Questions related to mathematical physics which include application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories

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why $c$ in Einstein equation is Squared? [on hold]

why the speed of light is Squared in $E=mc^2$ - I want explain I am not a specialist in mathematics
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0answers
8 views

side information from equations

Consider system of equations (linear or nonlinear) generated from financial or physical problems. First, the solution to the equations will give information about the problem. Besides the solution, is ...
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0answers
52 views

What if segments are not infinitely divisible?

I almost got myself mixed up I a philosophical discussion again. Somebody was talking about the Planck time and length which are, according to him, the minimal possible time and distance, and how ...
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2answers
50 views

Solving a differential equation?

I'm trying to analyze the transient state of a RC circuit. My book gives me the following differential equation: $$\frac{d(v(t))}{dt} + av(t) = c$$ for some constants $a$ and $c$. The book thens ...
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0answers
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Finding the distance from a parabola (ballistic trajectory) to a point (for use in collision detection)

I need to have some form of collision detection / prevention for an object moving along a ballistic trajectory and a second stationary object on the same plane plane. The ballistic trajectory is ...
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2answers
21 views

what are some typical systems of equations generating from practical problems?

I want to know some typical forms of system of equations generating from practical problems in engineering/economics/physics,etc. Some examples or research articles would be good. Specifically, I am ...
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0answers
12 views

How to calculate direction of ball upon collision?

I'm creating a game (Breakout) that involves a paddle and ball. I'm having trouble calculating the direction that I should send the ball after collision with the paddle. Currently, upon collision ...
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0answers
43 views

Approximate an integral

In a physics textbook, I came across the integral $$I(r_1,r_0)=\int_{r_0}^{r_1}\frac{1}{1-2m/r}\left[1-\frac{r_0^2(1-2m/r)}{r^2(1-2m/r_0)}\right]^{-1/2}dr$$ The author said that the integrand can be ...
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0answers
5 views

Finding the gravitational potential of a tilted disc?

Referring to this question: http://physics.stackexchange.com/questions/62637/the-potential-and-the-intensity-of-the-gravitational-field-in-the-axis-of-a-circ Suppose the disc was tilted at a 30 ...
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0answers
23 views

Complex Number Plane Physics Math Problem

Show that if the line through the origin and the point z is rotated 90°about the origin, it becomes the line through the origin and the point iz. Use this idea in the following problem: Let ...
2
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1answer
33 views

A question about the Laws of Thermodynamics [closed]

Many popular and semi-popular books about cosmology have appeared during the last few years in which the ultimate fate of the Universe is conjectured. One such scenario stipulates that space will ...
1
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1answer
67 views

When are $\Delta x$, $\delta x$, $dx$, and $\text{đ}x$ exactly the same? When are they approximately the same?

As a follow-up to this related question, I'd like to know under what circumstances, if any, $\Delta x$, $\delta x$ and $dx$ all mean the same thing, and under what circumstances they can all be said ...
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4answers
43 views

Second order differential equation for acceleration

Can you help me understand and solve this question: A bullet is fired vertically upwards with an initial velocity of $u$. Form a second order differential equation for acceleration and by ...
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2answers
89 views

A problem about symplectic manifolds in Arnold's book

There is a problem in Arnold's Mathematical Methods of Classical Mechanics which says that: Show that the map $A: \mathbb{R}^{2n} \rightarrow \mathbb{R}^{2n}$ sending $(p, q) \rightarrow (P(p,q), ...
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0answers
30 views

Clarification on some notation and “assumptions” in page 143-144 of the book “Quantum Fields and Strings: A Course for Mathematicians, Volume 1”

I was trying to read the chapter $1$ (at page $143$) of this book Quantum Fields and Strings: A Course for Mathematicians, Volume 1 that is supposed to be an introduction to modern quantum field ...
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0answers
21 views

Circular motion h.w [closed]

Need help with homework in this subject. That's the question: Earth rotates around the sun and makes a whole for 365.25 days. The distance between the center of the earth to the center of the sun 150 ...
4
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1answer
367 views

Damped Harmonic Oscillator and Response Function

This is another one of those questions that I feel like I am almost there, but not quite, and it's the math that gets me. But here goes: For a driven damped harmonic oscillator, show that the full ...
2
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1answer
61 views

What's the proper interpretation of canceling infinitesimals?

In most textbooks of physics I've found this demonstration of work-kinetic energy theorem: $$\begin{align} W &= \int_{x_{1}}^{x_{2}} F(x)\ dx \tag{1}\\ &= \int_{x_{1}}^{x_{2}} m\cdot a\ dx ...
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2answers
7k views

Can you find the resultant force between these two vectors?

Determine the magnitude of the resultant force on an object if force $A$ is pulling the object with $150$ lbs of force and force $B$ is pulling with $300$ lbs, and the angle between the two forces is ...
2
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1answer
69 views

Calculating stiffness and dampening for an oscillation to settle at a given time

The Problem How can I calculate a stiffness (k) and dampening (b) coefficient for an under-damped oscillation such that the system settles by a given time (t)? The Environment Given the ...
1
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1answer
68 views

How can the tension force be computed to test if a shape is moving or not?

Source Given the coordinates of n 3D joints (1kg each) connected by m rods. Assume rods have zero mass and joints with z=0 are fixed to the ground while others are free to move, will the shape be ...
3
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1answer
50 views

How to compute force on joints of a 3D structure of balls connected by rods?

Source Given the coordinates of n 3D joints (1kg each) connected by m rods. Assume rods have zero mass and joints with z=0 are fixed to the ground while others are free to move, will the shape be ...
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0answers
35 views

Variable density in the equation of motion

At a fixed point in time, consider the equation of motion $$ \nabla \cdot \boldsymbol \sigma(u) + \boldsymbol f = \rho \ddot{\boldsymbol u} \quad \text{in $\Omega \subset \mathbb R^d$} $$ for a ...
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1answer
12 views

When finding the frequencies of normal modes, can you have a negative frequency?

Do you simply just consider the positive solutions? I tried a google search but didn't find anything quickly. The work I am studying is Lagrangian systems.
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0answers
20 views

stroboscope effect

I have a disc with a line drawn on one of his radius that is turning with frequency $f$, and I want to sample the place of the line to find the frequency of the disc. So we know from the ...
4
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2answers
92 views

What are integrating factors, really?

I can follow the rationale for integrating factors well enough, but they still feel like voodoo to me. Every single description of integrating factors I've seen (and I've seen quite a few, including ...
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0answers
17 views

Britney gallivant's paper folding formulas

According to a few youtube videos and Newscientist, formulas exist (based on algebraic/mathematical premises, thereby making this a valid math question) to describe the limits of paper folding. The ...
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0answers
23 views

Why is chemotaxis considered an emergent behavior?

this is an applied math question. I could have posted this under a biological stackexchange, but the idea of emergent behavior or emergent properties of a system seems more appropriate to an applied ...
3
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1answer
44 views

Interpretation of Riemann rearrangement theorem [closed]

There's a common thing that happens in mathematics, which is that all theorems are created equal, but some are more equal than others. Here are two examples of what I mean by that. (1) In Euclid, the ...
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1answer
377 views

A Ferris wheel has a radius of 20 m. Passengers get on halfway up on the right side.

A Ferris wheel has a radius of 20 m. Passengers get on halfway up on the right side. The direction of rotation is counter clockwise. The bottom of the Ferris wheel is 2 m off the ground. It rotates ...
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0answers
16 views

Integration problem related to physics problem

I want to know how to solve this (acytually this is the flux on any non-adjacent side of a cube due to a charge q on the vertice of the cube, side length: l) $$a=\int_0^l\int_0^l ...
3
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1answer
111 views

Verify that $\nabla(A\cdot B) = (B\cdot\nabla)A + (A\cdot\nabla)B + B\times(\nabla\times A) + A\times(\nabla\times B)$

I'm trying to verify the following identity $$\nabla(\textbf{A}\cdot\textbf{B}) = (\textbf{B}\cdot\nabla)\textbf{A} + (\textbf{A}\cdot\nabla)\textbf{B} + \textbf{B}\times(\nabla\times\textbf{A}) + ...
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2answers
35 views

Physics Related Watt Question

A 550 kg dragster accelerates from rest to a final speed of 110 m/s in 400 m (about a quarter of a mile) and encounters an average frictional force of 1200 N. What is its average power output in watts ...
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3answers
4k views

Derivation of Newton's second law of motion. [closed]

Can somebody help me determine the derivative and proof of Isaac Newton's second law of motion ($F=ma$)? How can this be done using calculus?
2
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0answers
61 views

How to maximize speed of rest position approach of nonlinearly damped spring oscillator?

Inspired by comments to answer for this question: Suppose we have a system which is described by the equation $$\ddot x=-x+g(\dot x),$$ with initial conditions $x(0)=1$, $\dot x(0)=0$. If ...
2
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1answer
35 views

How can I prove the tangential acceleration equation?

This is my assignment for this weekend. $$a=a_{TT}+a_{NN} = \frac{d^2 s}{dt^2}\vec{T} + \kappa \frac{ds}{dt} 2\vec{N}$$ Actually, I want to why $a_N=\kappa (ds/dt)$ hold Please help me.
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3answers
129 views

What do I need to read to understand dimensions and spacetime?

The concept of dimension seems to be: In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point ...
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2answers
261 views

How to calculate work

What is the work done by the force of gravity on a particle of mass $m$ as it moves radially from $7500 ~\text{km}$ to $9400 ~\text{km}$ from the center of the earth?
2
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4answers
12k views

Derivative of position is velocity and of velocity is acceleration?

This is more of a personal question (i.e. not school related), but how has it been proven that the derivative of position is velocity and derivative of velocity is acceleration? I did some Google ...
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1answer
21 views

Oscillating Object - Homework [closed]

I am forced to post this question here as physics SE refuses homework questions even if tagged with their (severely misleading) 'homework' tag. See my question at: ...
4
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0answers
33 views

C. Neumann passage in Latin from *Annali di Matematica Pura ed Applicata*

Neumann, Carl. “Theoria nova phaenomenis electricis applicanda.” Annali di Matematica Pura ed Applicata 2, no. 1 (August 1868): 120–128. doi:10.1007/BF02419606. p. 121: Nova introducitur ...
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1answer
35 views

Explanation on equations please [closed]

I've got seemingly two different equations for velocity in orbit: $$v_1 = \sqrt{ \frac{2GM}{R}} $$ and $$v = \sqrt{ \frac{Gm_e}{R}}$$ What is the difference between these two? I'm quite sure that ...
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1answer
35 views

Proving the moment of inertia formula for right cylinder

I have a question on whether I can do this with an integral: When I tried solving this, I got (1/2)(M^2)(R^2) instead of (1/2)MR^2 Problem: http://i.imgur.com/QDdEEse.jpg *Sorry for lack of TeX. ...
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2answers
267 views

How long can a flea stay in the air?

Part A: If a flea can jump straight up to a height of 0.420m , what is its initial speed as it leaves the ground? Answer: $v=2.87$ m/s Part B: How long is it in the air? So I was using the formula ...
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0answers
57 views

Retarded function?

How was the sign of the retarded green function chosen? A friend told me it had something to do with the Fourier Transform, but I didn't really understand him. The same explanation might apply to the ...
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1answer
593 views

Physics Conservation of Energy Problem

In the figure below, a block is released from rest at height d = 24 cm and slides down a frictionless ramp and onto a first plateau, which has length d and where the coefficient of kinetic friction is ...
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0answers
23 views

Shooting a grenade - angle throwing

In my 3D simulation/game I need to shoot a grenade from a grenade launcher. The movement of the grenade is already setup by someone else. all I need is to give him the pitch angle of the grenade ...
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2answers
12 views

Helmholtz decomposition - motivation

Our lecturer presented us the Helmholtz decomposition of smooth vector fields. He added a proof, but he didn't provide any single motivation - e.g. where Helmholtz used the decomposition or for which ...
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1answer
24 views

Fastest direction in circular trajectory [closed]

I have a point P and a vector V. This point is describing a uniform circular trajectory with linear velocity lv and angular velocity av. This trajectory passes through a point P', how do I find out if ...
2
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0answers
21 views

Solution to the “cubic” Helmholtz equation

What is known about the solutions of the differential equation in three-dimensions $$ \nabla^2 \phi = -\kappa^2 (\phi + (1/3!)\phi^3) $$ Without the cubic term, this gives a linear operator ...