Curve Definition and 1000 Threads

Homework Statement The figure shows a plot of potential energy U versus position x of a 0.220 kg particle that can travel only along an x axis under the influence of a conservative force. The graph has these values: UA = 9 J, UC = 20 J and UD = 24 J. The particle is released at the point where...

I'm studying Calculus and i can see that the definition of the tangent to a point on a curve is y= f'(a)(x-a)+b this must mean that f'(a) = (y-b)/(x-a) But that to me seems troubeling, because f'(a) is the slope at ONE point, while (y-b)/(x-a) is a quotient with the difference between...

Homework Statement If the coefficient of static friction is 0.38 (wet pavement), at what range of speeds can a car safely make the curve? [Hint: Consider the direction of the friction force when the car goes too slow or too fast.] Homework Equations I am trying to figure out the Vmax 3. The...

I was reading about the tangent vector at a point on a curve. It is formulated as r' = Lim Δt→0 [r(t+Δt) - r(t)] / Δt (sorry for the misrepresentation of the 'Lim Δt→0 ') where r(t) is a position vector to the curve and t is a parameter and r' is the derivative of r(t). All I can...

If I'm correct in thinking light curves towards objects with less entropy; why wouldn't the path of least resistance be towards entropy?

Homework Statement Homework EquationsThe Attempt at a Solution Since the tangent moves at uniform angular speed ,the particle also moves with constant angular speed . Is it correct ? If it is right then the particle has only radial acceleration given by ##ω^2r## ,where 'r' is the radius of...

-3x2 - 8x*y + 3y2 = 1 . Specifie also the axis of the given curve.

Homework Statement Calculate the tangent vector to a curve $$r=R(1-\varepsilon \sin ^2 \varphi)$$ as a function of ##\varphi## Homework EquationsThe Attempt at a Solution Ok, I tried like this: I defined a vector $$(f(\varphi),\varphi)=(R(1-\varepsilon \sin ^2 \varphi),\varphi)$$ and than I...

Homework Statement Homework Equations (y-y1)/(x-x1)=mThe Attempt at a Solution I have attempted part i but I don't know how to do part ii. As point B is still part of the curve and the normal, do I still sub with the same normal eqn? :/ I have no idea how to start... Please help thanks[/B]

Hello, If for a curve in Cartesian coordinates ##||\dot{{\mathbf r}}||=\mbox{const}## (i.e. the curve is constant speed) will the speed of the curve change in cylindrical and spherical coordinates? Could someone experienced share how the transition from flat Euclidian space to curved space...

Homework Statement [/B] I'm trying to write a program in MATLAB which demonstrates a tautochrone curve and how the starting point of a ball is irrelevant as to the time it takes to get to the lowest point in the curve (without friction). At the moment I'm just trying to model it using a simple...

Can we plot stress-strain curve if we only have yield strength, tensile strength, and elongation data? For example if i have: Yield strength = 300 MPa Tensile Strength = 600 MPa Elongation = 50% How to plot the stress-strain curve? Thanks

Homework Statement Let f(x,y)=arctan(x/y) and u={(√2)/2,(√2)/2} d.) Verify that ∇fp is orthogonal to the level curve through P for P=(x,y)≠(0,0) where y=mx for m≠0 are level curves for f. Homework Equations The Attempt at a Solution ∇f={(y)/(x^2+y^2),(-y)/(x^2+y^2)} m=1/tan(k) where...

Hello, everyone! My question is really simple, in fact I even feel a bit ambarrassed of asking it. :x Imagine that a car is making a constant radius turn, of a given radius R. For the purposes of this question is enough to say that the car may be thought as an isosceles trapezium, or even as a...

On a stationary, non-periodic signal (black) a smooth causal filter is calculated (green/red). It is sampled discretely (every distance unit of 1 on the X-axis). My goal is to find which "path" it is "travelling" on so I can extrapolate the current shape until it is completed (reaches a...

Hello everyone, I am not a physicist nor do I know that much about physics. I do however have a physics question and this seemed like a great place to get an answer. I will present my situation the best I can. I work in the Horizontal Directional Drilling industry. This industry installs...

Homework Statement Find the points on the curve xy^2+x^2y=16 when the tangent line is horizontal The attempt at a solution I found the derivative of the curve -(y(2x+y))/(x(x+2y)) then I found what values of y make the derivative equal 0 y=0,-2x Then I went to plug into the original curve to...

Having some trouble with this.. Need to find equation of a line with a slope of -1 that is tangent to the curve y=1/(x-1). So, rearranging slope formula as y=-1x+k and setting the equations equal, y=-1x+k=1/(x-1) y=(-1x+k)(x-1)=1 Here is where my multiplication is either totally wrong or I am...

Hello, I am currently trying to parametrize a surface constructed by thickening a rather complicated curve, defining its normal, binormal and tangent vectors. Even using Mathematica simplification, the resulting vectors are page long expressions and the reason for it is because I have four...

Find the area of the regions shown in the figures. These are the graphs used : y = x^2 x = 2 Sin ^2 (y) I know that I need to set the two equations equal to each other in order to find the points of intersection, but I run into some trouble when trying to simplify it for y. This is what...

Homework Statement For a crystalline metal material - Elastic modulus E - Poisson ratio v - A table with test data of stresses vs. total strains, from a monotonic uniaxial tension test, which generates a stress-strain curve. How would you use this data to find the corresponding pure shear...

Homework Statement The problem: the distribution of pressure of the left side of the circular cylinder Homework Equations ρ= the density of water γ=ρg P=ρgh circle O = a long wooden circular cylinder The Attempt at a Solution MY QUESTION: Please see the curve...

I've been a bit lost figuring out what damper I should be using for the front suspension I am designing. Right now I'm running a wheel rate of 60 lbf/in at the front with a ride frequency of 1.2254 Hz. The front is also supporting a sprung mass of 391.68 lbf. Comfort is the end requirement of...

I am trying to understand how the width of a supernova light curve depends on the redshift of its component frequencies. Let us make the simple assumption that the light curve is Gaussian. The inverse Fourier transform of a Gaussian is given by: $$\large e^{-\alpha...

Hi, I've been thinking about how to calculate a permeability curve, I thought this would be an easy to find online but unfortunately I haven't had any luck. From what I can graphically see below: It appears to me that mu for a ferromagnetic material is proportional to the derivative of B vs H...

Hi, If you've got an arbitary magnetic Flux1 and Flux2, traveling in the same or opposite directions, through a core, it doesn't matter with regards to the point on the saturation curve does it? Opposing or in the same direction it'll still be at the same point on the mag curve won't it?Thanks...

Are there closed curve solutions for ##\mathbf{v}(t) \in \mathbb{R}^3## satisfying this constraint? $$\mathbf{v}(t) \cdot \frac{d^2}{dt^2}\mathbf{v} = 0 $$

Homework Statement Calculate ∫C \frac{dz}{z(z+a)} where C is the unit disk Δ(1) with counterclockwise orientation where a is a complex number with |a| < 1. Homework Equations ∫L \frac{dz}{(z-p)}= 2πiν(L,p) The Attempt at a Solution Using partial fraction decomposition, ∫C...

Homework Statement Let's say I have a Langmuir probe I-V characteristic from the Helimak experiment. The plasma ions are singly ionized argon. The probe has an effective area of 0.000016 m^2. Estimate the floating potential, electron density, and temperature. Based only on the nature of the...

Assume perfect sphere lands on a surface given by the function z = 2x2 -3y2 at point (2,1,5). I am trying to find a unit vector of the direction in which this perfect sphere will roll. If I get grad F I'll get a vector field that is perpendicular to the level curves f(x,y) = z = 2x2 -3y2. This...

Homework Statement i trying to figure out why the head-flow curve changes at the speeds of 90, 80 and 70 revs and was told that i might want to look into reynolds number for this as the head coefficient is somewhat dependant on this. Homework Equations Ch=gH/(Nd)^2 Cf=Q/Nd^3 pi=f(Q/Nd^3, re)...

Hey! :o Find the curve $\overrightarrow{\sigma}(t)$ that describes the following curve or trajectory. Make a graph. $$\{(x, y) \mid 4x^2+y^2=1\}$$ How can I find such a curve??

Hey! :o Let $\overrightarrow{\sigma}$ a curve in $\mathbb{R}^3$ with zero acceleration. Show that $\overrightarrow{\sigma}$ is a straight line or a point. Let $\overrightarrow{\sigma}(t)=(x(t),y(t),z(t))$ be the curve. We have that...

Homework Statement A race car going around a flat, unbanked circular track gradually increases speed as it completes one full trip around the track. Which of the following can explain why the car gains speed? (A) Energy stored in the fuel is converted to mechanical energy. (B) A component of...

Area under decay curve exp(-0.6969t/h) where t is the time (with t=0 initially) and h is a constant "half life" is analytically integrable, but what if the half life is increasing with time? I. e. if h(t) = H + at. (Note exp(-0.6969) is not exactly 0.5 but close and easy to remember.) This...

Homework Statement Find an equation of the tangent line to the curve at the given point. Homework Equations y=x¼ Point = (1,1) The Attempt at a Solution [/B] Derivative of y is y' = ¼x-¾ Plugging in the derivative to the equation for a line: y-1=¼(x-1)-¾. My book's answer is Y=¼x+¾, but I...

The arc length of any curve defined by ##y = f(x)## is found as follows: $$ds = \sqrt{dx^2 + dy^2}$$ $$ds = \sqrt{dx^2(1 + {\frac{dy}{dx}}^2)}$$ $$ds = \sqrt{dx^2} \sqrt{1 + [f'(x)]^2}$$ $$ds = \sqrt{1 + [f'(x)]^2} dx$$ Isn't ##\sqrt{dx^2}## equal to ##|dx|##, and not ##dx##?

Last semester I was very upset to learn that I had scored 25% on the final exam for my linear circuits course and was ready to change majors...until I learned that the class average on the final was 19%. And the average final grade for the class was 40%. I ended up getting an A, despite a final...

Hi everyone ın fact at the beginning ı want to select three points every curve Idid it But now I shold find which points ont the same time AND THEN I shold save its How can do it My code is here #include <iostream> #include <iostream> #include "opencv2/highgui/highgui.hpp" #include...

Hello to everyone. I would like to ask a question: I'm analyzing the properties of CO2 for a project and I have noticed that for temperatures between 220 -300 K the Clasius Clapeyron curve is linear on 1/T, that is in the Antoine equation of the form logP = A-B/(T+C), C is almost 0. In my...

I hope this is in the right forum. I'm trying to see how to calculate rotation curves for a spiral galaxy. The data I have is brightness profile (mag/arcsec^2) and observed rotation curve - to see how it fits. from what I found I need the total mass, and for that I need the surface mass density...

Whats the difference between a level set and a level curve, with regards to multi-variable calculus?

Hi all, I was wondering if anyone could help me with calculating the angle of lean on a motorbike on a banked curve (with friction). If possible proofs would be very useful. Thanks Lee

Let's say I want to calculate some instantaneous speeds during a trip from city a to city b. I start down the highway from an initial speed of zero then increased to 55. After 15 minutes I increase to 70. Down to 60 for 2 minutes. Then up to 80 for 15. Back down to 70. Then a slow decrease to...

Dear users, I deal with following problem. I've got a data of Intenzity of chemiluminezcence as a function of temperature. The data should be fitted by following equation: I found that in origin one can fit also data with integral function, with fittin parameters P, A, i, E. The beta and...

Homework Statement Sketch a picture of the cone x = sqrt(y^2+z^2) , and elliptic paraboloid x = 2−y^2−z^2 on the same grid. Although the picture does not have to be perfect, indicate clearly the orientation of both figures relative to coordinate axes. Identify the curve at the intersection of...

Homework Statement Find the domain of the function f(x,y) = 1/sqrt(x^2-y). Sketch the level curves f=1, f=1/2, f=1/3. Homework EquationsThe Attempt at a Solution Domain is rather simple to find: x^2>y AND x^2-y cannot equal 0. Level curves are also simple to find. They are simply parabolas...

Homework Statement Use, using the result that for a simple closed curve C in the plane the area enclosed is: A = (1/2)∫(x dy - y dx) to find the area inside the curve x^(2/3) + y^(2/3) = 4 Homework Equations Green's Theorem: ∫P dx + Q dy = ∫∫ dQ/dx - dP/dy The Attempt at a Solution I...

How can we determine which curve has larger slope just by looking at curves. http://www.meritnation.com/img/shared/userimages/mn_images/image/a_2_12_2.png Which curve has larger slope?

I went through this article: http://users.df.uba.ar/sgil/physics_paper_doc/papers_phys/ondas_optics/caustica1.pdf But I think that when we do F=0, we are assuming the centre of the curve to be the origin and assuming the curve to be a circle, because only then will we be able to say that OP=ON...