Smooth Definition and 219 Threads

I've been presented with the following problems: SITUATION: A ball is rolling without slipping with velocity v on a horizontal surface. It reaches an incline, which forms an angle \theta with the horizontal. In which situation will the ball reach the highest point, when the incline has a...

e^{-x^2}\cos \left( e^{x^2} \right) Mathematica doesn't have an algorithm for it, does a closed form exist for the Fourier transform? It's continuously differentiable on all intervals in R, and it converges to zero at the infinities (the derivative blows up there).

Is it correct that the definition of a smooth manifold is an equivalence class (under diffeomorphism) of atlasses ? (this discussion is related to a discussion I try to start in general relativity concerning the hole argument).

Hi. I'm a bit stuck with that next question (and that's quite an understatement): Let f:M->N be a continuous map, with M and N smooth manifolds of dimensions m,n correspondingly. Define f*:C(N)->C(M) by f*(g)=g o f. Assume now that f*(C^infty(N)) subset C^infty(M). Then f is...

A uniform board is leaning against a smooth vertical wall. The board is at an angle above the horizontal ground. The coefficient of static friction between the ground and the lower end of the board is 0.350. Find the smallest value for the angle , such that the lower end of the board does not...

I know there are some, but I can't think of any examples. I asked my teacher after class but she couldn't think of any either.

Where can I buy smooth pinion for a friction drive system? I can't find any on web.

I gota problem with the fixed collar on a smooth rod. The collar is like a rigid metal T shapped pipe, and the top of the t is where the shaft of the rod goes through. (Its in any basic statics book). It says this type of set up has a normal force perpendicular to the axis of the rod, (OK that's...

I was reviewing my book when I got to thinking about a special type of connection, the "member fixed connected to collar on smooth rod" It prevents a force in the direction normal to the rod, and also prevents a moment. The first part is fine, but the moment part worried me a little bit. Since...

Hello everyone, I have read on the Internet that you can get the "brick oven effect" -- uniform heat distribution and crisp bread crusts -- from a regular gas or electric oven by placing tiles and/or firebricks under the food, and tiles above the food (bricks are too heavy to go above). 1...

Question:A body of mass is placed on a smooth horizontal surface. The mass of the body is decreased exponentially with disintegration constant λ. Assuming that the mass is ejected backwards with a relative velocity u.If initially the body was at rest, the speed of the body at time t is...

I just put slick tires on My Bicycle, my beloved Fuji. It used to have nubby tires. Now the ride is so smooth... They say that there is not a significant decrease in traction on smooth tires, because the rubber-coated nylon tires actually take on the shape of the pavement pebbles as they...

I think I did this problem correctly however I am not 100% sure. Unfortunatley the Dynamics book that I have only gives answers to even numbered problems and I cannot check me work. Anyway here is the problem from the book. The smooth circular bar rotates with constant angular velocity...

"Particles A, B and C , each of mass m, lie at rest in a straight line in the order stated. A is projected directly towards B with velocity u. The coefficient of restitution is 0.5 in each impact that follows. Show that there will be three impacts in total and find the final velocities of...

Bravo Europe Union, Shame on you France, Damn the Chinese are smooth... http://news.bbc.co.uk/2/hi/europe/3637807.stm Good Job to the EU for standing ground on true human rights and democracy. Shame on France (and Germany to an extent) for looking to cash in on the Humanitarian crisis...

http://researchnews.osu.edu/archive/fuzzball.htm

i am trying to solve this problem: Give the paraboloid y_{3}=(y_{1})^2+(y_{2})^2 the structure of a smooth manifold. But i am unsure what it means by structure. Can anyone give me some help here?

You don't need to solve this, just tell me what problem it is... although if you do solve it you'll be a million dollars richer. Prove the existence of smooth solutions to a certain model of incompressible fluid dynamics. This is the ... problem?

Linux for Windows Addicts INTRODUCTION Everyone has a stance in the OS debates, but I've really never taken a side. I have Mandrake on one machine and I could do some commands and simple stuff, but I didn't really know what Linux was all about. I've been a Windows person forever and I took...