What is Arc: Definition and 485 Discussions

An electric arc, or arc discharge, is an electrical breakdown of a gas that produces a prolonged electrical discharge. The current through a normally nonconductive medium such as air produces a plasma; the plasma may produce visible light. An arc discharge is characterized by a lower voltage than a glow discharge and relies on thermionic emission of electrons from the electrodes supporting the arc. An archaic term is voltaic arc, as used in the phrase "voltaic arc lamp".
Techniques for arc suppression can be used to reduce the duration or likelihood of arc formation.
In the late 1800s, electric arc lighting was in wide use for public lighting.
Some low-pressure electric arcs are used in many applications. For example, fluorescent tubes, mercury, sodium, and metal-halide lamps are used for lighting; xenon arc lamps have been used for movie projectors. Electric arcs can be utilized for manufacturing processes, such as electric arc welding and electric arc furnaces for steel recycling.

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  1. M

    Find Arc Length of r(t): Solving Homework Problem

    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...
  2. R

    Calculating Arc Length of a Vector Function

    Homework Statement Find Arc Length: r(t)=t^3 i+tj+(1/2)\sqrt{6}t^2k 1\leqt\leq3Homework Equations The arc length formula: integrate: sqrt((dx/dt)^2+(dy/dt)^2+(dz/dt)^2) dtThe Attempt at a Solution I can find the derivative and plug into the formula, it's just the simplification that is...
  3. R

    Volumetric modulated arc therapy

    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...
  4. Z

    Find the Arc Length of a Curved Line

    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
  5. T

    What is the Conversion Factor for Nautical Miles to Statute Miles?

    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...
  6. S

    Finding Arc Length of x & y from 0 to 4

    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...
  7. B

    Find the arc length of a curve over an interval

    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...
  8. Battlemage!

    Basic Calculus III- Arc Length Parameter and Length- Getting a negative length

    Homework Statement Find the Arc Length Parameter along the curve from the point where t = 0 by evaluating the integral: s = ∫ |v(τ)| dτ from 0 to t Then find the length of the indicated portion of the curve. Homework Equations The vector I am using for this: r(t) = (etcos t)i + (etsin...
  9. W

    Find the arc length for the given interval (parametric curve)

    Find the arc length. x = sqrt(t) y = 6t - 2 Interval from 0 to 5 inclusive. Whenever I do this, I get a long answer with big numbers in the numerator all divided by 48. Can someone walk me through the steps? THanks.
  10. James889

    Trying to calculate arc length

    Hi, Im trying to calculate the arc length of the function f(x)=x\sqrt{x} From x=1 to x=7 But I am getting the wrong answer and I am not sure why. The formula is \int^{7}_{1}\sqrt{f'(x) + 1} The derivative of f(x) =\frac{x}{2\sqrt{x}} + \sqrt{x} Squaring yields ~~\frac{x}{4} + 2x +1 which...
  11. C

    Arc length for these parametric equations

    Homework Statement Find the arc length of the curve described by the parametric equations: x=2e^t & y=3e^3t/2 ln3≤t≤2ln3 Homework Equations S = ∫(a->b) √[(dy/dt)^2 + (dx/dt)^2]dt The Attempt at a Solution Differentiated the two parametrics: dy/dt = 2e^t dx/dt = (3/2)*3e^3t/2 =...
  12. B

    Does zero arc length mediation of EM cause the wavefunction

    The path taken by a ray of light, from an event E1 to event E2, follows a zero arc length curve such that E2 ∫ds = 0 1. E1 Where S is the interval along the null geodesic path between the...
  13. R

    Calculating the Center of Mass of an Arc

    Homework Statement There is an arc with an angle of 2\alpha and radius R What is its center of mass. (It is implied that it is to be measured from the center of the circle the arc is a part of.Homework Equations Integration, trigonometry.The Attempt at a Solution Well, the formula for a center...
  14. M

    Arc Length 3-D: Find Length Between (8,4,0) & (24,36,4log(3))

    Homework Statement Consider the path f{r}(t) = (8t, 4t^2, 4log(t) ) defined for t > 0. Find the length of the curve between the points (8, 4, 0) and (24, 36, 4log(3)). Homework Equations \int|r' (t)|dt The Attempt at a Solution r(t)=(8t, 4t^2, 4log(t)) r'(t)=(8, 8t, 4/(ln(10)t)) |r'...
  15. L

    Help with Arc Length Problem: Evaluating Integral from x=8 to x=27

    Homework Statement Hello, I have an arc length problem that I’m stuck on, and I would really appreciate it if someone could help me out. I understand the arc length formula and everything, it’s evaluating the integral produced by it. The author in the book I got this problem from tells the...
  16. I

    Find Length of Arc for x = 3y^(4/3) - 3/32y^(2/3)

    Homework Statement find the length of the arc x = 3y^ (4/3) - 3/32y^(2/3) and y lies between 0 and 216 Homework Equations l = integral sqrt (1 + (dy / dx )^2) The Attempt at a Solution after integration i got this y + 3/16y ^(-4/3) / (-4/3) i have to apply 0 and...
  17. R

    Arc Length & Parametric Curves

    Homework Statement Find the length of the curve y=x^2-4|x|-x from x=-4 to x=4. The Attempt at a Solution I realized there is a corner at x=0 so i tried to get around this by pluggin in x for x>=0 and -x for x<0. However, my integrals don't match the answer...
  18. G

    Solve Arc Length Problem: Find Circumference of Wing Section

    Homework Statement I'm trying to compute the circumference of a wing section. I have broken up the airfoil circumference into arc pieces and used cubic splines to come up with an equation for each piece. For example, the arc nearest the leading edge of the wing is the function: y =...
  19. T

    What is the arc length of a falling prey described by a parabolic trajectory?

    Homework Statement A hawk flying at 2 m/s at an altitude of 80 m accidentally drops its prey. The parabolic trajectory of the falling prey is described by the equation below until it hits the ground, where y is its height above the ground and x is its horizontal distance traveled in meters...
  20. I

    Why Does the Line Integral of a Square Path's Perimeter Equal Zero?

    When I take the line integral around a square shape path "C" as follows: From A to B to C to D to A C1 = A(0, 0) to B (4, 0) t i 0 <= t <= 4 C2 = B (4, 0) to C (4, 7) 4 i + (t - 4) j 4 <= t <= 11 C3 = C (4, 7) to D (0, 7) (15 - t) i + 7 j 11 <= t <= 15 C4 = D (0, 7)...
  21. F

    How Do You Compute Arc Length and Surface Area for the Exponential Curve e^x?

    C: y=f(x)=e^x, where x is all real numbers. Compute the arc-length function S for C relative to C's y-intercept Computer the area S for the surface generated by revolving the curve C*:y=f(x)=e&x, where x is [0,a] and a is a positive constant, about the x-axis I've been trying this problem for 2...
  22. J

    What Is the Radius of an Arc for a Pilot Experiencing 5G at 700m/s?

    Homework Statement Im having trouble figuring out which equation to use for this problem. The problem states: "Consider a pilot at the lowest point of a circular arc banking upward. Find the tightest radius arc that an untrained individual can fly ( a total of +5 G, G standing for the normal...
  23. H

    Solving Arc Length Integral for y=ln(1-x^2) - 0 to 1/2

    Homework Statement ok, the original prob is : find the length of the curve of y=ln(1-x^2) x between 0, 1/2. Homework Equations The Attempt at a Solution ive made it this far: my integral is -1 + 2/1-x^2.....ok so i decompose the second part but in doing so i get a...
  24. P

    Why do Certain Vegetables Arc in the Microwave?

    Hello, This is my first post, so please forgive me if this has been covered before. In my searches I was unable to find any previous threads specifically about this question. I made a statement in a link sharing forum that was immediately disputed. I'm not interested in winning an argument so...
  25. M

    Arc legth of curve C in first octant

    Let C be the curve obtained by intersecting the sphere x^2 + y^2 + z^2 = a^2 with the surface root(x^2 + y^2)cosh(arctan(y/x))=a. Find the length in the first octant that joins the points A (a,0,0) and B(x,y,z). Im not sure what to do. Should i change it into different types of coordinates?
  26. G

    Evaluation of a (parabolic) line integral with respect to arc length

    Homework Statement Evaluate the line integral \[ \int_c yz\,ds.\] where C is a parabola with z=y^2 , x=1 for 0<=y<=2Homework Equations A hint was given by the teacher to substitute p=t^2 , dp=(2t)dt and use integration by parts. I also know from other line integrals with respect to arc length...
  27. S

    Calculating Arc Length for Parametric Equations with Simple Integration

    Homework Statement x = 1+3t^2 y=3+2t^3 0<= x <=4 Homework Equations L = integral from a to b of \sqrt{[dx/dt]^2 + [dy/dt]^2} dx The Attempt at a Solution dx/dt = 6t dy/dt = 6t^2 L = integral from 0 to 4 of \sqrt{(6t)^2 +(6t^2)^2} dx = " \sqrt{36t^2 +36t^4} dx = "...
  28. W

    Arc Length to Radius Ratio: Why Equal?

    (F) Thanks in advance (F)
  29. J

    Is Acceleration a Scalar Multiple of Arc Length?

    Homework Statement Show that d^2 R / dt^2 is NOT a scalar which is a multiple of d^2 R / ds^2 where R is a vector, s is arc length Homework Equations and The Attempt at a Solution I was thinking maybe it has something to do with the fact k = |d^2 R / ds^2| a = d^2 R / dt^2 = d|v|/dt * T + k...
  30. M

    Electric Arc Current Estimate: 80kV, 1" Gap

    Hello, I am trying to find an estimated value (or range) for the current of an electric arc. I imagine this may be a function of the voltage producing the arc, the distance between the electrodes, and other parameters. If this is true, then take the voltage to be around 80kV and the...
  31. N

    Calculating Arc Length of y=x^2 from 0 to 10 using Trig Substitution"

    Homework Statement Find the arclength of the function y=x^2 when x is between 0 and 10. Homework Equations Arclength here is \int_{0}^{10} \sqrt{1+(2x)^2} dx (It's intended to be the integral from 0 to 10 of the quare root of 1+(2x)^2. My latex skills suck.) The Attempt at a...
  32. N

    How Does Arc Length Calculation Relate to Surface Problems?

    HELP
  33. V

    Arc Length of y^2=4(x+4)^3 from x=0 to x=2

    Homework Statement Find the arc length of the equation y^2=4(x+4)^3 from x=0 to x=2 Homework Equations L=\int_{a}^{b}\sqrt{1+f'(x)}dx The Attempt at a Solution L=\int_{0}^{2}\sqrt{1+9(x+4)}dx which simplifies in to L=\int_{0}^{2}\sqrt{9x+37}dx and I'm stuck there--how should i try...
  34. C

    Arc length and straight lines(Need clarification please)

    Homework Statement Here is difficult one guys, Lets imagine that an object movement along a curve is described by the parameterized function called \omega: I \rightarrow \mathbb{R}^3 which moves on the interval [a,b]\subset I. and this depended on motor which supplies the constant...
  35. G

    Arc length (mostly a problem with integration)

    Homework Statement Find the arc length oh the graph f(x)=cosx on the integral [0,\frac{\pi}{2}] Homework Equations \int^{b}_{a}\sqrt{1+{f'(x)}^{2}}dx The Attempt at a Solution Alright so I took the derivative of f(x) to get f'(x)=-sinx then I squared it to get sin^{2}x so I could...
  36. B

    Centroid of a semicircular arc

    Homework Statement Here, I have two ways of finding the y-coordinate centroid of a semicircular arc using polar coordinates. First one is considering a circle of radius a, centred at the origin. What I have done is \int ds = \int_0^{\pi} a d\theta = \pi a and then \int y ds = \int r^2 sin...
  37. L

    How Can I Calculate Arc Length Without a Calculator?

    How in gods name do I do that? I attempted that integral and... it just can't be integrated! What I tried: That doesn't help one bit... How do I do this? NOTE: No graphing calculator is to be used.
  38. B

    What is the Arc Length of y=\sqrt{x} from x=0 to x=2?

    Homework Statement Find the arc length of y=\sqrt{x} from x=0 to x=2. The Attempt at a Solution I don't know, this is a nastier integral than it looks. From the substitutions, s = \int_0^2 \sqrt{1 + \frac{1}{4x}} dx. From doing this over and over again I already know the answer will have...
  39. M

    Using a plasma arc instead of fission for a reactor style rocket

    Gas core reactor rockets use nuclear gas reacting to super heat and therefore pressurize hydrogen. They operate at about 25000 C. Why not use a high intensity plasma arc which routinely operate at about 13,000 C but if designed to can go much higher by at least several fold. I got bored...
  40. S

    Finding the Integral of xdx on Arc C

    Homework Statement Let C be the arc of y=x2 from (0,0) to (1,1). Evaluate \intxdxHomework Equations C1: x=t y=t2 -1 \leq t \leq 1 so -1 \leq x \leq 1 The Attempt at a Solution dx is x' dt, right? For some reason, I just can't figure this out. Any help?
  41. P

    Arc Length in Parametric equation

    I know this is very simple, but the end integral just kills me Homework Statement Given equation in Parametric form x=\sqrt{2t+1}), y=6t Find arc length Homework Equations The Attempt at a Solution take x' & y' then Take integral of \int\sqrt{1/(2t+1) + 36} This is where I got stuck ...is...
  42. K

    Y = sin pi * x Arc Length/Surface Revolution

    Homework Statement y = sin \pix Using arc length and surface revoultion on x-axis 0 <= x <= 1 The Attempt at a Solution d/dx sin \pix = \pi cos \pix (\pi cos\pix)^2 = \pi^2 cos^2\pix \int sin pi * x * 2 * pi * \sqrt{1 + pi^2 * cos^2 (pi*x)} u = pi cos (pi * x) du = -pi^2 * sin...
  43. K

    Arc Length of y = (2/3) * (x^2-1) ^ (3/2): Solve It

    Homework Statement y = (2/3) * (x^2 - 1) ^ (3/2) 1 <= x <= 3 Length = ?Homework Equations L = \int\sqrt{1 + (dy/dx)^2} dxThe Attempt at a Solution dy/dx y = (2/3) * (x^2 - 1) ^ (3/2) = 2x * sqrt(x - 1) Any ideas for a proper substitution? The answer on wolfram seems ridiculous. :bugeye:
  44. N

    Line integral - finding the arc length

    a curve is given as 3 parameters of t: x=a(3t - t^3), y=3a(t^2), z=a(3t + t^3) i have to find the arc length measured from origin and curvature as functions of t. would i be correct in using the integral at the bottom of page 2 here: http://homepages.ius.edu/wclang/m311/fall2005/notes17.2.pdf
  45. J

    Calculating Arc Length in Polar Coordinates

    Homework Statement Find The length of r=sin³(x/3) 0<x<3pi/2 2. The attempt at a solution well first i found r'=3.cos(x/3).1/3.sin²(x/3)=cos(x/3)sin²(x/3) r²=cos²(x/3)sin^4(x/3) then i put the formula integral of radical (r'²+r²)dx and I'm stuck here any help?
  46. R

    Finding Arc Length of f(x) = (4-x^2)^(1/2)

    Homework Statement What is the arc length of f(x) = (4-x^2)^(1/2)? Homework Equations The Attempt at a Solution
  47. D

    How to Calculate Arc Length for Parametric Curves in 3D Space?

    Homework Statement x = \frac{u^{2} + v^{2}}{2} y = uv z = z Find the arc length given: u(t) = cos(t), v(t) = sin(t), z = \frac{2t^{\frac{3}{2}}}{3} Homework Equations ds^{2} = dx^{2} + dy^{2} + dz^{2} In curvilinear coordinates thhis becomes ds =...
  48. D

    Calculate Arc Length of Hypocycloid Function | Homework Help

    Homework Statement Find the arc length of r(t) = cos(t)^3 i + sin(t)^3 j from t = 0 to t = 2 * Pi It's a hypocycloid that's four cusped. Homework Equations s = \int\sqrt{x'^2 + y'^2} The Attempt at a Solution x = cos(t)^3 y = sin(t)^3 x' = -3cos(t)^2*sin(t) y' =...
  49. T

    Arc length of a curve (trigonometric identity)

    Homework Statement find arc length of the segment of the 2space curbe that is defined by the parametric equations x(t) = t-sin(t) y(t) = 1+cos(t) 0 ≤ t ≤ 4π The Attempt at a Solution I've found dx/dt and dy/dt respectively and put them into the arc length equation, i.e...
  50. J

    How do I integrate sqrt(t^2 + 8)?

    I am trying to figure out the following arc length problem, and it's really coming down to a question over intregration. Compute the length of the curve r(t)=(4t)i +(4t)j+(t^2+6k) over the interval 0 to 6. I have dr/dt = (4, 4, 2t) , and then used the arc length equation: L= integral...
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