Tagged Questions

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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0answers
16 views

Lubrication Theory: Quick Question!

Basically, I'm modelling the flow of a "coating" process -- a fluid flow between a flat moving plane and a stationary cylinder, 2D, cartesian coordinates. Subscript 0 is the at the minimum height b/w ...
-5
votes
1answer
32 views

Calculating the mass of the earth [on hold]

The formula I am using to calculate the mass of the earth is: M = ar2/G = 5.98 × 1024 kg. a being the acceleration of gravity (9.8 m/s squared), r being the radius of the earth ((6.4) *(10^6)), and ...
0
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2answers
31 views

how to calculate speed of two object that are moving toward each other?

Two cars started their journey from point A and B 150 km apart on the same road towards each other.The car started from A traveled at a constant speed 10 km/hr more than that of hat also traveled at a ...
1
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0answers
16 views

fluid flow through an orfice [migrated]

Forgive me for my ignorance. What would be the method to determine the pressure a non compressible fluid creates when forced though an orifice? Keep in mind this orifice does not have a constant ...
2
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2answers
52 views

Proving that total energy is constant?

A mass $m$ is moving along the $x$-axis under the influence of a force $F(x)$ according to Newton’s Second Law, i.e., $F = ma$ . Note that $F(x)$ depends only on $x$, so that it is a conservative ...
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0answers
23 views

Linear approximation and relative changes?

Given PV^y = c, where y and c are constant, and P and V are the pressure and volume respectively. Using the linear approximation, find the relation between the relative changes in pressure and ...
4
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0answers
49 views

Sorting out some integrals from physics

I'm doing some physics for a change, and I'm trying to sort things out a bit. From the definitions of mass, torque, momentum and angular momentum I've come up with the following integrals: ...
2
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0answers
9 views

locality and unitarity of Feynman path integral [on hold]

I'd like to know if the action being real is enough to the resulting evolution to be unitary. And if the action being the integral of a (relativistic invariant) lagrangian density is enough for the ...
5
votes
1answer
99 views

What is the space that we live in? [on hold]

Not sure if this question is trivial to some experts; but what is the three dimensional space that we live in? If this question is too difficult to describe, can we at least tell its topology? Is it ...
2
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0answers
28 views

Period of a pendulum

Consider the pendulum problem $\frac{d^2x}{dt^2}+\sin(x)=0$ $\frac{dx}{dt}(0)=v_0=0$ $x(0)=x_0$ Show that the period ...
1
vote
2answers
27 views

What is the algebra to rearrange the constant acceleration formula?

I'm working through The Cartoon Guide to Physics and I can't figure out how an equation was rearranged for the constant acceleration formula $d = {1\over2}gt^2$. The object will fall 4 ft and the ...
0
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3answers
27 views

Right way to transform $s(t)=1/2g*t^2$ to $v$

My problem is, that I have the following: $$s(t)=\frac {gt^2}{2}$$ and I need to transform it to get $v$. Just can't find the right way to do it.
3
votes
1answer
51 views

spring representation of graphs

Suppose we have a finite graph $G$ which we want to embed in ${\bf R}^d$; fix the positions of some nodes and connect all the nodes of the graphs with ideal springs of varying strength; (i.e. there is ...
1
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0answers
62 views

Car traveling on a bumpy road (ODE)

The suspension system of a car traveling on a bumpy road has a stiffness of $k = 5\times 10^6$ N/m and the effective mass of the car on the suspension is $m = 750$ kg. The road bumps can be considered ...
0
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0answers
15 views

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 ...
1
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0answers
27 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 ...
0
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0answers
16 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 ...
1
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1answer
29 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
18 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 ...
2
votes
2answers
55 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 ...
0
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2answers
39 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 ...
1
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0answers
29 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 ...
0
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1answer
24 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. ...
0
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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 ...
1
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1answer
53 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 ...
0
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0answers
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 ...
-3
votes
1answer
23 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.
1
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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 ...
1
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0answers
23 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?
0
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1answer
18 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
23 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 ...
0
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1answer
26 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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0answers
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.
0
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0answers
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 ...
1
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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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0answers
47 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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0answers
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!
0
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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 ...
2
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0answers
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 ...
1
vote
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 ...
0
votes
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 ...
1
vote
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 = ...
1
vote
1answer
30 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 ...
0
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0answers
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 ...
0
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1answer
37 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 : ...
0
votes
1answer
31 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 ...
4
votes
0answers
59 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, ...
5
votes
1answer
103 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 ...
8
votes
1answer
130 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 ...
1
vote
1answer
20 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 ...