Arc Definition and 478 Threads

Homework Statement A charge of 25nC is uniformly distributed along a circular arc (radius = 2.0 m) that is subtended by a 90-degree angle. What is the magnitude of the electric field at the center of the circle along which the arc lies? I'm not getting the right answer however, so if someone...

Homework Statement Find the arc length of polar curve 9+9cosθ Homework Equations L = integral of sqrt(r^2 + (dr/dθ)^2 dθ dr/dθ = -9sinθ r = 9+9cosθ )The Attempt at a Solution 1. Simplifying the integral r^2 = (9+9cosθ^2) = 81 +162cosθ + 81cos^2(θ) (dr/dθ)^2 = 81sin^2(θ)...

I quote a question from Yahoo! Answers I have given a link to the topic there so the OP can see my response.

although the anthropic landscape looks appealing, I am not big fan of the string theory, due to untestable extra dimensions. In isolation, without sensory information(experiments) the humans(theoretical physicists) start to hallucinate(String theory). But what if higher dimensions can be probed...

Given t\in Ithe arc length of a regular parametrized curve \alpha : I \to \mathbb{R}^3 from the point t_0 is by definition s(t) = \int^t_{t_0}|\alpha'(t)|dt where |\alpha'(t)| = \sqrt{(x'(t))^2+(y'(t))^2+(z'(t))^2} is the length of the vector \alpha'(t). Since \alpha'(t) \ne 0 the arc length s...

Given t\in Ithe arc length of a regular parametrized curve \alpha : I \to \mathbb{R}^3 from the point t_0 is by definition s(t) = \int^t_{t_0}|\alpha'(t)|dt where |\alpha'(t)| = \sqrt{(x'(t))^2+(y'(t))^2+(z'(t))^2} is the length of the vector \alpha'(t). Since \alpha'(t) \ne 0 the arc length s...

Homework Statement Find the arc length of the graph, on the interval [1/2, 2], of y = \frac{x^3}{6} + \frac{1}{2x} Homework Equations s = \int^b_a \sqrt{1 + [f'(x)]^2}dx The Attempt at a Solution I began with s = \int_{1/2}^2 \sqrt{1 + (\frac{x^2}{2} - \frac{1}{2x^2})^2}dx...

Hello, I have an arc with an arc length = 46.88 mm and radius = 44 mm. I have an intersecting arc with an arc length = 26.69 mm and radius = 43.4 mm. A circle with radius = 24 mm fits between the two arcs. How can I determine the contact points of the circle and the two arc lines?

hello every body .. According to the picture: Circle radius (Radius) and height (High) is known to us. Given that the height of the draw the tangent line , I looking for the equation for length of the arc (Arc Length) was calculated based on height changes. (sorry for my written...

1. A van der Graaf generator is used in classroom demonstrations to illustrate the production of large electric fields with visible arcs. The threshold field for air to reach dielectric breakdown is 3*10^6 V/m. In a particular demo, the van der Graaf dome is a hollow sphere of 25 cm...

How do you construct the arc of the circle as a straight line by geometry not by an equation? Thank you

Hi, I'm working through thinkpython and there is an exercise which requires drawing flowers and arcs. I'm having some trouble understanding the arc function. def arc(t, r, angle): """Draws an arc with the given radius and angle. t: Turtle r: radius angle: angle subtended by the...

Homework Statement Prove. Homework Equations arctan(x) = x - \displaystyle \frac{x^3}{3} + \frac{x^5}{5} - \frac{x^7}{7} + \frac{x^9}{9} for -1 < x < 1. The Attempt at a Solution \displaystyle \sum^{∞}_{n=1} \frac{x^{n+2}}{n+2}

When does the arc of the space curvature is large and when is it small?

Homework Statement Find the arc length of the curve (t) = (1; 3t2; t3) over the interval 0  t  1. Homework Equations L=sqrt(f'(t)^2+g'(t)^2+...+n'(t)^2) (integrated from a to b) int(udv)=uv-int(vdu) The Attempt at a Solution Seems like it should be fairly straightforward-- the...

Homework Statement Joe is traveling from point A across a circular lake to a cabin on the other side at point B. The straight line distance from A to B is 3 miles and is the diameter of the lake. He travels in a canoe on a straight line from A to C. She then takes the circular trail from C to...

The centerfield fence at a ballpark is 10 ft high and 400 ft from home plate. The ball is 3 ft above the ground when hit, and leaves with an angle theta degrees with the horizontal. The bat speed is 100 mph. Use the parametric equations x = (v0cos(theta))t y = h + (v0sin(theta))t - 16t^2 a...

This is an example in book by Howard Anton: Vector form of line is ##\vec r=\vec r_0+t\vec v## where ##\vec v## is parallel with the line. So both ##\vec r## and ##\vec r_0## are POSITION VECTORS. To change parameters, 1)Let u=t ##\Rightarrow\; \vec r=\vec r_0+u\vec v##. 2) ##\frac {d\vec...

Calculate the length of the curve We got the formula $$\int_a^b\sqrt{1+[f'(x)]^2}$$ and $$f'(x)=\frac{x}{36}-\frac{9}{x} <=> \frac{x^2-324}{36x}$$ so now we got $$\int_9^{9e}\sqrt{1+(\frac{x^2-324}{36x})^2}$$ we can rewrite that as $$\int_9^{9e}\sqrt{1+\frac{(x^2-324)^2}{1296x^2}}$$ then do...

Homework Statement Show that \gamma : [a, b] \rightarrow \Re^{2} is a parameterization of \Gamma if and only if the length of the curve from \gamma(a) to \gamma(s) is s - a; i.e., \int ^{s}_{a} \left| \gamma ' (t) \right| dt = s - a. Homework Equations The Attempt at a Solution Part 1...

Homework Statement Prove that any curve \Gamma can be parameterized by arc length. Homework Equations Hint: If η is any parameterization (of \Gamma I am guessing), let h(s) = \int^{s}_{a} \left| \eta ' (t) \right| dt and consider \gamma = \eta \circ h^{-1}. The Attempt at a Solution...

Homework Statement Explain why ∫(1+(1/x2)1/2dx over [1,e] = ∫(1+e2x)1/2dx over [0,1] The Attempt at a Solution The two original functions are ln(x) and ex and are both symmetrical about the line y = x. If I take either of the functions and translate it over the line y = x the two...

Homework Statement Homework Equations The arc length equation? The Attempt at a Solution I don't know where to begin.

Homework Statement Find the Arc Length from (0,3) clockwise to (2,sqrt(5)) along the circle defined by x2 + y2 = 9 Homework Equations Arc Length formula for integrals The Attempt at a Solution I have the correct answer at 3arcsin(2/3), but I tried to do this without calculus the first time...

Could someone please explain why PQ in the diagram below is rΔθ? Isn't rΔθ arc length? The best reason I can think of is that it's only an approximation for when the angle is very small, so PQ≈arclength=rΔθ. Not 100% sure though. http://imageshack.us/scaled/landing/199/feynmanangle.jpg...

Homework Statement A van is moving on a horizontal circular bend in the road of radius 75m. The bend is banked at arctan(1/3) to the horizontal. The maximum speed at which the van can be driven around the bend without slipping is 25m/s. Calculate the coefficient of friction between the road...

Homework Statement the graph of the equation x^(2/3) + y^(2/3) = 7^(2/3) is one of the family of curves called asteroids. Homework Equations find the length of first-quadrant and multiply by 8. 1. y=(7^(2/3) - x^(2/3))^(3/2)) ; 7sqrt(2)/4 <= x <= 7 The Attempt at a Solution...

How to calculate length of arc? Please Help! First of all, Hi, I'm Brandon! :) 18 Years old currently doing A Levels - Uni End of this year! (Not Homework - Coursework!) So I have this design of a speaker system for my Product Design course in A-Level. There are 3 arcs in my design that I...

Homework Statement (see attachment) Homework Equations The Attempt at a Solution Do I need to take torque about C here? Any help is appreciated, Thanks!

Homework Statement A pilot of mass 50 kg comes out of a vertical dive in a circular arc such that her upward acceleration is 6g. (a) What is the magnitude of the force exerted by the airplane seat on the pilot at the bottom of the arc? (b) If the speed of the plane is 390 km/h, what...

Homework Statement See attachment Homework Equations eAB=(Lf-Lo)/(Lo) The Attempt at a Solution Ok, this is not for HW. I am preparing for a mechanics of materials class next semester. I don't understand when CB goes through the 0.3 degree arc, they say the height is still 300mm. Shouldn't...

Good morning, I'm trying to compute the arclength (geodesic distance) between two n-dimensional points over a n-dimensional sphere (hypersphere). Do you know if it is possible? If yes, please, I'd be very pleased if you, as experts, provide me this knowledge. Thank you very much

Arc area of a sphere? (a piece of r^2*sinθ*ΔrΔθΔφ) Hello, this is not a homework question. I'm trying to self-derive the divergence formula in spherical coordinates, and I'm doing this by taking a small arc-volume about the point (r,θ,φ), where r is the radial distance from the origin, θ is the...

I am exploring what electricity can do and I have a question. First, can I use ionized gas to make an electric arc at low current? Second, If I can do this, what kind of ionized gas could I use (that is bottled), can I use?

I don't understand why finding the arc length is always difficult. I understand the formula and know pretty much all the integration methods, but whenever I try to find the arc length of a function like 8x2 = 27y3 from 1 to 8 it's unusually difficult. I would start by solving for x...

x = t + cot t y = t - sin t 0 ≤ t ≤ 2π Somehow the answer is: 2π ∫sqrt(3 - 2*sin t - 2*cos t) dt 0 I'm afraid I don't know where to start on this one. I don't need someone to walk me through it (probably) but a point in the right direction would be appreciated.

Hello everyone, I am having a bit of an issue evaluating the arc length of the function 1/2(e^x+e^-x) interval [0,2]. We were instructed to solve using the arc length formula square root of 1+(dy/dx)^2. The solution should be 3.627 according to my CAS. However my calculations are yielding 3.511...

Yesterday on another forum, someone asked for the launch angle which will maximize the arc-length of the trajectory for a projectile, assuming gravity is the only force on the projectile after the launch. I eliminated the parameter t to get the trajectory: $\displaystyle...

1. v=s/t where s represents the displacement 2. s=rθ where s represents the arc length v=rθ /t Why can substitute here? I guess that is not same things. An arc length is not a straight line but displacement is which is shortest distance between initial and final point.

Need help finding the length of an arc...must be dependent on a specific diameter. Basically, I want to hang outdoor string lights (I have a rectangular backyard). These lights will be attached to a flexible bar that will go from one fence to another. The height of the fence is 4 feet tall...

Hi folks. I'm working on an arc length problem, and my answer doesn't match the answer that our professor gave, so I was hoping that someone could point out where I'm going wrong here. Homework Statement Find the arc length determined by x^2=y^3 from (0,0) to (1,1).all of the work is in the...

Homework Statement Find an arc length parametrization of the circle in the plane z=5 with radius 6 and center (4,1,5) Homework Equations ||r'(t)||=r'(u) s=integral r'(u)du The Attempt at a Solution I get the equation of the circle to be (x-4)^2+(y-1)^2+(z-5)^2=6^2 Not sure where...

If we divide the polar curve into infinitely thin sectors, the arc length of a single sector can be approximated by ds = \frac{dθ}{2π}2πr = rdθ. So why can't we model the arc length of the curve as \int^{β}_{α} rdθ It turns out that the correct formula is actually...

Homework Statement Find the x-component of the electric field at the origin due to the full arc length for a charge of 3.8 μC and a radius of 1.9 m. The value of the Coulomb constant is 8.98755 × 109 N · m2/C2. Homework Equations E = kq/r^2 dq = q dθ λ = Q/ (R θ) The Attempt...

A 180 degree circular arc (i.e. a half sphere) is obvious: When you rotate this about its two end points, you get a sphere. What about for something less than 180 degrees (e.g. 90)?: I believe this forms an ellipsoid, with coefficients a and b being equal, with respect to...

I don't understand the intuition/proof of why arc length = arc angle * radius. This may be partially because I don't fully understand the concept of radians, but anyhow please help.

I have a parabola centered at x=0, equation: y = a*x^2 + c, where a is always negative and c always positive. I need to find a way to calculate a and c, if i know: the arc length above the x axis, and the base width, knowing the base width i also know the x-axis intersections x1,2 =...

Exercise #27 from a textbook called Kiselev's Geometry / Book I. Planimetry: Using only compass, construct a 1 degree arc on a circle, if a 19 degree arc of this circle is given.Please, check my reasoning on this one. I just want to make sure that I'm getting it right. My solution: Using a...

Homework Statement 27. Use the parametrization x = tcost, y = tsint of the Archimedean spiral to find the arc length of the first full turn of this spiral (corresponding to 0 <= t <= 2∏ ). Homework Equations The Attempt at a Solution I use onenote and a tablet, so my exact attempt in in the...

Homework Statement r(t)=ti+2tj+(t^2-3)k or r(t)=(t, 2t, t^2-3) 0≤t≤2 Homework Equations arc length formula ∫[the scalar of dr/dt] I know I can calculate the arc length through the equation above, but the questions asks for me to utilize this formula. ∫√(t^2+a^2) dt =...