Arc Definition and 478 Threads

Hi all, I was thinking about measuring the temperature of an arc discharge. The size of the discharge is very small, in the order of micrometer. So it is not possible to put a thermocouple near the it. Thank you very much.

Homework Statement Find an arc length parametrization of the curve r(t) = <e^t(cos t), -e^t(sin t)>, 0 =< t =< pi/2, which has the same orientation and has r(0) as a reference point. Homework Equations s = int[0,t] (||r'(t)||) The Attempt at a Solution So I found the derivative of r(t), and...

Hi everyone, I started what I thought would be a simple algebra/trig problem and quickly learned that I was dead wrong. At least I think I am wrong. I need to determine how much the speed of a particle moving along an arc segment changes as the length of the distance to the center point...

Homework Statement Say there are two arcs which are part of the circumference of a circle within a circle with the same angles, but since one arc belongs to the circle outside, that arc is longer than the arc inside it. If the first arc has length s, then the second arc has length s + \Delta s...

Hey all, When it comes to arc lamps, it looks like the safety concern everybody talks about is in regards to UV exposure. This, however, seems to be more suited for Hg sources instead for Xe sources. My question is in regards to whether there should be any concerns with the IR portion of the...

Homework Statement Find the length of the cardioid with equation r = 1 + cos (theta) located in the first quadrant Homework Equations f (theta) = 1 + cos (theta) f'(theta) = -sin (theta) s = antiderivative (0 to (pi/2)) sq rt (f(theta)^(2) + f'(theta)^(2)) d(theta) The Attempt at...

Homework Statement Find the length of r = theta^(2) for 0<=theta<=pi Homework Equations Arc length s = antiderivative of sq rt (f (theta)^(2) + f (derivative theta)^(2)) The Attempt at a Solution I have worked my way to the antiderivative of sq rt (theta^(4) + 4(theta)^(2)) but I'm...

In the polar formula for arc length, ds^{2}=dr^{2}+r^{2}d{\theta}^{2}, what is the exact meaning of the r^2 term multiplying d{\theta}^2? Is it an initial distance from the origin? A final distance from the origin? The change in r from point a to point b? This baffles me to no end and nothing...

Homework Statement 1. Find the length of the curve from t=0 to t=1. r(t) = <2t, t^2, (1/3)t^3> 2. 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)cos2t, 2, e^(2t)sin2t>Homework Equations S = \int{r'(t)} dt...

What does the arc length parametrization mean?

Homework Statement find the arc length of f(x) (x^(5/4))/5. The integration limits are from 0 to 4. Homework Equations The arc length formula is integrate sqrt(1 + (f'(x))^2) The Attempt at a Solution f'(x) = (5/4)*(1/5)*x^(1/4) = x^(1/4)/4 integral of sqrt(1 +...

A current I = 3 A flows through a wire perpendicular to the paper and towards the reader at A and back in the opposite direction at C. Consider the wires below the plane at A and C to be semi-infinite. In the figure, L1 = 3 m, R = 6 m, and L2 = 6 m and there is a B = 2.37 T magnetic field into...

Hello, If we consider a Euclidean plane \mathbb{R}^2 with the ordinary inner product, and we "distort" it through a cartesian->polar transformation, how should I compute the shortest arc between two points (r,\theta) and (r',\theta') ?

Homework Statement Sketch y = cos-1(2x) and y = sin-1(3x) Homework Equations The Attempt at a Solution This is my attempt cos-1(2x) = y, which means cos y = 2x produce a table with y from (-pi/2 to pi/2) What I want to confirm is the 2x. I need do 1/2 x instead of 2x when...

Homework Statement Find the total length of the cardioid r=a(1-cos theta) Homework Equations ds2=r2dtheta2+dr2 ds= integral from beta to alpha sqrt[r2 + (dr/d theta)2]dtheta The Attempt at a Solution dr=a(sin theta)d theta ds2=a2(1-cos theta)2d theta2 + a2sin2theta (d...

Homework Statement Consider the graph (see attachment) of r = 1 +2cos\Theta in polar coordinates. SET UP integrals to find 1. the area inside the large loop minus the area of the small loop. 2. the arc length of the small loop 3. the surface area of the surface formed by...

I was watching the visualizer while listening to a song in winamp, and this particular one has two speakers that shoot sine waves. I was watching it and I thought to my self: "it would be great if I reproduce that in real life". After thinking about it my thoughts went to back to that arc...

I saw THIS video and THIS OTHER ONE I was really quite surprised that such a thing was actually made to work. I'm curious how one could create an arc such as that, and then modulate it to match an audio signal. From my interpretation the extreme voltage causes an arc between the contacts...

Homework Statement tan(2x) - 3 cot (2x) = 0 Homework Equations Trigonometry Knowledge. The Attempt at a Solution tan(2x) - 3cot(2x) = 0 tan(2x) - 3/tan(2x) = 0 [tan(2x)]^2 - 3 = 0 [tan(2x)]^2 = 3 Is there such thing as Arc Tangent that's squared??

Homework Statement For the curve y=\sqrt{x} , between x = 0and x = 2, find (a) the area under the curve, (b) the arc length, (c) the volume of the solid generated when the area is revolved about the x axis, (d) the curved area of this solid. Homework Equations ds = \sqrt {1+(y')^{2}}dx...

Hi, I've been having some issues in solving this problem. Homework Statement Find the arc length of r=2/(1-cosθ) from π/2 to πHomework Equations L =(integrate) sqrt(r2+(dr/dθ)2)dθ The Attempt at a Solution I found (dr/dθ) = (-2sinθ)/(1-cosθ)2 so (dr/dθ)2 = (4sin2θ)/(1-cosθ)4 Then r2 =...

Homework Statement As test of strength, a diabolical trainer sets up the following apparatus. The trainee must maintain a variable pulling force which is always tangent to a nearly frictionless, semicircular surface . By slowly varying the force, a block with mass 23.0 kg is moved (at a very...

I am having trouble doing exactly what the title says. I have two points and the arc length between them (this is a bending beam type of a situation). Essentially I know where the ends of the beam are and how long the bent beam is and I need to get the equation of the circle. And yes I...

Homework Statement Find the arc length of the projectile from launch until the time it hits the ground, given that 0 V is 100 feet/sec and is 45 degrees. Homework Equations Arc Length= ∫_a^b▒√(█(1+(f^' (x) )^2@)) dx Arc Length of Curve= ∫_a^b▒〖v(t)dt=∫_a^b▒√((dx/dt)^2+(dy/dt) )〗^2...

Homework Statement http://i47.tinypic.com/1z6naa.jpg Note... I used wolfram alpha to get the answer, I did not get it myself... So I still need help. The answer shown is correct, so you'll know if you got it. Homework Equations Integral [0, ln(4)] sqrt(1+(dy/dx)^2) The Attempt at a...

Homework Statement Find the arc length of the curve: y=\frac{x^5}{6}+\frac{1}{10x^3} 1\leqx\leq2 Homework Equations ds=\sqrt{dx^2+dy^2} ds=\sqrt{1+\frac{dy}{dx}^2}dx The Attempt at a Solution \frac{dy}{dx}=\frac{5}{6}x^4-\frac{3}{10x^4}...

Find the exact length of the curve analytically by antidifferentiation: y = (x3/3) + x2 + x + (1/(4x +4)) on the interval 0 < x < 2So I set it up using the length of a curve formula: L = \int\sqrt{1+(x^2+2x+1+(\frac{-1}{4(x+1)^2}} And simplified it to L =...

Arc length of y=ln((e^(x)+1)/(e^(x)-1)) on [a,b] Using L=\int\sqrt{1+(y')^2}dx on [a,b] I am having difficulties differentiating y and plugging the results back into get a useful integral. So far I have y'=2e^(x)/(e^(2x)-1)

Hey guys, I'm studying for a test in calc 3 tomorrow and have run into a problem. On the practice test we have a problem "Find the length of the curve: r=theta^2, 0≤theta≤pi/2" I know the length of a curve in polar coordinates is int(sqrt(r^2 + (dr/dtheta)^2))dtheta...but when I get to where...

Homework Statement Trying to either derive or find a formula for the volume given by the space carved out from the area between an arc and the center of a circle. Essentially, the area between an arc and the center of a circle rotated 360 degrees, almost a cone shape with the upper boundary...

In a line integral with respect to arc length, we have something like f(x, y)ds "inside" the integral sign. The ds tells us that we are working with the arc length function s, taking diferences (s_K+1 - s_k) in the sums that tend to the line integral. Question: do we shall understand that...

If we have a fly in a room, its position respect to some frame of reference will change with time, so if we want to describe the fly's movement with a parametrized curve, it is easy to see the convenience of taking time as the parameter. I read that we can also take the length of the curve as...

Why is arc length of a function f(x) from a to b defined as \int_a^b \sqrt{1+(f'(x))^2} dx? Where they get the idea of squaring the derivative, adding 1, taking the square root, and then integrating it is beyond me.

In calculus, the definition of the arc length of some curve C is the limit of the sum of the lengths of finitely many line segments which approximate C. This is a perfectly valid approach to calculating arc length and obviously it will allow you calculate correctly the length of any...

OK all since I do not have a physics background I figured I would come to the WWW and search those who did. I am needing some questions answered... here is the badckground info...I work and a Cryogenic plant that has a max of 17000 gallons of Liquid Oxygen and 12000 of liquid nitriogen on hand...

? i used the implicit function theorem to find dy/dx, then applied that to the arc length formula, but i have to integrate with respect to x and there is the implicit function y[x] inside the radical. also, if it matters, the curve is assumed to be closed.

please help urgent! in the following question, E=65 GPa V=0.3 find the new length of the arc BD?? i have found the stresses xx=-56Mpa yy=0 xy=-28Mpa using hookes law i can find the strains xx=-8.615e-5 yy=2.58e-4 0.5*xy==-1.12e-3 but how do i calculate the...

Homework Statement A charge Q is arranged evenly on a wire bent into an arc or radius R as shown in the Figure. What is the electric field at the center of the arc as a function of the opening angle theta? Sketch a graph of the electric field as a function of theta for 0<theta<180 degrees...

in the following question, E=65 GPa V=0.3 find the new length of the arc BD?? i have found the stresses \sigmaxx=-56Mpa \sigmayy=0 \sigmaxy=-28Mpa using hookes law i can find the strains \epsilonxx=-8.615e-5 \epsilonyy=2.58e-4 0.5*\epsilonxy=\gamma=-1.12e-3 but how do i calculate the...

Homework Statement Find the length of the path traced out by a particle moving on a curve according to the given equation during the time interval specified in each case. r(t) = (c2/a)cos3t i + (c2/b)sin3t j where i and j are the usual unit vectors, 0 \leq t \leq 2\pi, c2 = a2 - b2, and 0...

I was about to go out to the car to check how many amps were being drawn from a parasitic component in the circuit. Battery has been dieing if I leave it connected for a few days. The 12VDC test light connected from the positive battery post to the positive cable(after pulling cable off) shows...

I have a brass rod with a 90 degree bend. I want to measure the outer and inner radii by placing a piece of string along both of them, and then straightening the string out to determine the linear measurement. Is this an accurate method?

why rainbow has a shape of arc and why its "ends" are bent down. Can anyone explain why rainbow has a shape of arc and why its "ends" are bent down.

Hey guys, Got a bit of a problem with a question I found in a textbook. I can do most of it but there's one little part I'm really struggling with: A curve C is given parametrically by: x=t-tanht, y=secht, t\geq0 The length of arc C measured from the point (0,1) to a general point...

Homework Statement Find the arc length of r(t)= <10sqrt(2), e^10t, e^-10t>, 0 <_ t <_ 1. <_ is greater than or equal to. Homework Equations arc length= integral(magnitude of the derivative of r(t)) The Attempt at a Solution i thought I figured the answer out and got an arc...

Homework Statement volumetric modulated arc therapy (vmat) is a new technology in radiation therapy. It gives radiation treatment in a single 360 degree or less arc. During VMAT delivery on medical linear accelerator dose rate, gantry speed and MLC shapes can be simultaneously varied when...

Homework Statement find the arc length x=2e^t, y=e^-t, z=2t Homework Equations The Attempt at a Solution dr/dt=2e^ti-e^-tj+2 ds/dt=sqrt((4e^2t)+(e^-2t)+4)) dt =integral from 0 to 1 sqrt(4e^4t+4e^2t+1)/e^t sorry about the lack of latex, I have no idea how to integrate this function

Homework Statement Given: The diameter of the Earth is 8000 miles If angle ACB has measure 1', then the distance between A and B is a nautical mile. Approximate the number of and (statute) miles in a nautical mile. Homework Equations Arc Length Therom: s=r(theta) The...

Homework Statement Find the length of \ x =t^{3} \ y =t^{2} 0 \leqt\leq 4 Homework Equations I would write the formula for the arc length but I don't know how to make a definite integral. The Attempt at a Solution I have the whole thing set up and I'm ready to integrate but I...

Homework Statement I'm trying to find the arc length of a curve over an interval and I've arrived at \int (y4 +2y2 +1)1/2 dy and now I'm pretty sure i should use a u substitution in order to integrate. I tried using u=y2 so du=2y dy so dy=du/2y Then you have \int (u2+2u+1)1/2 and...