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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33 views

At 2:00pm a car's speedometer reads 30mph, and at 2:10pm it reads 35mph. Use the Mean Value Theorem to find an acceleration the car must achieve.

I'm only assuming that f(a) and f(b) are assigned to each respective velocity, but I'm not sure how the mean value theorem can be applied to distance rate and time.
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0answers
40 views

How do you get the curvature tensor of the Schwarzschild Solution?

So, on the Wikipedia page on the derivation of the Schwärzschild solution , I get everything up to the part about the Ricci tensor. What were the components of the tensor that were used? Could ...
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2answers
62 views

Need help with integral to evaluate electric field around a spherical shell.

I was trying to prove that the electric field at a distance $x>R$ from the centre of a charged shell is $\dfrac{kQ}{x^2}$. I did the physics part but I got stuck when I encountered the following ...
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0answers
38 views

Identities with dirac deltas

How are you supposed to verify or derive common physics text 'identities' involving dirac deltas like $$ \lim_{t \to 0} \mbox{sign}(t) \frac {\partial}{\partial t} \frac{\partial}{\partial x^i} ...
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1answer
49 views

Equilibrium Of Forces - Vector Condition

A body is in equilibrium under 3 forces A,B,C.Show that A x B = B x C = C x A (x represents cross product). Well I know the longish method of writing A= a i + b j + c k form and then balancing along ...
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1answer
7 views

Finding the velocity $v$ for which the total time the object moves from its initial position to the position where it stops is minimal

A body first moves with a constant velocity $v$ along a track with a length of $L=5 \ [m]$ and then decelerates with an acceleration $a=2 \ [\frac{m}{s^2}]$ till it stops. How to find the velocity $v$ ...
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1answer
57 views

Application of differential equation (wave equation)

I am not 100% sure what is "steady-state solution w(x)". I tried to solve the question by first making equation (1) equals to zero; then integrate it twice with respect to x and substituted u=0,x=0 ...
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1answer
77 views

Help solving a Rectilinear Motion problem - straight roads

Problem: Amar drives 16 km directly west from Upper East Side to Central Park at a speed of 90 km/h, then directly south 8.0 km/h to 7th Avenue at a speed of 80 km/h, then finally 34 km southeast to ...
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0answers
19 views

Taylor series of Lagrangian

Take a look at the Lagrangian defined here. $L=\frac12 a(q)\dot q^2 - V(q)$. You can think of $a$ and $V$ as functions. It seems as though $L$ depends only on $q$. If $q_0$ is a point for which ...
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59 views

Force between two finite parallel current carrying wires

Most standard physics textbooks compute the force two infinite wires exert on each other, but they remain silent about the case where the wires are finite. Let's say we have two parallel wires ...
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0answers
18 views

Find electrostatic energy of three-parallel-plates capacitor

Question: A capacitor consists of three identical and parallel thin metal circular plates, area A, in the planes z = −H, z = a and z = H, (−H < a < H), centres on z axis, and at potentials 0, V ...
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1answer
72 views

Simple question on group theory

Suppose we have the following system of differential equations: \begin{cases} \frac{dx_{i}}{dt}=f_{i}\left(\boldsymbol{x},\boldsymbol{y}\right), & i=1,\ldots M\\ \\ ...
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1answer
62 views

How can I find out the center of mass of thin plate in the shape of a rectangle?

How can I find out the center of mass of thin plate in the shape of a rectangle ABCD If the density at any point is the product of the distances of the point from two adjacent sides AB and AD? ...
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2answers
32 views

Physics Word Problem Concerning Finding Power

A twin engine jet aircraft is climbing at a 10 degree angle at 260 ft/s. The thrust developed by a jet engine is 1000 lb. The power developed by the aircraft is ______ (2000 lb)* (260 ft/s) = ...
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1answer
56 views

Solid Angle Integrals

I'm currently working on solving a solid angle calculation for my physics project. I'm trying to solve it computationally using python - but my coding skills are basic at best. I need some hints/tips ...
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1answer
33 views

How Do You Solve for Landing Speed?

A ball is thrown eastward into the air from the origin (in the direction of the positive x − axis ). The initial velocity is 50i + 80k. The spin of the ball results in a southward acceleration of 4 ft ...
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1answer
36 views

Formula for 2 vectors

Hello StackExchange people, I have an issue. I need to create a formula to find degrees and size at a problem like the following: So I have $0-359$ degrees and a length of $2$ lines, and I need to ...
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2answers
103 views

Finding total distance and time for a bouncing ball - application of series

Problem: A ball is thrown straight upward so that it reaches a height $h$. It falls down and bounces repeatedly. After each bounce, it returns to a certain fraction $f$ of its previous height. Find ...
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2answers
63 views

Second-order nonlinear ordinary differential equation. Newton's second law.

I have this problem, I will try to give as close translation to English as possible: "A point with mass m moves towards a center due to force $m·k^2/(r^3)$, where $r$ is the distance from the center. ...
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0answers
45 views

Sum over all compositions of $n$ into exactly $k$ terms (overlaps of $SU(k)$ coherent states)

Given two $k$-dimensional vectors, $\vec{x}$ and $\vec{y}$, I would like to find, $$ d(\vec{x}, \vec{y}) = \left|\sum_{t_1 + t_2 + \cdots + t_k = n} \prod_{1\leq q \leq k} (x_q\times ...
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1answer
60 views

Why does the vector field $(\sin (\theta), - \cos(\theta), 0)$ indicate sideways motion?

If I study a physical system, such as a car, and let it drive forward a little bit, say a distance $m$, then I can draw out the right triangle and find the car's position at $(m\cos \theta, ...
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0answers
32 views

Meaning of Torricelli's Equation ($v^2=u^2+2as$)

The equation of motion $v^2=u^2+2as$ is usually presented as the particular formulation of the SUVAT system which doesn't involve t. It is derived from the others using some (perhaps well-motivated) ...
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0answers
37 views

partial differential equation applicational problem

As a Maths student with not much knowledge in physics, I dont understand how the "string" can be "cut" into half at x=L/2. Also, how many initial conditions(data) does this question have apart from ...
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1answer
18 views

Find out the angular speed in terms of time.

Here is the equation that describes the motion of a planet under the gravitational field generated by a fixed star: $u=\frac el\cos\theta+\frac 1l$, where $u$ is the reciprocal of the radial distance ...
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0answers
74 views

Could you explain the failure of the Hodge decomposition to exist for non-compact manifolds?

I'm a physicist and the mathematics around the Hodge Decomposition is way formal than I can currently follow (I'm trying to better myself but it'll take a while). Specifically what I'm ...
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3answers
110 views

infinitesimal intervals in physics

The density of states of a system in an interval $[E, E+dE]$ is given implicity by $dV = D(E)dE$ (Or I suppose explicitly, by $D(E) = \frac {dV}{dE}$, but we'll be integrating it anyway, so it doesn't ...
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0answers
51 views

Thermodynamics: find exit temp and velocity of air out of a nozzle?

I don't know if I can really ask a thermodynamics question here on this math site but I need help and this was the best site for when I needed help in math class. Concerning thermodynamics, I have ...
2
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1answer
108 views

Eigenvectors of almost-Toeplitz tridiagonal matrix.

I'm reading a book about semi-conductors, and when figuring out how dopants affect the energy-levels, one wishes to find the eigenvalues (and vectors) of a NxN tridiagonal matrix of the form ...
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1answer
24 views

re-arrange equation $L=2^{10(v-1)} v^2$

Is it possible to re-arrange this equation to make v the subject? $$L=v^2 . 2^{10(v-1)}$$ If so, what is the answer? If it helps (which by excluding zero it should)... $$0<v<1$$ I have tried ...
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1answer
79 views

How to find direction of velocity V2 to reach an object travelling at velocity V1, such that it takes least time?

If an object A is currently at point P1 moving with constant velocity V1, and there is another object, object B which currently at point P2 which can move with velocity v2, then what should be the ...
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1answer
34 views

Work done in a vector field

Say a particle is moving along a path $\gamma$ in a vector field, then the total work done by the force $\vec{F}$ on the particle is $\displaystyle \int_{\gamma}{\vec F}.d\vec{r}$. Say if this value ...
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2answers
150 views

Undamped spring mass system

I have this study guide for an upcoming test for DE class I'm trying to figure out. A mass of 400 grams stretches a spring by 5 centimeters. (a) Find the spring constant k, the angular frequency ω, ...
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1answer
66 views

Can an integral of a function that is not well behaved be finite?

Consider the following integral which gives the time period of simple pendulum where $\theta_0$ is the initial inclination of pendulum with vertical. ...
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0answers
24 views

Projectile landing on an elevated point

A golfer is standing on a fairway and hits a shot to a green that is elevated 6.0 m above the point where she is standing. If the ball leaves her club with a velocity of 43 m/s at an angle of 40.0 ...
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0answers
31 views

Tangential and normal components of acceleration of a point moving along a curve

If a point is moving along a curve in polar coordinates, is the tangential component of its acceleration given by $r\left(d^2\theta \over dt^2\right)$ and the normal component by $r\left(d\theta \over ...
2
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0answers
74 views

Index notation confusion in tensor algebra

I have some confusions regarding index notation in tensor algebra. Let's assume $\vec{v}$ is a vector belonging to vector space $V$. Choosing a basis set $\{\vec{e}_\nu\}$, $\vec{v}=x^\nu\vec{e}_\nu$ ...
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1answer
46 views

Olbers' Paradox in an Euclidean universe with randomly located stars

This question is inspired by Olbers' Paradox. Imagine a universe $U$ shaped like $R^3$ with points $P$ randomly distributed in a Poisson fashion throughout, with density parameter $\lambda$ such that ...
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2answers
293 views

Setting up a differential equation to find time constant for RC-circuit

Problem: Calculate the time constant for charging the capacitor in the circuit shown in the figure. What is the maximum charge on the capacitor? Attempt at solution: Let current $I_1$ flow from the ...
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2answers
51 views

Water Density and Fluid Force (question below) [closed]

I've been trying to study the question and the answer below. Can someone tell me how to start this problem myself? I don't understand why they named one fourth of the circle equation the whole ...
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0answers
17 views

Approximations of the kind $x<<y$

I have an expression for a force due to charged particle given as $$F=\frac{kQq}{2L}\left(\frac{1}{\sqrt{R^2+(H+L)^2}}-\frac{1}{\sqrt{R^2+(H-L)^2}}\right)$$ where $R$, $L$ and $H$ are distance ...
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0answers
23 views

How do you calculate certain variables of two or more events that occur simultaneously compared to the same events happening subsequently.

Say you have two hoses, A and B, that fill up a pool of equal size at different rates. Hose A fills up a pool in 10 mins, hose B in 20 mins. Thus A = 1p/10m, B = 1p/20m. Lets say that Hose A filling ...
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1answer
78 views

Solutions to Kepler problem/Motion in central field

It is clear that particals in a repulsive central field given by a point mass at the origin are moving along hyperbolas, e.g. given by the expression ${x^2 \over a^2} - {y^2 \over b^2} = 1$ (after a ...
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4answers
91 views

How to solve $a \cos \alpha + b \sin \alpha = c$ for $\alpha$?

I'm solving a physics problem and I came down to solving an equation of the form $$a \cos \alpha + b \sin \alpha = c$$ Can someone help me to solve this? Thanks in advance!
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1answer
94 views

Vectors problem, Please Help!

A buoy is floating in water and is tied to a post. The water is creating a force of $3$ N on a bearing of $125^\circ$ and the wind is creating a force of $2$ N on a bearing of $230^\circ$ What force ...
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0answers
68 views

Attempt to solve the brachistochrone problem

I am attempting to solve the brachistochrone problem for fun. I don't have too much experience with differential equations and wanted to see if I am on the right path. My attempt Assumptions ...
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1answer
53 views

Integration of partial derivative $\frac{dL}{dq}$ with respect to $t$ where $q$ is implicitly a function of $t$

Is $\int_{t1}^{t2} \frac{\partial L}{\partial q}\delta{q} dt$ equal to $\left[\frac{\partial L}{\partial \dot{q}}\delta{q}\right]_{t1}^{t2} $ if $q$ implicitly depends on $t$ ? If not I ...
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2answers
19 views

Finding the derivative Maxwell Boltmann distribution

I need to basically show that the slope is $0$ when $\epsilon = kT$ $f(\epsilon)=\left(\frac{8 \pi}{m}\right)\left(\frac{m}{2 \pi kT}\right)^{\frac{3}{2}}\epsilon e^{\frac{-\epsilon}{kT}}$ So I ...
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0answers
43 views

According to Liouville's theorem, why is the measure on an energy-surface different from the measure on the phase space in general

I recently read Khinchin's derivation of Liouville's theorem. I was able to follow the math for the most part, however I was hoping for an intuitive understanding about why the form of the measure on ...
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0answers
24 views

Continuity of the divergence of a static electric field

Let $\rho:\Bbb R^3\to\Bbb R$ be a continuous charge density function. Define the electric field $\vec E:\Bbb R^3\to\Bbb R^3$ by $$\vec E(\vec r)=k\cdot\int_{\Bbb R^3}\rho(\vec{r}')\cdot\frac{\vec ...
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1answer
53 views

Velocity vector

We suppose that a ship, that is at the position $(1, 0)$ of a nautical map (with the North at the positive direction $y$) and it "sees" a rock at the position $(2, 4)$, is directed to North and is ...