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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Questions about the formula for inductive reactance and $Z_t$

I am currently on the inductors unit in my Navy schooling and I have two questions about these formulas that I learned about. As I'm aware, the ability of an inductor to concentrate a magnetic field ...
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22 views

Compare time it takes to travel a curve and a line

Suppose you have a right triangle ABC with hypotenuse AB, AC is along gravity direction, C is the right angle. c1 is AB, c2 is a smooth and convex curve within the triangle connecting A and B. You ...
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14 views

Equal time path

Given two points A and B, where A is at a higher position than B. It's easy to find the time it takes a mass point to travel from A and B over a straight slope under gravity. Now can you find a smooth ...
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1answer
27 views

Time it takes a mass point to go down a curve under gravity

An age old question. How to calculate the time it takes a mass point to go down a frictionless curve under gravity? P.S. The curve is convex and smooth and can be of any kind of shape.
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1answer
16 views

Applying thin lens formula

Let's say we have an object that in reality has a size A m, know it appears on the image plane with a size A'. We want to know the distance between the optical center (the lens) and the object. What ...
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2answers
42 views

Quaternion - Spinor relationship?

I've known for some time about the rotation group action of the ('pure') quaternions on $ \mathbf{R}^3 $ by conjugation. I've recently encountered spinors and notice similarities in their definitions ...
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2answers
34 views

When $a\ll b$, how to approximate $f = \int_0^a \sqrt{b^2+x^2}/\sqrt{a^2-x^2} \, \, dx$?

Suppose $a\ll b$. How do I then approximate $$\int_0^a \frac{\sqrt{b^2+x^2}}{\sqrt{a^2-x^2}}dx$$ ? I think that maybe Taylor approximation may help, but I am not sure how to proceed. My physics ...
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27 views

Convert time derivative to a function of time

Physics: I am asking for help to derive a general expression for the total amount of energy lost as a function of time from a radiating object. I'll simplify my problem like this: Say for example ...
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1answer
23 views

Finding moments $M_x$ and $M_y$ and center mass of a region

Set up integrals for the moments, $M_x$ and $M_y$, and the center of mass of the region (constant density, do not evaluate integrals) The region is a tall rectangle with a semi-circle on top. ...
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1answer
30 views

How does the hermitian conjugate of an unitary operator act?

I know that $$ A| v \rangle = \sum _n e^{i\alpha n} | n \rangle $$ where $A$ is an unitary operator, and $ \left \{ |n\rangle \right \} $ is an orthonormal complete basis. In that case, is it true ...
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1answer
39 views

Partial derivative with respect to metric tensor $\frac{\partial}{\partial{g_{kn}}}(g_{pj}g_{ql})$

$$-\frac{1}{4\mu_0}F^{pq}F^{jl} \frac{\partial}{\partial{g_{kn}}}(g_{pj}g_{ql})=+\frac{1}{4\mu_0} F^{pq} F^{lj} 2 \delta^k_p \delta^n_j g_{ql}$$ I need to know how to derive ...
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physics-drawing the diagram [closed]

Suppose that a car moves up north 100 km for 2 h and then turns towards east and travels in this direction 60 km for 1 h. a. Draw in the following diagram the displacement vector of the car?
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1answer
16 views

Suppose that displacement (in meters), for an object moving along the axis, as a function of time (in seconds) is given as [closed]

Suppose that displacement Δx (in meters), for an object moving along the axis, as a function of time t (in seconds) is given as: Δx = at + bt² a) What are the SI units of the real coefficients a and ...
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17 views

About diagonalizing a matrix for a quadratic expression (with the goal of uncoupling mixed terms)

my question is originated from a physical problem. I will try to present the problem as simple as possible, but I fear it will still be long since I'm bad at expressing myself briefly. It starts with ...
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1answer
21 views

Boyles law math problem [closed]

Let $$ P_1 = 1.37 atm \\ P_2 = 0.22 atm \\ V_1 = 1 L \\ $$ Boyle's Law says $$ P_1 * V_1 = P_2 * V_2 $$ What is the missing variable answer $V_2$? I'm having trouble.
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23 views

In need of formula: Gravity at Specific Coordinates [closed]

Doing Research on the gravitational pull at a specific set of coordinates. Does anyone know how to solve this mathematically? Please Help. Thanks
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1answer
18 views

mathematical justification or creating a mathematical problem of the last part of a gauss theorem proof

this page proves the gauss theorem. First they prove that there has to be charge allocated in the origo of a function and that this is where you get the gauss formula and therefore you can integrate ...
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22 views

On the Name of the Amplituhedron

Shouldn't the 'amplituhedron' really be called an 'amplitutope' since it's really a polytope and not strictly a polyhedron?
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1answer
14 views

Displacement vectors

A rabbit trying to escape a fox runs north for 8.0m, darts northwest for 1.0m, then drops 1.0m down a hole into its burrow. What is the magnitude of the net displacement of the rabbit? So I drew two ...
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2answers
21 views

Displacement vectors

You walk 53 m to the north, then turn 60 degrees to your right and walk another 45 m. Determine the direction of your displacement vector. Express your answer as an angle relative to east. So I did ...
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1answer
25 views

physical meaning of heat equation

consider the heat equation $u_t=a(t)u_{xx}+f(x,t)$, $0<x<L$, $0<t<T$ subject to the initial condition $u(x,0)=g(x)$ and boundary conditions $u(1,t)=0,$ $u_x(0,t)+hu(0,t)=0$ where ...
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20 views

How to move a body to a point using only velocity? [closed]

If I have two bodies, how can I move one of them at a constant velocity until it reaches the other's position? This is two dimensional x,y.
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14 views

Explaniation of symbols in Moment of Inertia

Im looking for an explaination of what the TWO axix symbols (x,y and z) in the down right next to the capital I (Moment of Inertia) mean. I have looked on google and youtube, all my math and physics ...
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1answer
24 views

Proving these are equal

We have the following equality (in physics) $$c^2t^2-x^2 = c^2t'^2-x'^2$$ where: $t' = \gamma (t- \dfrac{vx}{c^2})$ $x' = \gamma(x-vt)$ $\gamma = \dfrac{1}{\sqrt{1-\dfrac{v^2}{c^2}}}$ My ...
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43 views

Proof of Kepler's first law

Has Kepler ever provided proof of his first law? I've found some articles on the web which use some of the Newton's formulas to prove it but Kepler died before Newton was born. So how did Kepler ...
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8 views

Meaning of ideal membrane

I'm studying from a mathematical point of view the bidimensional vibrating membrane. How can I define an ideal membrane? What are the assumptions when I say 'ideal'? Thanks!
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2answers
30 views

From which equation of motion was this formula derived from in physics

When solving problems involving projectile motion I use: $\sqrt{2 * \dfrac{\text{height above ground}}{9.8}}$ Eg calculate the time it takes for a bomb to impact if it is travelling 4.9km above ...
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26 views

Launch angle required to hit coordinate (x,y) with air resistance

Finding Angle of Elevation to hit X, Y and Wikipedia Angle required to hit coordinate work, but don't calculate air resistance. Is there a way to find the launch angle of a projectile required to hit ...
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2answers
63 views

Separation of variables PDEs

In this answer, he has three cases $(\lambda = 0, \lambda \lt 0, \lambda \gt 0)$. I understand the first does imply it is linear, hence it isn't consistent with the initial conditions, and looking at ...
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1answer
52 views

PDEs for string deflection.

Okay, I have to find $u(x,t)$ for the string of length $L=\pi$ when $c^2=1$. I know: $$\text{wave equation}: \frac{\partial^2 u}{\partial t^2} = c^2 \frac{\partial^2 u}{\partial x^2}$$ $$u(x,0)=\frac ...
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1answer
46 views

How to integrate Gravitational force?

The gravitational force is given by $$ F = \dfrac{-Gm_1m_2}{r^2} $$ But, since F = ma, then for an object placed at r distance away from the centre of the earth it would experience $$ a = ...
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1answer
29 views

Integrating the Schechter function…

I'm trying to integrate this equation over all L. I really have no idea where to start for some reason :S $$\phi(L)dL=\phi_0\left(\dfrac L{L\star}\right)^\alpha\exp\left(-\dfrac ...
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21 views

Momentum Representation vs Position Representation

I have a question involving the representation of operators in momentum representation and position representation. The question is a little long, so I'll do my best to explain it. We are given an ...
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1answer
34 views

Calculating the electric field of a disk

I'm having trouble regarding how to calculate the electric field of a disk. Here's the scheme: The exercise states that the disk is uniformely charged. This is what I did: Density charge : ...
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1answer
30 views

Finding the acceleration

So I am given a problem stated as: a point moves in the plane at speed 1 along the curve $y = x^2$. Find the acceleration at the point (x,y). I know that the velocity is y' = 2x, and that at a ...
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57 views

Rolling a ball into a cone; what should the forces overall be?

Suppose there is a cone, with the apex pointing down, and the top of the cone at height $h$, apex half-angle $\psi$, ball of mass $m$, and the initial velocity into the cone (completely horizontal, ...
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1answer
100 views

Guide to mathematical physics?

I am currently a math phd student specializing in algebraic geometry aspiring to work at the boundaries of the the fields of mathematics and physics and so, was looking into the field of mathematical ...
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1answer
128 views

Reference request: books that describe application of physical reasoning to mathematical problems

I am searching for more books like Uspenski's Some applications of mechanics to mathematics and Levi's The Mathematical Mechanic. In other words, I am looking for books that show interesting and ...
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1answer
19 views

What's the total of battery if 50mA of current are provided to a load for 1 hour?

What's the total charge that moves from one terminal of a battery to the other if 50mA of current are provided to a load for 1 hour? I think I'm suppose to use the formula I = Q/t, where I is the ...
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1answer
67 views

how to solve the system of differential equations for this particle?

I'm trying to solve this problem A particle of mass m moves under the action of gravity on the inner surface of a paraboloid of revolution $x^2+y^2=az$ which assumed frictionless. Obtain the ...
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Explain why we describe the flow of fluid passing through volume with this equation

I am new to this Q&A site. Recently I came across this expression while watching a video http://www.youtube.com/watch?v=GveJWPr9UOk/ about the mass of fluid flowing in through a cube. You can find ...
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1answer
52 views

Electromagnetism and thermodynamics(Statistical mechanics) books for the mathematician?

I found some very good classical and quantum mechanics,special relativity,gauge theory books for the mathematicians,but I couldn't find anything on electromagnetism or thermodynamics,are they of not ...
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3answers
39 views

Physical meaning of limit

Does the concept of "limit" have a well-defined physical meaning (like, for example, the derivative)?
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1answer
16 views

Regularity of the surface of a crystal

If I want to model the surface of any random crystal, is it safe to assume that it is the graph of a Lipschitz function. Is there a precise result from physicists? How wrong would it be if I assume ...
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2answers
49 views

Height and velocity of ball thrown vertically

A ball is thrown upward from roof of 32 foot building with velocity of $112$ ft/sec. The height after $t$ seconds is: $s(t)=32+112t-16t^2$. (a) Find the maximum height that the ball reaches. ...
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2answers
102 views

Set theory and physics [closed]

I would like to know if there are some physical concepts (preferably accessible ones like force, torque, ...) that can be significantly better understood when looked at in the light of concepts taken ...
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3answers
34 views

A silly question about potential functions

Why have physicists had the idea to define a potential function of a gradient vector field $\vec F$ to be a function $g$ such that $\vec F=-\nabla g$? What changes if we don't put the negative sign? I ...
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1answer
24 views

Simultaneous Suvat help [closed]

I learnt this in college but can't for the life of me remember how to do it. I've searched stack exchange and the internet for answers but it isn't clicking. It doesn't help my teacher has decided to ...
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Question about forces and orthogonality

Two forces $F_1$ and $F_2$ meet at a point, the resultant is $R$ (parallelogram rule) , the measure of angle between them is $120$ degree , if the direction of $F_2$ is reversed the resultant will be ...
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3answers
59 views

Can someone check my work for this problem? Newton's second law of motion

At 560 metric tons, the airbus A-380 is the world's largest airliner. Whats the upward force on an A-380 when the plane is flying (a) at a constant altitude and (b) accelerating upward at 1.1 m/s^2 ...