Arc Definition and 478 Threads

Homework Statement So, the question gives a particle traveling over a path \gamma, and I need the arc length. Homework Equations The path is \gamma(t) : [1,4] \to ℝ^3, t \mapsto (t^2/2, t, ln(2t)). We want the arc length over 1 \le t \le 4. The Attempt at a Solution First, the...

Homework Statement I was wondering if I did this problem correctly as I don't have the solution, also wanted to make sure that my limits of integration were correct as they tend to be tricky in finding arc length in polar coordinates. x(t)=arcsint y(t)=ln(sqrt(1-t^2)) Homework...

Homework Statement Find arc length of the graph of r(t) = ti + ( (t6/6) - (6/t4) )j + t√3 k 1≤t≤2 Homework Equations Arc length = ∫ ||dr/dt|| dt (Integral from t0 to t1 of norm of derivative of r) The Attempt at a Solution dr/dt = i + (t5 + 24/(t3) )j + √3 k 12 = 1 (√3)2 = 3 (t5 + 24/(t3)...

I am reading Thurston's book on the Geometry and Topology of 3-manifolds, and he describes the metric in the Poincare disk model of hyperbolic space as follows: ... the following formula for the hyperbolic metric ds^2 as a function of the Euclidean metric x^2: ds^2 = \frac{4}{(1-r^2)^2} dx^2...

Dear colleagues, If an arc or a spark traveling in vacuum is actually the electrons jumping across vacuum, do they travel at near light speed? From another point of view, devices like thyratrons use ionized gas molecules to conduct electricity, at what speed are those ionized molecules...

Hi everyone! I have two questions, one about area of surface of revolution and another is about arc length... I really fail to do this two question despite many times of trying so I hope someone can help me 1. Find the area of the surface of revolution generated by revolving the arc of the...

So, i have a point in the coordinate system, and an arc defined by two vectors of equal length starting in the same point. The arc is always smaller than 180. How would i check if the point is on the arc? (the point is always on the circle, just need to check if it is in between these two...

Alright, so I'm building the singing arc that's in this schematic. http://www.volny.cz/jmartis/flyback_singingarc.png Now my first problem is obtaining a 60 volt input. Will I get a usable 60 volts (consider current spikes) if I bridge rectify a 120 volt wall current, obtaining a -60 and...

If the circumference of the region bounded by the curve y=cosh(x) and the lines y=0 x=a and x=-a is 2a+4, where a>0 find the area of the surface obtained by rotating the part of the curve y=cosh(x) between x=a x=-a and around the x axis. This is my homework question.I tried to solve it.I...

Hi everyone ... I am a first time poster from South Africa. I have been visiting the forum for some time. I am busy teaching myself calculus and physics. I have hiccup with the concept of definite integral and arc length of a function. In my understanding these should be the same thing...

Could one burn aluminium wires by striking up an electric arc between them and then feeding them towards each other as they are consumed (like an arc light)? I assume the aluminium oxide would be burnt off as a vapour by the high temperature of the electric arc and thus would not inhibit the...

Homework Statement Find the arc length of the ellipse or deformed circle. r^2=x^2+(y/β)^2 r=radius β=dilation constant k="random" constant Homework Equations The Attempt at a Solution I suspect it's impossible but I can't prove that. After working it out I got stuck with these...

The Marvel Avenger's Movie is coming out in a month's time. While many superheroes like the Hulk and Spiderman require much more biological research to come true, superheroes like Iron Man, Batman, Black Widow rely on engineering technology. Which of our current-day technology has the...

∫Homework Statement Use the integration tables to find the exact arc length of the curve f(x)=ln x 1≤x≤e Reference the table number formula used Then approx. your answer and compare that to the approx. "straight line distance" between 2 points coordinates of two points...

Homework Statement Let c(t) be a path and T the unit tangent vector. What is \int_c \mathbf{T} \cdot d\mathbf{s} Homework Equations The unit tangent vector of c(t) is c'(t) over the magnitude of c'(t) : \mathbf{T} = \frac{c'(t)}{||c'(t)||} The length of c(t) can be represented by ...

Homework Statement Give an expression to find V of Arc of uniform charge (at the center, or origin) Homework Equations V=kQ/R The Attempt at a Solution the solution is kQ/R. I'm wondering why an arc can be treated like a point charge... Is this reason partly connected to a...

Homework Statement Find the length of the polar curve. Complete the cardioid r=1+cosθHomework Equations L=∫αβ√[f(θ)2+f'(θ)2] dθ The Attempt at a Solution Given f(θ)2 is equal to cos2θ+2cosθ+1 and f'(θ)2=sin2θ I arrive at the integral ∫αβ√[2cosθ+2] dθ which I cannot for the life of me...

Reparametrize the curve R(t) in terms of arc length measured from the point where t = 0 R(t) is defined by x = et, y = \sqrt{2}t, z = -e-t Arc length S = ∫ ||R'(t)||dt ||R'(t)||= sqrt{\dot{x}2 + \dot{y}2 + \dot{z}2}The attempt at a solution Getting R'(t) ==> x = et, y = \sqrt{2}, z = e-t...

->ds/dt where s is the arc length in cartesian coordinates is ((dx/dt)^2+(dy/dt)^2)^(1/2). -> Therefore by the chain rule ds/dt = ds/dp * dp/dt, but if I substitute dx/dt=dx/dp* dp/dt and dy/dt= dy/dp* dp/dt in the formula above, I get ds/dt=ds/dp * |dp/dt|?? What is happening? ->Even by...

Hi all, Does anyone know the specific names of the high-curvature arc and the low-curvature arc on an ellipse? Or, do they have special names after all? Anyone help me figure this out, thank you very much! Regards.

How can I find the radius of a circle by knowing two points and its arc length? Do I have to use a numerical method to solve for a trigonometric equation or is there any algebraic or geometric method?

Homework Statement Hey all, I'm trying to calculate the length of the cardioid r(θ)=1+cosθ (polar coordinates) and I figured I'd try to do it in one integral from 0 to 2Pi. Homework Equations So the integral is \int_{0}^{2\pi} \sqrt{r^2 + (\frac{dr}{d\theta})^2}d\theta The Attempt at a...

According to my newspaper, today is the traditional date of the birthday of Joan of Arc in 1412. It's generally accepted she was born in that year but the birthdate may have been chosen because today is a feast day in both the Roman and Orthodox Catholic Churches (The Epiphany). Many of the...

Determine the length of arc and the area of the sector subtended by an angle of 60° in circle of radius 3 m Ok First change 60to radian measure. 60 x pi / 180° = 2pi / 6 Then.. I used the formula s = rθ 3(2pi/6) = 6pi/6 = pi <--- Is this right?? And how can I find the area which...

Homework Statement This is probably very simple, but I'm teaching myself arc length via Paul's Online Calculus Notes and there's a simplification on the page: I was wondering why the first Δx^2 was simplified to 1? I understand the other Δx^2 came out of the square root.

Hello everyone. My first post so bear with me. I'm planning on buliding an arcgenerator (and possibly an arc speaker later on if this works) with my arduino and a coil. I'm relatively to electrical engineering, so there are a few things I need some help with. If I've understood things...

What can I do with a "CENCO High Pressure Mercury Arc Lamp"? I'm a high school physics teacher. I inherited a "CENCO High Pressure Mercury Arc Lamp." Are there any useful demos and/or labs I can use this for?

When we see an arc between a Jacobs ladder is this because a charge density builds up between the rods and then the E field between the rods is strong enough to rip electrons off the molecules in the air and the start to conduct.

http://www.up98.org/upload/server1/01/z/cllb59cvnwaigmmar6b5.jpeg What is the method of calculating arc length in In the image above . x & y is known Thanks .

Homework Statement Find the arc length of y=x*e^(x^6) where 0 ≤ x ≤ 3 Homework Equations The Attempt at a Solution I took the derivative of the equation and squared it to get (e^2(x^6))(1+12(x^6)+36(x^12)) then plugged it into the proper formula to get: 3...

Can you create an arc in a vaccum?

Homework Statement In the 1968 Olympic Games, University of Oregon jumper Dick Fosbury introduced a new technique of high jumping called the "Fosbury flop." It contributed to raising the world record by about 30 cm and is presently used by nearly every world-class jumper. In this technique...

Homework Statement A car is tested along specifically designed track. First, the car is driven along a straight section of track of length (r). If the car starts from rest under a maximum (constant) acceleration, it takes an amount of time (t) to cover the distance (r). The car is then brought...

Homework Statement A car is driven along straight section of track length (r). The car started from rest and the time it took to cover r distance is (t). If the same car is then tested on a circular arc of radius r, starting from rest and continues to speed up at the maximum possible rate that...

Homework Statement A charge Q is distributed evenly on a wire bent into an arc of radius R, as shown in the figure below.What is the mathematical expression that describes the electric field at the center of the arc (point P indicated) as a function of the angle θ? Sketch a graph of the...

Homework Statement Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve. Homework Equations r(t) = (-3tcost)i + (3tsint)j + (2\sqrt{2})t(3/2)k 0 ≤ t ≤ ∏ The Attempt at a Solution So I found dr/dt (I think), which is v(t) =...

I'm trying to find the equation for a circle given two points in x, y and the starting angle, arc length, and two points along the circle. I need to find the equation because I need to translate a sprite along the curved path from one point to another. The situation ends up looking like this:A...

in physics we were doing a problem that essentially involved vectors and in the end we were left with 2 displacements. how would i find the angle between them if it was not a right triangle? i asked someone and they said that i could find it using artan(Ry/Rx) ...R being one of the displacements

Homework Statement Reparametrize the curve with respect to arc length measured from the point where t=0 in the direction of increasing t. r(t) = [e^(2t)cos(2t)]i+2j+[e^(2t)sin(2t)]k Homework Equations i know that the derivative of the arc length with respect to t = magnitude of...

I have an arc welding plant and I realized that I am wasting energy when it is not used but powered on. Can anyone please suggest a way to get rid of this problem? That is, plant gets "active" when it is welding and is "idling" when it is not welding.

Homework Statement y=\frac{1}{3}\left(x^2+2\right)^{3/2} Homework Equations \int_{a}^{b}\sqrt{1+\left(\frac{dy}{dx}\right)^{2}}dx The Attempt at a Solution \frac{dy}{dx}=x\sqrt{x^2+2} \int_{0}^{3}\sqrt{1+\left(x\sqrt{x^2+2}\right)^{2}}dx=\int_{0}^{3}\sqrt{1+x^4+2x^2}dx I'm stuck...

I know the sin(arccos(x)) = (1-x^2)^0.5 I was wondering what some of the others are: cos(arcsin(X)) tan(arcsin(X)) tan(arccos(x)) sin(arctan(x)) cos(arctan(x)) also the reverse: arcsin(cos(x)) arcsin(tan(X)) arccos(Sin(X)) arccos(tan(X)) arctan(sin(X)) arctan(cos(X))

I'm interested in understanding why high energy discharges arc rather than just travel in a more direct straight path. Thanks for the enlightenment.

Hi, I am trying to collimate light from a mercury arc lamp. I know this question has been asked before here https://www.physicsforums.com/showthread.php?t=413437&highlight=collimation but it was first posted last year and since my situation is a bit different it didn't quite answer all of my...

Homework Statement My textbook [Engineering Mathematics, Stroud, 6th Edition, page932] runs through the derivation of the integral formula for arc length. I got confused at one of the steps: [partial](ds/dx)=sqrt(1+([partial](dy/dx))^2) if [partial]dx tends to 0...

I'm just wondering because I'm really confused right now. My teacher gave us the formula: K= \frac{1}{2}sr for area of a given sector where "s" is the arc length and "r" is the given radius. the formula for the arc length is: s=\Theta r Though, I can't seem to understand how he came up...

So sorry if this has been discussed elsewhere before. I know it may be trivial but for some reason I just can't get it. I simply can't seem to integrate the square root of (1 + 1/4x). This problem has been highlighted for a reason, but I'm missing the point. Any input is much appreciated.

There are line integral with respect to arc length and line integral with respect x/y. I know \int_C Pdx+Qdy is useful to calculate the work. When do we need the line integral with respect to arc length?

Homework Statement Determine the arc length of the function on the given interval x = (y^4)/8 + 1/(4y^2) from 1 to 2 The arc length formula \int (f'(x)2 + 1).5 dx The Attempt at a Solution I used the arc length formula but don't know where to go from here. Usually these...

Dear all, I feel this should be a simple problem but I can't solve it. Could you give me a hand? Imagine if an arc is bounded by a rectangle of dimensions width and height. The arc starts in the bottom left corner of the rectangle, and ends in the bottom right corner. The apex of the...