Arc Definition and 478 Threads

I have a question on the formulas for arc length and surface area. Do you use the formula: s= \int_{c}^{d}\sqrt{1+[g'(y)]^2}dy only when you are provided with a function x=g(y)?? Can you convert that to y=g(x) and solve it by replacing g'(y) with y(x), changing the bounds and the dy to dx...

Curves are functions from an interval of the real numbers to a differentiable manifold. Given a metric on the manifold, arc length is a property of the image of the curves, not of the curves itself. In other word, it is independent of the parametrization of the curve. In the case of the...

good day, this place is great, and i just got questions an AC electric arc furnace melts metal by way three electrodes and electric arcs generated by potential differences inside the furnace i had the opportunity to watch one in action and understanding the programming i see it controls...

Doran/Lasenby define a proper interval as: \delta \tau = \int \sqrt{\frac{dx}{d\lambda} \cdot \frac{dx}{d\lambda}} d\lambda (c=1, x= (t,x1,x2,x3) is a spacetime event, and the dot product has a +,-,-,- signature) and say that this is called the proper time. I can see that this...

Homework Statement Length of curve: y=1/2(ex-e-x) from 0 to 2 Homework Equations s = ∫√[1+(dy/dx)^2] dx The Attempt at a Solution [sqrt(4+2e^(-x)+e^x)]*[-1+e^x]/[1+e^x]. = 3.323971

Can someone help me find these calculations or give me a point in the right directions? If I have a hollow insulating cylinder (has a diameter of 5 cm and a length of 14 cm) with two (conductive) sharp metal point contacts at each end (measuring 2cm each leaving 10 cm exactly between the...

Can someone help me find these calculations or give me a point in the right directions? If I have a hollow insulating cylinder (has a diameter of 5 cm and a length of 14 cm) with two (conductive) sharp metal point contacts at each end (measuring 2cm each leaving 10 cm exactly between the...

Simplifying an arc length problem I have L= Int(-2..2) sqrt(16*cosh(4*t)^2+9*sinh(4*t)^2+9) and can use Maple to simplify this to sqrt(25*cosh(4*t)^2) but I just can't see how that is done. (or how to get maple to show me the steps!) Can anyone help by showing the steps, including any...

When an electrical arc occurs, is the blue/white/purple arc the electricity itself, or is it a result of the electricity interacting with something in the air?

Homework Statement Find the length pf the curve over the given interval. r=1+\sin\theta 0\preceq\theta\preceq\2\pi The Attempt at a Solution Ok I set it up as: 2\pi \int\sqrt((1+\sin\theta)^2+cos^2\theta) 0 and by simplifying and integrating, I get...

We all know as to why we see a rainbow. But why do we see it in a the form a circular arc. Why not a straight line or anything else? I was reading one book and that gave some reason that eyes make the a particular angle at the light from the drops of water. We all know the first part that we...

Homework Statement Find the length of the spiral of r=1/theta for theta\geq2 \pi Homework Equations \int\sqrt{r^{2}+r'^{2}} The Attempt at a Solution I thought of the formula for polar arc length, which is the integral of the square root of the sum of the square of r and the square...

So this seems to be a pretty straightforward question but I keep getting the arc length to be 0 and I redid this question many times.. Find the length of the parametrized curve given by x(t) =t^{2}-8t + 24 y(t) =t^{2}-8t -7 How many units of distance are covered by the point P(t)...

Homework Statement Given: R(t)= <(1/2)t^2, (4/3)t^(3/2), 2*sqrt(3)t> Find: Arc length function s(t) where t_0 =0 Homework Equations Is this the correct formula? ∫[0,t] sqrt( derivative^2 + derivative^2 +derivative^2) dt ∫[0,t] sqrt(t^2 + 4t + 12) dt The Attempt at a Solution...

Homework Statement A curce,C, has equation y=x^{\frac{1}{2}}-\frac{1}{3}x^{\frac{3}{2}}+\lambda where \lambda>0 and 0\leq x \leq 3 The length of C is denoted by s. Show that s=2\sqrt{3} The area of the surface generated when C is rotated through one revolution about the x-axis is denoted...

1.Homework Statement y=x^{\frac}{1}{2}}- \frac{1}{3}x^{\frac{3}{2}}+\lambda For 0 \leq x \leq 3 Show that the arc length,s=2\sqrt{3} Homework Equations s=\int_{x_1} ^{x_2} \sqrt{1+ (\frac{dy}{dx})^2} dx The Attempt at a Solution \frac{dy}{dx}=\frac{1}{2\sqrt{x}} -...

I have 3 points defined on an arc of a circle.I need to identify whether they lie on the major arc or minor arc.How is it possible? I know the three points. I know the radius of the circle

Homework Statement Determine the field at the center of curvature of an arc of arbitary angle \alpha (\alpha is with the x-axis) Homework Equations E=\frac{kQ}{R^2}\widehat{r} S=R\alpha \lambda=\frac{Q}{S} The Attempt at a Solution I divide the arc into small pieces ds...

I'm working on this problem x^5/6+1/(10x^3) [1,2] and I got the equation: sqrt(1+(5x^4/6-3/10^4)^2) or sqrt(1+25x^8/36+9/100x^8-1/2) I'm not sure how to integrate the last part, is there some sort of obvious substitution I'm missing?

It's easy question,but I don't know whether I solved it correctly. Homework Statement Calculate the length of the curve given by r=a\sin^3 \frac{\theta}{3} in polar coordinates. Here, a > 0 is some number. Homework Equations l=\int \sqrt{r^2(\theta)+(\frac{dr}{d\theta})^2}d\theta...

Can anybody help? Mathematical Physics. I'm seeking an analytical expression for the path length of a point that follows a helical path with the helix wound about an axis to form a torus. The arc path length of a helix is simple to compute, but when its formed into a torus there is a...

I need help with this homework problem: Making a turn, a jetliner flies 2.1km on a circular path of radius 3.4km. Through what angle does it turn? Any ideas that would help me in doing it?? thanks

Hi! Here's my question on finding arc length. If I've taken the derivative correctly, is there anyway I can simplify it before putting it into the arc length formula? Homework Statement Find the arc length where 0\leqx\leq2 y=(x^{3}/3)+x^{2}+x+1/(4x+4) Homework Equations...

Homework Statement A circular arc of charge has a radius R and contains a total charge Q. If the angle of the arc is 90 degrees find: a) the charge density of the arc b) the electric field at point P in terms of the charge density L and the radius of the arc R L should really be lambda...

Homework Statement I need to find the second moment of area for a hollow cylindrical arc. When I searched the web, they had formulas for several shapes but I couldn't find this one The profile of my part is a little unusual as follows: R: Outer Radius = 35.089" r: Inner Radius = 35.050"...

[SOLVED] Arc Length Problem y=\sqrt{x^{3}} So you plug it into the formula for arc length. (integral of the sqrt of 1+y'^2) And it yields \int \sqrt{1+(\frac{3x^{2}}{2\sqrt{x^{3}}})^{2}dx From there you would use trig substitution, 1+tan^2theta = sec^2theta. But converting the dx to...

Is there a general formula for calculating the arc length between two points along an ellipse?

Homework Statement Find the point on the curve r(t) = (5Sint)i + (5Cost)j + 12tk at a distance 26pi units along the curve from the point (0,5,0) in the direction of increasing arc length. Homework Equations L = int (|v|) from 0 to T. The Attempt at a Solution T comes to be 2pi...

Homework Statement My book says if you write a plane curve in polar coordinates by p = p(?), a<=?<=b then the arc length is ??(p^2+(p')^2)d? (the integral is from a to b). It doesn't tell me how they got this equation though and I can't figure it out myself. what does the equation p(?) mean...

If I have 2 limit sensors set in a circular arc around a rotating servo motor, and the angle between them is 83°, approximately what is the angular range of motion that I can achieve? Please take into account, and let me know what clearances I need to be aware of (i.e. how many degrees clearance...

so I need to construct a device that creates a high voltage arc for an experiment, unfortunatly I don't know how to amplify the voltage without a series of transformers. I believe there is a way of doing this with a few capacitors, and right now I have about a dozen 12 MFD capacitors, and a...

What exactly happens to the gas molecules in an electric arc? Oxygen turns to ozone, methane turns to acetelyene.

Hi all, I have two lines in three dimensional form [P1(x1,y1,z1),P2(x2,y2,z2), and P3(x3,y3,z3), P4(x4,y4,z4) ] joined by a fillet, with known radius. i want to know the, start of the fillet(bend), end of the fillet, center of the fillet in a mathematical expression. with the above...

This is not a homework problem, but a friend and I were discussing this and have not come to an agreement as yet. Supposing that we are in a car which is traveling a left curve in the road which is of constant radius, and we still have some way to go before the road becomes straight again...

Homework Statement A hawk flies in a horizontal arc of radius 13.5 m with a speed of 3.9 m/s. What is its centripetal acceleration? (I correctly found this to be 1.1267 m/s².) Next question is: If it continues to fly along the same horizontal arc but increases its speed at a rate of...

Guys, I need your kind assistance. I am studying arcs length. Suppose a vectorial function with domain [a, b] (interval in R) and range in RxR. This range is a curve in the RxR plane. Take a partition P of [a, b]: a= t0, t1, t2,..., tn = b. We have a straight line which goes from F(t0) to...

Homework Statement A cable hangs between two poles of equal height and 39 feet apart. At a point on the ground directly under the cable and x feet from the point on the ground halfway between the poles the height of the cable in feet is h(x)=10 +(0.4)( x^{1.5}) The cable weighs 12.5...

Homework Statement Just started Calc II last month, it's been smooth so far but I've run into a bit of snag involving the application of integrals in the calculation of arc length. The formula you use is the definite integral of (1+(d/dx)^2)^.5. Often once you derive the d/dx and...

Homework Statement Evalute: a) lim (x->0) (arctan x)/x b) lim (x->1) (arctan(x) - pi/4)/(x-1) Homework Equations Inverse tangent, trig identities. Kline's calculus, which I am teaching myself from, does not have that much detail on limits. The Attempt at a Solution For (a), I...

What would be the minimum direct or alternating voltage and current needed to produce an electric arc in air at a distance of one inch ?

1 Find the area bounded by the curve x = t - \frac{1}{t} , y = t + \frac{1}{t} and the line y = 2.5 . I know that A = \int_{\alpha}^{\beta} g(t)f'(t) \; dt I ended up with \int_{1}^{2} 2.5-(t+\frac{1}{t})(1+\frac{1}{t^{2}}) 2 Find the length of the curve: x = a(\cos \theta + \theta...

Hello there In the derivative of the arc secant, why is the absolute value of x ( which is present in the denominator) taken? Is this to prevent the possible of having a zero ( and making the whole expression undefined ? ) Thanks

An insulating rod of length l is bent into a circular arc of radius R that subtends an angle theta from the center of the circle. The rod has a charge Q ditributed uniformly along its length. Find the electric potential at the center of the circular arc. Struggling with this problem. I...

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

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...

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...

..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...

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...

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} =...

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...