar. The argument went as follows: -Torsion = 0 => B=v, which is a constant -(α⋅v)'=(T⋅v)'= 0 => α⋅v= a, which is a constant (where α is a function describing the path and...

Ok Hi everyone! I was working on what would happen if you apply a linear increasing voltage to a series capacitor resistor. The question is : If the capacitor voltage is plotted, is the cap voltage curve hyperbolic? I've done some plots on the cap voltage and it sure looks hyperbolic but I...

On a plane with a selected origin point and a selected zero rotation direction, identify each point p with (rp,θp), where rp is the distance to the origin and θp is the angle in [0, 2π). Define an order ≤* between points p and q as b p=*q if they are identical, p <* q if [1] rp < rq, or [2]...

Prove that for every $x\in (0,\,1)$ the following inequality holds: $\displaystyle \int_0^1 \sqrt{1+(\cos y)^2} dy>\sqrt{x^2+(\sin x)^2}$

Who can share the primary sources where material models are formulated: Ludwik, Holomon, Swift, Wok, Ludwikson, Hill and others?

Use the equivalence volume from the pH curve to calculate the concentration of the acid, HA. I'm not sure which equation to use or how to approach this question (Attached). Please elaborate on the steps on how to answer the question. Thank you!

This is 'Boas mathematical Methods in the Physical Sciences' homework p484.(Calculus of Variations) problem2 section4 number 2 The bead is rolling on the cycloid curve.(Figure 4.4) And the book explain that 'Then if the right-hand endpoint is (x, y) and the origin is the left-hand endpoint...

Here is my attempt at a solution: y = f(x) yp - ym = dy/dx(xp-xm) ym = 0 yp = dy/dx(xp-xm) xm=ypdy/dx + xm xm is midpoint of OT xm = (ypdy/dx + xm) /2 Not sure where to go from there because the solution from the link uses with the midpoint of the points A and B intersecting the x-axis...

Suppose you are analyzing this image. The question to answer is: Explain why the alpha particle's path has a larger radius than either of the beta particle paths. Justify your answer using either momentum or charge-to-mass ratio. When you are answering this, suppose you know that , in...

I'm studying 'A Most Incomprehensible Thing - Notes towards a very gentle introduction to the mathematics of relativity' by Collier, specifically the section 'More detail - contravariant vectors'. To give some background, I'm aware that basis vectors in tangent space are given by...

Find the x-coordinate of the point on $f(x)=\dfrac{4}{\sqrt{x}}$ that is closest to the origin. a. $1$ b. $2$ c $\sqrt{2}$ d $2\sqrt{2}$ e $\sqrt[3]{2}$ not real sure but, this appears to be dx and slope problem I thot there was an equation for shortest distance between a point...

What forces act at air particle at curved streamline, looking from inertial and non-inertial frame of reference? (show free body diagram)

Find the equation of the curve that passes through the point $(1,2)$ and has a slope of $(3+\dfrac{1}{x})y$ at any point $(x,y)$ on the curve. ok this is weird I woild assume the curve would be an parabola and an IVP soluiton...

In Stokes' theorem, the closed line integral of f=the surface integral of curl f on ANY surface bounded by the same curve. But in Gauss' theorem, the surface integral of f on a surface=the volume integral of div f on a unique volume bounded by the surface. A surface can only enclose 1 volume...

a.) 4 critical values b.) there are no points of inflection c.) 2 local maxes and mins d.)

a) I found this part to be quite straight forward. From the Parallel transport equation we obtain the differential equations for the different components of ##X^\mu##: $$ \begin{align*} \frac{\partial X^{\theta}}{\partial \varphi} &=X^{\varphi} \sin \theta_{0} \cos \theta_{0}, \\ \frac{\partial...

θ=90°= π /2 so the instantaneous angular velocity dθ/dt= lim∆ t -> 0 (θ(t + ∆ t)-θ(t))/(∆ t) When I calculate it out it is π /2 radians per second. Is this correct?

Let's say we have a curve in 2D space that we can represent in both cartesian and polar coordinates, i.e. ##y = y(x)## and ##r = r(\theta)##. If you want the tangent at any point ##(x,y) = (a,b)## on the curve you can just do the first order Taylor expansion at that point $$y(x) = y'(a)x +...

The title and summary pretty much say it all. I was wondering if it's possible to accurately determine the area enclosed by the curve ## y=x \text{ csch}(x+y)## and the ##x##-axis? I first tried solving for ##y## and then ##x##, however it doesn't appear possible to solve for either variable. I...

I am following the proof to show that the complex torus is the same as the projective algebraic curve. First we consider the complex torus minus a point, punctured torus, and show there is a biholomorphic map or holomorphic isomorphism with the affine algebraic curve in ##\mathbb{C}^2##...

##x(3)=9-6=3##, ##y(3)=27+9=36##. ##\frac{y'(3)}{x'(3)}=\frac{3\times9+3}{2\times3}=\frac{30}{6}=5##. ##y=5(x-3)+36=5x+21##.

"A man of mass M stands on a railroad car which is rounding an unbanked turn of radius R at speed v. His center of mass is height L above the car, and his feet are distance d apart. The man is facing the direction of motion. How much weight is on each of his feet?" I came five equations, and...

$\textsf{What is the area of the region in the first quadrant bounded by the graph of}$ $$y=e^{x/2} \textit{ and the line } x=2$$ a. 2e-2 b. 2e c. $\dfrac{e}{2}-1$ d. $\dfrac{e-1}{2}$ e. e-1Integrate $\displaystyle \int e^{x/2}=2e^{x/2}$ take the limits...

Do all stars in their life cycle (t) emit energy (E) that follow a bell shape curve? If yes, is the curve symmetrical always? How is this related to nuclear and thermal time scale?

What does "F(r,θ) = 0" mean here?

My initial attempt: Total Centripetal force on the cylinder would be given by $$\textbf{F}_{net} = mR\omega^2 \textbf{e}_1+mr_{cm}\omega^2 \textbf{e}_2$$ where the vectors e_1 and e_2 have magnitude 1 and point radially outwards (and continuously changing as the cylinder rolls down) as marked in...

let ##f : R^3 → R## the function ##f(x,y,z)=(\frac {x^3} {3} +y^2 z)## let ##\gamma## :[0,## \pi ##] ##\rightarrow## ##R^3## the curve ##\gamma (t)##(cos t, t cos t, t + sin t) oriented in the direction of increasing t. The work along ##\gamma## of the vector field F=##\nabla f## is: what i...

Hello! I want to fit a function to the curve I attached (the first image shows the full curve, while the second one is a zoom-in in the final region). Please ignore the vertical lines, what I care about is the main, central curve. It basically goes down slowly and then it has a fast rise. What...

Hello, I'm currently working on an assignment which requires me to choose an optimal curve of power generation based on data points generated by a script I wrote (attached for reference, TideHeight1s is the source data for the script, the txt file contains the code for the .m script). The...

Hello all I am trying to work out the forces involved of a moving train around a curve traveling at a constant speed. I have the following:- The image on the left is a cross section of a train traveling around a curve, you can think of the train moving away from you. The image on the right...

Hello, I'm trying to obtain a polarization curve for a fuel cell (two electrodes in HCl). From what I've seen in literatures, current is applied and the voltage is measured. Is it still the same to change the voltage and measure the current instead? For some reason our equipment only have the...

I was solving problems about the period of a pendulum inside an elevator. They're all the same. If the elevator accelerates upwards you have that the period is shorter and it's longer if the direction is downwards. But I tried to solve something more difficult and I thought about a pendulum...

Summary: Consider a train carriage rolling along a curve that forms a left turn on the track. The carriage speed is directed along the y-axis (into the plane of the paper) in the figure. The trolley will have a tendency to curl in the curve in the specified direction. A flywheel is inserted...

Ok so I think that the equation for centripetal force is the mv^2/r and this SHOULD equal the horizontal component of the normal force on the car. Vertical component of normal force and gravity would cancel out. However, when I input the numbers into the equations I don't get equivalent values...

Honestly I don't know where to begin. I started differentiating alpha trying to show that its absolute value is constant, but the equation got complicated and didn't seem right.

This question has been bothering me for a long time. It is simple enough to determine whether or not a curve is timelike. You simply use this formula: gab(dxa/ds)(dxb/ds) (where x(s) is our parameterized curve). Assuming a (- + + +) signature, if the answer to the above summation is negative...

Continuing on from the summary, the chapter has given a graphed example. We are shown a regular cosine wave with phase angle 0 and another with phase angle (-Pi/4) in order to illustrate that the second curve is shifted rightward to the regular cosine curve because of the negative value. Now, my...

Homework Statement: Below graph shows the I - Vg curve for different MOSFET, which curve is impossible for MOSFET? Homework Equations: I - Vg I am inclined to select 1), as it is not likely to have a sharp transition from subthreshold to Quadritica region. However, graph 5 also looks strange...

Find the slope of the tangent line to the graph of $$f(x)=-x^2+4\sqrt{x}$$ at $x=4$ (A) $8-$ (B) $-10$ (C) $-9$ (D) $-5$ (E) $-7$

I've been refurbishing my understanding of some relativistic concepts and I've been specifically studying the concepts of spacelike, timelike and lightlike curves. According to the notes that I have been reading, curves on a Lorentzian manifold can be classified as follows: If you have a...

So ##T+U=\frac{1}{2}m(\dot{x}^{2}+\dot{y}^{2})-mgy=constant##. If I derive this with respect to ##t## $$\dot{x}\ddot{x}+\dot{y}\ddot{y}-g\dot{y}=0$$ Then I use ##\dot{y}=\dot{x}\frac{dy}{dx},\ddot{y}=\ddot{x}\frac{dy}{dx}+\dot{x}^{2}\frac{d^{2}y}{dx^{2}}## to get...

This is just a conceptual question. I get that when a car is turning on an unbanked curve, the friction provides the centripetal force. I don't understand why this is though. I thought friction is supposed to oppose the direction of motion. But that would imply that the direction...

The question says that the process is melting, so temperature must increase. Hence, Delta T > 0. Also, it is given that the slope for its fusion curve is -ve, which means that as we increase temperature, the pressure will decrease. So, Delta P < 0. The question asks to prove that the substance...