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. C

    Calculating Arc Length for Given Equation with Integration Method

    If y = \frac{x^{3}}{6} + \frac{1}{2x}\ and \frac{1}{2}\leq x\leq 1 . Find the arc length. So \frac{dy}{dx} = \frac{x^{2}}{2} - \frac{1}{2x^{2}} . So I got \frac{1}{2} \int^{1}_{\frac{1}{2}} \sqrt{2+x^{4} + x^{-4}} dx . How would you evaulate this? Thanks
  2. D

    How to Simplify the Integral in an Arc Length Problem with Parametric Equations?

    Okay, so I was given the parametric equations of x = (cos(t))^2 and y = cos(t). So I found dy/dt = -sin(t) and dx/dt = -2sin(t)cos(t). This is where I am getting stuck, so I have the L = integral from 0 to 4pi (sqrt((dx/dt)^2+(dy/dt)^2)) , but I don't know how to simplify this to get the answer...
  3. B

    Arc Length for a metal project

    Hello everyone. I'm a metal worker trying to do the layout for a project using a few nice curves. To do that, I need to get arc length, but I'm having trouble finding it for f(x)=x^3. If anyone can give me a nudge in the right direction for integrating (1+(3x^2)^2)^1/2, it would be greatly...
  4. C

    Solving Arc Length Problem: 45 Degrees & x-Axis

    ..Or I think this is considered that... Here's the problem as written then I'll get to it: Find the length of the curve y^2=x^3 from the orign to the point where the tangent makes an angle of 45 degrees with the x-axis. Okay, by me posting this, I don't want anyone (nor am I looking for...
  5. D

    Circular arc of charge, integration question

    I have a circular arc of wire centered at the point (0,0). It has a radius of r, extends from \theta = -60 to \theta = 60 and also holds a charge q. For the differential electric field I have the following equation: dE = \frac{\lambda ds}{4 \pi \epsilon_0 r^2} Where ds is the length of a...
  6. K

    Arc length and parametric function

    I'm having trouble with the following: The problem is to find the arc length of the following parametric function: x=(e^-t)(cos t), y=(e^-t)(sin t) from 0 to \pi I found that \frac{\partial y}{\partial t} = e^{-t}(\cos{t}-\sin{t}) , \frac{\partial x}{\partial t} =...
  7. A

    Arc Length Problem: Find Length from y=125 to y=216

    Hey, I need some help with an arc length question. It is: Find the length of the curve: x=3y^(4/3)-(3/32)y^(2/3) from y=125 to y= 216 So i know i need to use Arc Length=sqrt(1+(dx/dy)^2) but i can't seem to get the right answer. I have the derivative as 4y^(1/3)-(1/16)y^(-1/3). Squaring...
  8. U

    How Do You Calculate Arc Length and Volume of Rotated Solids in Calculus?

    i have 2 calculus questions that are due in the next half n hour and i have no idea how to even start them. I hope somoene can help me in time. Question1 Find the volume of the solid obtained if the plane region E bounded by the curve y=x^2 and y=x^3 between x=0 and x=1 is rotated about the...
  9. S

    Calc 3 Project: Solve Arc Length Problem with y = 1/c cosh(cx + b) + a

    Hey I got a project assigned for my Calc 3 class, and I was wondering what to do with the following: A hanging cable has the shape y = 1/c cosh(cx + b) + a for some constants a,b,c with c>0. Suppose the ends are at P(0,10) and P2(30,5). If the length of the cable is known to be 100...
  10. P

    Solving Charged Circular Arc Problem: Q, R, \Delta E_x

    A uniformly charged circular arc AB is of radius R covers a quarter of a circle and is located in the second quadrant. The total charge on the arc is Q > 0. This problem has 4 parts, I got the first 2. 1. The direction of the electric field E due to the charge distribution at the origin is in...
  11. T

    Finding n for Arc Length of $\pi+e$ over Interval 0 to 6

    \int^{6}_{0} \sqrt{1-n^2x^2}dx=\pi+e I need to solve this for n. I believe there should only be one possible function of the form y=x^n that gives an arclength of \pi+e over the interval x=0 to x=6, and wish to find the value of n that such a function must have. Does anyone know how to do...
  12. N

    Find Arc Length Using Trapezoids

    Using trapezoids and N=4, find the length of the arc of the curve y=(1/3)x^3 from (0,0) to (1,1/3).
  13. D

    Solving Minimizing Arc Length: Euler-Lagrange Equations

    The problem I am working on asks me to find the curve on the surface z=x^(3/2) which minimizes arc length and connects the points (0,0,0) and (1,1,1). Here's what I did: Integral [sqrt(dx^2+dy^2+dz^2)] Integral [dx sqrt (1+(dy/dx)^2 +(dz/dx)^2] Integral [dx sqrt (1 + (dy/dx)^2 + 9x/4)]...
  14. S

    LaTeX Finding an arc length, and why isn't latex working for me?

    Finding an arc length I am attempting to find the arc length of y = cuberoot[x] between (1,1) and (8,2). I solved the integral from 1 to 2 of sqrt[1+(3y^2)^2]dy. I used a formula from a table of integrals in my text to solve this integral. The solution I get is 68.19. I can see that this...
  15. S

    I need a formula for Height equals length of arc.

    How do I find out what angle to fire a projectile so that the height it attains is equiv to the length of its arc? Whats a general formula? Assume the projectile is "fired" from ground level. Say, from a pea shooter or a sling shot.
  16. J

    Proving Graph G Connectivity After Removing Arc (i,j)

    I am having problems to prove this: Show that a graph G remains connected even after deleting an arc (i,j) iff arc (i,j) belongs to some cycle in G. Grapgh G = (N, A), N = set of points of nodes, and A = set of arcs; an arc is an edge from node i to a different node j from N. Any suggestions?
  17. G

    Verifying Arc Length of Vector: <2e^t, e^-t, 2t>

    Hello, I was wondering if someone could check and see that i did this problem right. You need to find the arc length of the vector from t=0 to 1: r= <2e^t,e^-t,2t> So first i took the derivative and got velocity. v=<2e^t,-e^-t,2> Next i used the formula for arc length. arc...
  18. I

    Find the arc length of the given function

    This is my last homework problem and I feel that I almost have it solved. The problem is as followed: f(x) = \sqrt{4-x^2} Find the arc length of the given function from x=0 to x=2. I know that I am supposed to use this formula to solve for arclength: \int_{0}^{2} \sqrt{1 +...
  19. M

    Inv, co, arc, arcco, inv co, etc

    Can anyone tell me what the difference is, if any, between inverse _, arc_, co_, and _^-1, when refereing to any of the trigonometric ratios? Also, what would arcco_, and inverse co_ refer to? Thank you.
  20. Cyrus

    Reparametrize the cure in terms of arc length instead of time

    Yikes, I am really starting to spam this place up! On the subject of curvature, it says that we can reparametrize the cure in terms of arc length instead of time. If we have time,t, and arc length s(t), we can write it as t=t(s). It seems to me that this is NOT true in general, if you...
  21. S

    Buying either a stick electrode arc welder

    i am looking into buying either a stick electrode arc welder or a semi-automatic flux spool fed arc welder does anyone have suggestions about using either/or? thanks
  22. T

    Calculus 2: Finding Arc Length | Florida A&M Univ.

    The arc length... Hello all, this is my first post. I am a Computer Engineering Student at Florida A&M University taking Calculus 2 over the summer semester. Should finding the arc length be so extensive?? Are their shortcuts that I am missing? If you don't know the formula, the arc...
  23. J

    Weird arc length question

    I want to find two functions f(n,x) and g(n,x) such that f(n,x)sin(g(n,x)) always has a constant arc length over some interval [a,b]. Where n increases the amplitude but decreases the period. Any suggestions?
  24. B

    Work Done by Gravity on Box on Ice Arc - Radius 8m, Angle 14 Degrees

    A perfect hemisphere of frictionless ice has radius R = 8 meters. Sitting on the top of the ice, motionless, is a box of mass m = 10 kg. The box starts to slide to the right, down the sloping surface of the ice. After it has moved by an angle 14 degrees from the top, how much work has...
  25. C

    Calculating Arc Length in Multivariate Calculus

    here is the problem, and I can't seem to get very far, compute the length of r(t) = <3t, 4cost, 4sint> from t=0 to t=1 i know the formula is integral from 0 to 1 of length of r'(t) but I keep coming up with 5, and it doesn't seem right, can someone please confirm or deny this. Thanks
  26. C

    Solving arcsin(sin 3π): Step-by-Step Guide

    srry to be a bother but can someone help me on how to do this, it explains it in the book but i don't understand. Here it is: arcsin(sin 3(pi)) i would really appreciate ur help, and thxs before hand. :smile:
  27. E

    Get Help with Arc Welding Machines & Technology

    Dear . . . Physics Forum May I Ask Some Help ? I need a website that makes me learn more about : 1. Arc Welding Machines . 2. Arc Welding Technology . 3. Welding Rodes Specifications . 4. The Calculations That We Need For How Deciding The Welding Rode Diameter Depending On The Working...
  28. P

    Stuck again - electric field and circular arc

    Hi there, I was hoping that somebody could help me. I'm stuck again! :cry: a rod with (lambda) coulombs of charge per meter of its length has the shape of a circular arc of radius R. The rod subtends an angle (theta). Shpw that the magnitude of the electric field at the centre of the...
  29. O

    Arc Length In Polar Cordinates

    Hello, i am a high school student currently taking ap calculus. i am currently working on a research project on arc length in polar coordinates. through all of my research thus far the one thing that has eluded my grasp so far that is really frustrating is the applications in real life for...
  30. W

    Definition of Arc Length Function

    Hello, I am having trouble remembering some of the material required for my current calculus course so I am reviewing some of the previous material that I have forgotten. I am having trouble following the definition of The Arc Length Function as presented in James Stewart's "Calculus...
  31. T

    The Correct Arc Length Formula for Finding a Function F(x)

    Find a function F(x) whose arc length L(x) from (1,1/2) to (x,F(x)), x>1 is (1/2)x^2 + (1/4)Ln(x). First some short hand notation. Int[f(x),dx], means the indefinite integral of the function f(x). Int[f(x),dx,a,b], means the definite integral where a is the lower bound and b is the...
  32. R

    Equations for Arc Plasma near Magnetic Fields

    Hi, I'm currently doing an research experiment into the behaviour of plasma around magnetic fields. I will be using an arc welding machine for the plasma and an electromagnet. (So I can adjust the field's intensity as an independant variable.) The arc should bend in the presence of a magnetic...
  33. K

    Analyzing Arc Equations - Why are x1,x2 & y1,y2 Half Circles?

    The first general circle formula is, (x-a)^2+(y-b)^2=r^2 Where M(a,b) and r:radius. I understand this well, but when the subject is arcs... (x-a)^2=r^2-(y-b)^2 x_\textrm{1,2} =a (+-) \sqrt{r^2-(y-b)^2} My teacher said that equations for x1 and x2 were half circles at right and...
  34. G

    Find the length of the specified arc of the given curve

    Calc help please! Plz help me out w/ the problem below. Thanks. Find the length of the specified arc of the given curve: y=1/3sqrt(x)*(3-x), 0<=x <=3 Formular to find arc length is integral from a to b of sqrt(1+f'(x)^2)dx I got to these steps below and not sure exactly wat to do next...
  35. D

    Parameterization of Arc Length Function

    I'm a little confused by the following in my textbook: Arc Length Function of a curve, 's', is defined by: s(t) = [inte]|r'(u)|du = [inte][squ]((dx/du)^2 + (dy/du)^2 + (dz/du)^2)du integrate both sides and you get ds/dt = |r'(t)|. Arc length is independent of the parameterization...
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