Curves Definition and 778 Threads

Homework Statement A car enters a turn whose radius is ##R##. The road is banked at angle ##\theta##, and the coefficient of friction between the wheels and the road is ##\mu_s##. Find the minimum and maximum speeds of the car to stay on the road without skidding sideways Homework Equations...

It is well known that a curve in ##\mathbb{R}^3## is uniquely (up to a position in the space) defined by its curvature ##\kappa(s)## and torsion ##\tau(s)##, here ##s## is the arc-length parameter. We will consider ##\kappa(s),\tau(s)\in C[0,\infty)## Thus a natural problem arises: to restore...

Why during a banked curve is the horizontal component of the normal force considered as the net force and the centripetal force? The horizontal component of Normal force, N·sinθ, is not even ponting towards the centre of the curvature.

Which galaxy has the largest angular momentum of all galaxies observed? What does its rotation curve look like? Which galaxy has the smallest angular momentum of all galaxies observed? What does its rotation curve look like? Which two galaxies are closest to one another? What do the rotation...

I am looking for a family of curves where if we consider one curve of them and get the tangent of that curve at any arbitrary point on the curve, then you will always find a point in the other curves where the tangent of this point is perpendicular to the tangent of the first point. My guess...

I am reading Maxwell's "a treatise on electricity and magnetism" and I came across a formula of "potential of two closed curves s and s' " ##M= \iint\dfrac{cos\varepsilon}{r} dsds'## where: ##M=## potential of two closed curves s and s' ##\varepsilon=## angle between elements ds and ds'...

Homework Statement Homework EquationsThe Attempt at a Solution I knew the answer was between A and B, but the inward curves and outward curves on the position time graph confused me , what exactly does it mean? -does A have an increasing velocity and then B has a decreasing velocity? I am...

Homework Statement "Areas of regions Make a sketch of the region and its bounding curves. Find the area of the region." "The region inside the curve ##r = \sqrt{cosθ}## and inside the circle ##r = \frac{\sqrt{2}}{2}##. Homework Equations ##A = \frac{1}{2}\int_α^β(f(θ)^2-g(θ)^2)dθ## Answer as...

Homework Statement Consider the parametric curve given by: x=6cos(2t), y=t5/2. Calculate the equation of the tangent to this curve at the point given by t=π/4, in the form y=mx+c. The tangent is given by y= Homework Equations The Attempt at a Solution [/B] the answer that I got was...

Apologies if this is a really stupid question, but what is the exact argument for why one can use proper time to parametrise timelike curves? Is it simply that the arclength of a timelike curve is its elapsed proper time and hence we are simply parametrising the curve by its arclength? Also, is...

What is the physical meaning of acoustic and optical branches in phonons dispersion curves ?

When I plot the isenthalpic curves in T-P plane, I see isenthalpic curves are not well defined in the lower temperature region in T-P plane. Inside the inversion curve Joule-Thomson coefficient is positive so gas cools and outside of the inversion curve Joule-Thomson coefficent is negative so...

Hello, In a physics paper, I have encountered an expression about genus of one dimensional anharmonic oscillators. More specifically, they classify cubic and quartic anharmonic oscillator as "genus one potentials" and higher order anharmonic oscillators as "higher genus potentials". I am new...

I am a medical researcher with little physics background but currently completing a study of the physical characteristics of arteries. I am trying to compare the stress-strain curve from my study with that of other studies. The problems are 1) the dimensions of the arteries in these other...

I'm having difficulty understanding the definition of homotopy. In the notes attached I'm not sure what the mapping does and why the cartesian product is used. does t represent the parameter and s any curve between phi(1) and phi(2)? Any help would be appreciated

Homework Statement Consider the parametric curve x=ln(t) and y= 1+t^2 i need to eliminate the parameter to find the cartesian equation Homework EquationsThe Attempt at a Solution if i solve for t using x I get that t=e^x but if i solve for t using y i get t=(y-1)^(1/2) when i plug in x into...

Homework Statement So I have to plot 2 sets of IV curves for my lab and find the operating points of where they cross. Problem is, they don't cross! I'm not sure if this is the right place to ask, but my professor isn't responding to my emails so here it is. This is what the circuit looks...

Homework Statement Find area bounded by functions y_1=\sqrt{4x-x^2} and y_2=x\sqrt{4x-x^2}. Homework Equations -Integration -Area The Attempt at a Solution From y_1=y_2\Rightarrow x=1. Intersection points of y_1 and [/itex]y_2[/itex] are A(0,0),B(1,\sqrt 3),C(4,0). Domain of y_1 and y_2 is...

Homework Statement ƒ(x,y) = ln(x2+4y2) Homework Equations I'm not really sure but I solved for y The Attempt at a Solution

Hi everybody, I hope some of you have worked with pulsars before or other x-ray data from NASA Heasarc. I need some data showing a very precise light curve of the crab pulsar and some other pulsar. It should be something like this: http://cdn.eso.org/images/screen/eso9948i.jpg Where the time...

Hi all, I'm hoping someone can help me out with this problem. I am following an example of a previous report to analyse some test results, but am having trouble with this step. The tests plot moment-rotation curves of a horizontal member fixed into a vertical member. You run 5 tests, and for...

Hi Folks, I am struggling to see how eqn 4.1.17 is determined using eqn 4.1.10 for problem 4.1.2. It is not clear to me what \frac{d\phi}{dt} is. I have inserted the eqns I think might be useful into the one jpeg. Any ideas? Sorry I can't make the picture any clearer given the size limit. Thanks

Hi Folks, I am struggling to see how eqn 4.1.17 is arrived at using using eqn 4.1.10 at bottom of attachment. Its not clear to me what \frac{d \phi}{dt} is...apart from what is given in eqn 2.1.30... Any ideas? Thanks

Hi Folks, I am puzzled how entries M_13 and M_23 were obtained in the following matrix M_{2f} as in attached picture. Coordinate systems S1 is attached to bottom left circle, S2 to top left circle and Sf is rigidly attached to the frame. If we assume \phi_{2}=0 we can see that entry 31...

I don't really understand how the centripetal force arises from driving on a banked curve. There are three forces acting on a car in circular motion on a banked curve: normal force, gravity, and applied force. Let's assume that there is no friction, and that somehow the car is already at a...

There are two series on a graph, series A is the prediction of a value over time, series B is a curve of observed values over time. How can one quantify how much series A resemble series B?

Homework Statement Hi,[/B] I am trying to get an envelope function for two sinusoidal curves (A, B) added up. a1,a2 are the amplitudes(metre), T1,T2 are the periods (hrs), B lags by dt from A at t=0. case-1: a1= 1, a2=0.5, p1=11,p2=10,dt=0 w1=2*pi/T1,w2=2*pi/T2 A = a1*cos(w1*t)...

Obviously, they exist as mathematical concepts, and those concepts are real, but in physical reality, everything is made up of subatomic particles and, if the theory is ever verified, strings. So if you try to construct a curve, circle or sphere, you are necessarily stacking a bunch of subatomic...

my father who is an MBA not a PhD asked me: Which is it more correct to say Mass curves space and bends light or Gravity curves space and bends light or Mass curves space and gravity bends light or some other phrasing? My answer was/is: Interesting distinction you're seeking Gravity causes...

Hi PF! Can anyone tell me what you think the best method is to calculate the % error between two curves? My thoughts were to take $$100\frac{ \sqrt{\int_a^b (f-g)^2 \, dx}}{\int_s f \, ds}$$ where the integral in the denominator is a line integral. What are your thoughts? Thanks for looking!

Homework Statement Given u(x.y), find the exact differential equation du = 0. What sort of curves are the solution curves u(x,y) = constant? (These are called the level curves of u). u = cos(x2 - y2)The Attempt at a Solution partial derivative du/dx = (-2x)sin(x2 - y2)dx partial derivative...

Hey! :o In some notes that I am reading there is the following: $$(\delta s)^2=(\delta x)^2+(\delta y)^2 \Rightarrow \left (\frac{\delta s}{\delta x}\right )^2=1+\left (\frac{\delta y}{\delta x}\right )^2$$ When $\delta x \rightarrow 0 $ we get $$(s'(x))^2=1+(y'(x))^2 \Rightarrow...

Would someone explain to me in lay men's terms exactly what a CTC is. I understand that it is a closed timeline curve and that it allows( in theory) time travel to one's past. My question is how does one get into a CTC: Do you have to be traveling in space and at a certain speed? Does one...

a) At what point do the curves r1(t) = (t, 2 − t, 35 + t2) and r2(s) = (7 − s, s − 5, s2) intersect? (x,y,z) = b) Find their angle of intersection, θ, correct to the nearest degree.

Solve the following Cauchy problem using the Method of characteristic curves: $x_1u_{x_1}+x_2u_{x_2}=\alpha u$ in $\mathbb{R}^{+}\times \mathbb{R}^{+}$ $u(x_1,1)=g(x)$ for all $x_1\in \mathbb{R}^{+}.$ Find the local solution for the problem.Hello. I get as solution $g(s)=s$, I want to know if...

I'm looking for experimental correlation curves in Violation of Bell inequalities. I found only one in http://arxiv.org/abs/quant-ph/9806043 Do you think as an amateur we could ask per mail this data to professionals having done this experiment ?

What is the exact difference between null geodesics and null curves? Please explain both qualitatively and quantitatively.

Hi everyone, Thanks for visiting my post. I was wondering if you guys know what kind of software I must use to draw complicated curves. I already have the equations. For example, for lemniscate I would use following: 2(x^2+y^2)=25(x^2-y^2) I appreciate the help.

I'd like of draw any curve using combination of line circle, elipse, parabola, hyperbola and straight. Of course several curves can't be designed with 100% of precision using just conic curves, but, can to be approximated. Acttualy, I don't want to reproduce a curve already designed but yes...

I am reading C. G. Gibson's book: Elementary Geometry of Algebraic Curves. I need some help with aspects of Example 1.4 The relevant text from Gibson's book is as follows: Question 1In the above text, Gibson writes the following: " ... ... Then a brief calculation verifies that any point p +...

In the analysis of Random vibration, we use the PSD curves as the input, I am confused as to why we simply don't use acceleration versus time graph but instead convert it into g^2/Hz and Hz.

I am reading Ernst Kunz book, "Introduction to Plane Algebraic Curves" I need help with some aspects of Kunz' proof of Theorem 1.3 ... The relevant text from Kunz is as follows:http://mathhelpboards.com/attachment.php?attachmentid=4559&stc=1In the above text we read the following: " ... ...

I am reading Ernst Kunz book, "Introduction to Plane Algebraic Curves" I need help with some aspects of Kunz' Definition 1.1. The relevant text from Kunz' book is as follows:In the above text, Kunz writes the following: " ... ... If K_0 \subset K is a subring and \Gamma = \mathscr{V} (f) for...

I am reading Ernst Kunz book, "Introduction to Plane Algebraic Curves" I need help with Exercise 1, Chapter 1 ... Indeed ... I am a bit overwhelmed by this problem .. Exercise 1 reads as follows: Hope someone can help ... ...To give a feel for the context and notation I am providing the...

I am reading Ernst Kunz book, "Introduction to Plane Algebraic Curves" I need help with Exercise 1, Chapter 1 ... Indeed ... I am a bit overwhelmed by this problem .. Exercise 1 reads as follows:https://www.physicsforums.com/attachments/4549Hope someone can help ... ...To give a feel for the...

I am reading Ernst Kunz book, "Introduction to Plane Algebraic Curves" I need help with interpreting Example 1.2. The relevant text pertaining to Example 1.2 is as follows: https://www.physicsforums.com/attachments/4548 Question 1 In Example 1.2 above how do we interpret aX + bY + c = 0? ...

can any tell me about laser diode, how it operate and I-v curve of laser diode?

Find the area of the region in the first quadrant bounded by the line $y=x$, the line $x=2$, the curve $y=\frac{1}{x^2}$ $$\int_{1}^{2}\left(x-\frac{1}{{x}^{2}}\right) \,dx$$ just seeing if this is the way to go.

I don't have a particular problem in mind here, so please move this thread if it's in the wrong section. I was wondering, when you're trying to find the area bounded between two curves, is there a foolproof way to choose which curve to be g(x) in (let S be the integral sign, haha)...

I am interested in whether it is necessary to account for the effects of the Hubble Redshift in determining the rotation velocities of galaxies exhibiting keplerian motion and, in particular, whether the associated spatial expansion of the Universe is known to result in spectral shifts that...