Path Definition and 1000 Threads

This is a mechanics question which has come up a number of times in end of year exams in my college, I hope this is the right forum to post it in. Homework Statement A particle travels around an elliptical path with a constant speed of 1 m/s. If the equation of the ellipse is (x^2)/3 + y^2...

Homework Statement Let G be a graph. 1. Let n be a natural number. Use induction to show for all n >= 2 Kn has a Hamiltonian path. 2. Explain how you could use the proof from #1 to show that for all n (natural number) n > 2 Kn has a Hamiltonian cycle. Homework Equations The...

This is more of a hypothetical "it doesn't work, but WHY?", but what stops something from being at point A now, then moving to a different point an instant later without traveling through the space in-between? What makes it so that the motion we observe is always (nearly) contiguous? Is there...

Homework Statement A model land-yacht runs on a horizontal frictionless oval track as shown (viewed from above) in the figure. The curved parts of the track are semi-circles of radius R = 0:5 m; the straight sides have length L = 1 m. The mass of the yacht (including its sails) is m = 0:5...

I have gained a place on the graduate rotational leadership programme at a major heavy industrial company which involves me going to different divisions to lead projects. I have been given a choice of either going down the R&D path or the Operations Management path. Being an engineer from a top...

The path of electrons emerging grom an accelerator must be bent by 90° by a 'bending magnet' so as not to strike a barrier in their path a distance d from their exit hole in the accelerator. Show that the field B in de bending magnet, which we assume is uniform and can extend over an area d*d...

Does the moon's orbit depends mainly on the gravity of Earth and the distance between it and between earth?

When doing a path integral to determine the work done by a particle : http://latex.codecogs.com/gif.latex?\int&space;\textbf{w}\cdot&space;d\mathbf{s} Where F is some vector. Now, I can't remember what ds is. I vaguely seem to remember that it is some unit vector parallel to and in the...

Hi Physics Forum, I know the question is broad, but I do wish for advice on this matter. I will be graduating in one month with my degree in Mechanical Engineering and I was hoping for some guidance based on my education and experience. I have completed three internships and one senior...

Homework Statement A satellite is at an altitude of 3R (R- Radius of the planet) circulating around the planet with a velocity v. In order to make its path elliptical the velocity is changed from v to βv. What should be maximum value of β such that the satellite doesn't collide with the...

I am trying to calculate the functional for real scalar field: W[J] = \int \mathcal{D} \phi \: exp \left[{ \int \frac{d^4 p}{(2 \pi)^4}[ \frac{1}{2} \tilde{\phi}(-p) i (p^2 - m^2 +i \epsilon) \tilde{\phi}(p)} +\tilde{J}(-p) \tilde{\phi}(p)] \right] Using this gaussian formula...

There is a circular gate rotating at a constant angular speed of ω. The circular gate has a tunnel across its diameter. The mission is to pass through the gate. (That is, come in one side of the gate, travel the whole diameter, and exit at the other side.) Also, craft is neutrally buoyant...

1. Homework Statement Vector field is F=-y\hat{x} + x\hat{y} Compute the line integral along the path c(t)=( cos(t), sin(t) ) with 0≤t≤∏2. The attempt at a solution i started computing f.dl but how much is dl ? I took it dx\hat{x} +dy\hat{y} I'm not sure if using Cartesian coordinates is right ?

They state that the Earth ground cable connecting ground to the neutral wire inside the transformer is a feedback path for electrons. From that information I would conclude that without it the circuit would not be complete and current wouldn't flow. Then they follow by saying that the use...

Is there an equation in which you can model the flight path of a golf ball? I know there must be as there are plenty of "Golf Ball Flight Simulators". Does anyone know of this equation? Would be quite helpful to me.

Just a question about simple moving body exercise. With no acceleration. Body moves with speed 15 m/s, time 12 seconds, mass 0.8 kg, and the force have a side effect 5 Newtons. Firstly, F=mg, so 0,8*0,98.Then I calculated the actual moving direction's force by pythagoros, that's 0,95N...

Why is this true? $$ h = rv_{\perp} = r(r\dot{\nu})\Rightarrow\dot{\nu} = \frac{h}{r^2} $$ Look at the last page http://www.mathhelpboards.com/f49/orbital-mechanics-notes-3682/#post16317 to see a visualization.

I really need some guidance on what to do with my life. I'm going to do my best to organize my thoughts into an understandable manner, but forgive me if it sounds like I'm merely venting, as I have a lot on my mind. Basically I started out college in Mechanical Engineering, and after about a...

Hi! Given a function r:\mathbb{R} \rightarrow \mathbb{R}^2, r(t) = (f_1(t), f_2(t)), is there a way to analytically determine if there are points (x1, x2) where r(t) = (x1, x2) for multiple t-values? Lets say i was to find such points for the function r(t) = (t^3-t, 3t^2 + 1) How...

Use Stokes's theorem to show that line integral of ##\vec{F}(\vec{r})## over an curve ##L##, given by ##\int_L \vec{F}(\vec{r}) d\vec{r}##, depends only on the start and endpoint of ##L##, but not on the trajectory of ##L## between those two points. Hint: Consider two different curves, ##L##...

Homework Statement Evaluate ∫ F ds over the curve C for: a) F = (x, -y) and r(t) = (cos t, sin t), 0 ≤ t ≤ 2∏ b) F = (yz, xz, xy) where the curve C consists of straight-line segments joining (1, 0, 0) to (0, 1, 0) to (0, 0, 1) Homework Equations The Attempt at a Solution a) I first found the...

I'm interested in how to understand exactly how radio waves will propagate in a particular situation. I know that they are absorbed by metal and water, pass through other materials albeit with loss of power, and reflect or bounce off of surfaces as well. How do I know whether a radio wave will...

Homework Statement Let ##\gamma(t)## be a path describing a level curve of ##f : \mathbb{R}^2 \to \mathbb{R}##. Show, for all ##t##, that ##( \nabla f ) (\gamma(t))## is orthogonal to ##\gamma ' (t)##Homework Equations ##\gamma(t) = ((x(t), y(t))## ##\gamma ' (t) = F(\gamma(t))## ##F = \nabla f...

Homework Statement A narrow parallel light beam of wavelength 632.8 nm is incident upon a diffraction ruler (i.e. the light reflects off of the grating rather than passing through it). The ruler has 600 lines per mm. Show that the expression for the condition for constructive interference is...

Can a flight path angle be 356 degrees?

Homework Statement Find the path ##\vec\gamma(t)## which represents the level curve ##f(x,y) = \displaystyle\frac{xy + 1}{x^2 + y^2}## corresponding to ##c=1##. Similarly, find the path for the curve ##x^{2/3} + y^{2/3} = 1## Homework Equations None.The Attempt at a Solution Since the level...

Homework Statement Find a path \gamma (t) representing the triangle (1, 0, 0) to (0, 2, 0) to (0, 0, 3) to (1, 0, 0) Homework Equations NoneThe Attempt at a Solution Well I followed the steps on how to get an equation of a plane that contains the 3 vertices and I got 6x + 3y + 2z - 6 = 0...

Last night the BBC repeated Brian Cox, A Night With the Stars (). At some point a calculation is done using a simplified version of Feynman’s path integral, where the mean time is estimated for a diamond to be found outside a small box: t>\frac{x Δx m}{h} The box was not expected to be...

1. Problem Statement Transform equation 1 into equation 2 to show they're equivalent. Homework Equations *Please note that I added a subscript to each variable indicating the units. The Attempt at a Solution The highlighted constant shown in my attempt at the solution is...

Hi guys. My long term goals including going to grad school and going into academia. I'm at a point in my undergrad curriculum where I need to declare a major for sure. I've jumped around a lot in the past 2 years between chemistry, math, physics, and chemical engineering. My first 2 research...

Hi, I am trying to derive a formula for the path taken of a body in a Gravitational Field using Classical Mechanics. I have attached a pdf file with my derivation so far. Basically I used conservation of energy and conservation of angular momentum to derive a diferential equation...

Say given a simple acyclic directed graph with n nodes , which includes a starting node s0 and ending node e0 (i.e., a kripke structure without loop) what is the maximum number of path from s0 to e0?

my lecturer keeps saying that path of contact of an involute gear is straight line but without the reason. i can't digest it as i can't find the reason for this behaviour. I'm trying my best to find the reason. Internet too can't find an answer. Books don't give a timeline of how it happens. Can...

Hi, I have an exam tomorrow for atmospheric chemistry and I was just going over some past papers. In one it asks the following question, "What is meant by "Mean Free Path"? How is this relevant to atmospheric chemistry. My answer was as follows "The mean free path is the average distance a...

I've just begun studying graph theory and I have some difficulty with this problem. Could you tell me how to go about solving it? I would really appreciate the least formal solution possible. In a graph G all vertices have degrees \le 3. Show that we can color its vertices in two colors so...

What is the amount of energy required to change path/trajectory of a photon by an infinitesimal amount? In a single particle (double slit) interference, the photons land up on one of the interference fringes. (when no-which-way) If we were to place a magnet to try to slightly change the path...

Good morning, Case: You have a single photon emitter (quantum dot?) that you can control when a photon is emitted and a photon detector some distance away. You release a photon which is subsequently detected. In what cases is it reasonable to assume that the photon has indeed traveled at c...

latex: "include" with path, not just filename Say, a co-worker and I are writing two separate sections for the same document; each will get large and have many figures. Somewhere, I read that 'include' is more convenient than 'input' for large documents and for actual (sub)documents than just...

The combination of special relativity and quantum mechanics in a single framework makes our understanding of such systems to be true only in 4D, Minkowski space...I have noticed that recent published work concerning 2D systems and I am not sure about this reduction of 4D to only 2D, does it mean...

Hi, I've been reading up a bit on the shortest path problem in graph theory and was wondering if the problem I'm trying to solve is a variation of the same graph theory problem. Say you have a grid of vertices and edges representing aisles and cross-aisles in a warehouse. In a standard...

North Korean leader, in rare address, seeks end to confrontation with South http://news.yahoo.com/north-korean-leader-rare-address-seeks-end-confrontation-024100592.html It would be great if N Korea can make peace with the south - finally - after 59 years. It does seem to make for a...

hi , how earlier scientist figure out that Earth has elliptical motion rather than circular around sun?

One says that bosons do not interact with one another. However, the presence of a gravitational field, and hence of gravitons (bosons) (assuming they exist), changes the probability of where a photon (boson) appears, which is the same sort of interaction as two fermions, no? And, the contrary...

Integral through a path in 2D (or ND) What's the usual "definition"? [Bold letters are vectors. eg: r] We have a scalar function f(r) and a path g(x)=y. I see two ways to reason: (1) The little infinitesimals are summed with the change of x and on the change of y separately. (2) The little...

Suppose it's the equinox, when the Earth's closest point to the sun is the equator. Would people who live somewhere along the equator see the sun rise directly from the east, move directly above so, and set directly to the west? For instance, if someone, living on the equator, were to put a...

Homework Statement Al right so i am given this diagram. They are asking about the time for the whole journey. The car is traveling on a steep hill through the section of AD and which continues on to DC with a small curved path.Find the time for this journey. The car starts from rest at point...

In the very first example of Feynman and Hibb's Path Integral book, they discuss a free particle with \mathcal{L} = \frac{m}{2} \dot{x}(t)^2 In calculating it's classical action, they perform a simple integral over some interval of time t_a \rightarrow t_b. S_{cl} = \frac{m}{2}...

I just want to make sure my thinking and free body is correct before I go further in a project I am working on; for some strange reason (probably the curved path) I am doubting myself. I will try and explain the problem but the attached image is probably the best description. There is a...

Homework Statement Given the graph, determine if the following sequences form a walk, path and/or a circuit. http://img843.imageshack.us/img843/5686/digraph.png 1. a, b, c, e 2. b, c, d, d, e, c, f 3. a, b, c, f, g, a 4. b, c, d, eHomework Equations The Attempt at a Solution 1. It's not...

How is the speed of light, and path of travel, effected in time-space distorted (by say, gravity)? We know that the sun/earth's gravity distorts time-space. So when a photon travels from sun to earth...as it nears the earth... how much length would the photon travel? Would it be slightly...