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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Physical Object to Pseudo-Riemannian Manifold

It is well known that Lorentzian mainfold is studied in general relativity. So this raises my curiosity about How about the classical mechanics? Does it correspond to the manifold $\mathbb{R}\times ...
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0answers
15 views

Concerning the notation $\chi (U)$ in one of the hipotesis for some propierties of curl and divergence

I have the following excercise: Let $U \subset \mathbb{R}^3$ be open, $X \in \chi (U)$ and $f \in C^{\infty}(U)$, prove the following: $$curl(\nabla f)=0 \\ div(curl(X))=0 \\ curl(f.X)= ...
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2answers
37 views

How to calculate the acceleration if the plane on which the object is sliding makes 40 degree angle with ground? [on hold]

An object placed on a ramp slides to the ground. If ramp makes angle of 40 degree with ground and object weighs 25 pounds, find the acceleration of the object.
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1answer
40 views

Magnetic field by current in an infinite cylinder

Let $V\subset\mathbb{R}^3$ be an infinitely high solid cylinder of radius $R$, with its axis coinciding with the $z$ axis, entirely enclosed by the cylinder's lateral surface. Then, for any constant ...
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2answers
29 views

Trigonometry word problem (involving wires)

A guy wire $78$ feet long runs from the top of a pole $56$ feet high to the ground and pulls on the pole with a force of $290$ pounds. What is the horizontal Pull on the top of the poll? I am not ...
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1answer
17 views

centroid of a right triangle

I'm asked to find the $M_x, M_y$ and the centroid of the shape created by the functions $5x/6$ and $x=6$ that has a density of $5$. I find $$M_y \int_0^5 \frac{5}{6} x^2dx = \left. \frac{5}{18} x^3 ...
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2answers
40 views

What kinds of motion obeys a higher order form of angular motion?

Angular velocity $\vec{\omega}$ can be defined in terms of velocity $\vec{v}$ and position $\vec{s}$ as: $$ \vec{\omega} = \frac{\vec{s} \times \vec{v}}{\left\lvert s\right\rvert^2} $$ Constant ...
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1answer
36 views

Finding when velocity is zero

Given trajectory $s(t) = 2t^3 - 15t^2 + 36t + 2$ find, when velocity $v = 0$. I'm doing this the following way: $$v = \frac{ds}{dt} = 6t^2 - 30t + 36.$$ Then making $v = 0$, i.e. $6t^2 - 30t + 36 = ...
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1answer
33 views

A projectile is launched with a velocity of 30 m/s at 40° to the ground. To two decimal places, what is its horizontal velocity in m/s?

A projectile is launched with a velocity of $30 \, m/s$ at $40^\circ$ to the ground. To two decimal places, what is its horizontal velocity in $m/s$? A ball is thrown downward from the top of a ...
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1answer
649 views

If a bead is suspended by 2 strings, one vertical, the other diagonally, why are the tensions equal?

I have a text book which gives two diagrams of beads suspended from strings with different angles, and worked examples to calculate the tension in the strings. The first bead is suspended by $2$ ...
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0answers
29 views

Show a beam is in equilibrium given the stress tensor

Having some trouble with this: https://gyazo.com/0835bdaa8e01cb976765aac94555f6ef I know how to show that at x_2 = -h the surface traction is zero, but I'm not sure how to show it's in equilibrium? ...
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1answer
62 views

Static self-gravitating gas spherically symmetric?

Let me state my problem in $\mathbb{R}^3$: Suppose we have an open set $U\subset \mathbb{R}^3$ and a positive $C^2$ density $\rho:U \to (0,+\infty)$ such that its total mass is finite: ...
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1answer
1k views

Calculating the average force (mathematical physics)

I am trying to calculate the average force with regards to this question: Calculate the average force that USA gold medalist Allyson Felix (mass = $55.3$ kg, height = $168$ cm) exerted backwards on ...
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3answers
223 views

Calculate moment of inertia of Koch snowflake

That's just a fun question. Please, be creative. Suppose having a Koch snowflake. The area inside this curve is having the total mass $M$ and the length of the first iteration is $L$ (a simple ...
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1answer
86 views

Integrate second order DE once

Given the vorticity equation $$\frac{D \omega}{Dt}=(\omega \cdot \nabla)\textbf{u}+ν\nabla^2ω$$ and $\textbf{u} = (−αr/2,v(r),αz) $ in cylindrical polars where alpha is positive constant. Find ...
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0answers
25 views

Is there any way to differentiate between a walking motion and any other movement given x-,y- and z-axis inputs from the hands and the head? [closed]

Not sure how much of this is math and how much is behavioural science/psychology, but anyway: Given three sensors (one on each hand and one on the head) that each give the position and acceleration in ...
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0answers
43 views

Finding the distance between two moving objects

In this case there is a missile whose initial position is $A(30,40)$ with a velocity of $[50,30]$ and an asteroid whose initial position is $B(400,250)$ with a velocity of $[-20,-30]$. The position of ...
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2answers
962 views

Orbital velocity decreases with radius, yet to increase altitude a spaceship must accelerate. Where does the velocity go?

The following has been bugging me recently and I can’t figure it out: The orbital equation of an object of negligible mass is: $$v = \sqrt[2]{MG \over r}$$ So in other words, v decreases as r ...
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0answers
31 views

About periodic trajectories of a Hamiltonian system

Consider a Hamiltonian system with Hamiltoniana $H (\mathbf{q}, \mathbf{p})$, where $H$ doesn't depend on time $t$. It is known that in some domain of phase space the trajectory of system are peiodic. ...
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1answer
909 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 ...
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0answers
46 views

Spring Problem with Frequency [closed]

Two masses of mass 'm' are connected by a spring with spring constant k at either end of the spring. a) What is the resonant frequency of the system in terms of m and k? b) If the masses are each ...
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1answer
15 views

Velocity along curve given velocity in one axis

Let's say that I have some particle travelling along a 2D trajectory mapped out by some infinitely differentiable function $f$ (in this case $f(x) = x^{-1}$). I know the velocity of the particle ...
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0answers
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(Differential Galois Theory) Where is the proof that the three-body-problem is unsolvable?

I'm looking for a proof, which shows that "the 3-body-problem" in physics is mathematically unsolvable. Does anyone know some URLs that contain a proof in mathematical detail? You know, in ...
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0answers
32 views

How to prove the orbit of planet is a circle or ellipse?

I think it is enough by $F=ma$ and $F=\frac{GMmr}{|r|^3}$.But I get stuck in a ODE $$ x'(t)=\frac{-GMx(t)}{(x^2(t)+y^2(t))^{3/2}} $$ How to deal it ? Or how to prove the orbit of planet is a circle ...
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1answer
8 views

Finding the radius of frustum cone?

I'm trying to understand how can i find the radius from the figure , the solution of the radius is given in the equation but I'm not getting how its derived enter image description here
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1answer
2k views

Calculate how long a ball will be in the air after being thrown

So I'm doing some online homework, and have done this specific problem 3 different times and gotten the same answer, but the answer I get seems to be wrong? The problem is as follows: (a) With ...
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2answers
397 views

Centre of Mass and Moment of Inertia of a sphere - spherical cap

I have been given a sphere of radius a, from this sphere a cap of hight h is cut off. 1) What is the centre of mass of the rest of the sphere? 2) What is the moment of inertia regarding the axis of ...
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2answers
60 views

Circuit Analysis problem (find the problem)

In this question, I know that $\text{C},\text{R},\text{T},\text{A}\in\mathbb{R}^+$ I've this circuit (the bottom of the resitor is connected to earth ($0$)): When I use Laplace transform I can find ...
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2answers
40 views

Second order non linear differential equation: Central force question

The problem is as below: I have derived that the particle satisfies the motion equation $$ \frac{d^2u}{d \theta ^2 } + u = \frac{F(1/u)}{mh^2u^2} $$ by Newton's Law, $u= 1/r$ and $h = r^2 \frac{d ...
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2answers
931 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 ...
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1answer
42 views

Ellipsoid moment of inertia matrix

Some background info: torque $\tau$ is defined as $$\tau = I*d\omega$$ Where $I$ is the moment of inertia matrix and $d\omega$ is an object's rotational acceleration. As I understand it, the inertia ...
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2answers
2k views

Finding Moment of Inertia (Rotational Inertia?) $I$ Using Integration?

I just came back from my Introduction to Rotational Kinematics class, and one of the important concepts they described was Rotational Inertia, or Moment of Inertia. It's basically the equivalent of ...
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1answer
28 views

Unique ground state of Schrödinger Operators

I'm reading a book and there is an argument that the ground state of a Schrödinger operator is unique. The problem is I think the argument is complete non-sense! These are lecture notes by Witten, I ...
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2answers
18 views

If the height of an upwardly thrown ball can be approximated by $h(t)=h_0+v_0t-\frac{g}{2}t^2$, what is $\frac{h(t_2)-h(t_1)}{t_2-t_1}$ conceptually?

I know that it describes the secant through $(t_1,h(t_1))$ and $(t_2,h(t_2))$, but I wouldn't know how to interpret it in "real life" terms. I also know that if $t_1$ tends towards $t_2$, I get the ...
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1answer
77 views

Employing Newton's Laws with differential equations [closed]

Going through some problem sheets from previous semesters and can't find a full solution for this question so was wondering what the answers might be. A particle of mass $m$ moves on the $x$ axis ...
3
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0answers
26 views

Dissipation term in wave equation

If we're given a string with mass density $\rho$ in units $\frac{M}{L^3}$ with constant cross-section $A$, tension $T$ in units $\frac{F}{L^2}$, and whose length is $L$; and then we assume that the ...
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1answer
892 views

Acceleration and Tangential Velocity Vector? <Completely Lost>

Find the resultant acceleration of a particle moving on a circle of radius 0.70 m, if its angular speed is 37 rpm and its tangential acceleration is 2.9 m/s2. Express the angle with respect to the ...
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1answer
28 views

Calculate position with increasing acceleration.

So if calculating the change in an object's position (with a constant acceleration) is done with this equation: $o = vt + (\frac12)a t^2$ $o$ is offset from original position $v$ is starting ...
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1answer
58 views

Parabolic slide

Given a friction-less slide $y=x^2$, place a particle on the slide at $(1,1)$. The particle is acted upon by constant gravity $g= 9.8$ units/s/s. At what time does it reach bottom? The ...
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1answer
27 views

Vector Force Application

I have this question for Math StackExchange Site. Suppose you would like to cros a $132 ft$ -wide river in a motor boat. Assume that the motorboat can travel at $7.0mph$ relative to the water and ...
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0answers
14 views

Modeling population density with PDE

If we know that the population density $u(x,t)$ in some lake varies as a function of $x>0$ and time $t$, where $x$ increases downwards with depth, and that the population diffuses with constant $D$ ...
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Writing PDE in the form of convervation law

What does one need to know in order to write $\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}+\frac{\partial^3 u}{\partial x^3}=0$ in the form of a conservation law, which contains the ...
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41 views

Why don't more celestial bodies exhibit higher-order rotations?

It is well known that the Earth spins on its axis. It is also well known that the Earth's axis also precesses, i.e. spins around a secondary axis, much more slowly. Less well known is that we have ...
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1answer
21 views

Computate the commutator $[p^n,x]=-ihnp^{n-1}$

Computate the commutator of $[p^n,x]=-ihnp^{n-1}$. With $p=-ih \frac{\delta}{\delta x}$ the impulse operator. $h$ stands for $\frac{h}{2\pi}$. Answer: I do it with induction over $n$. For $n=1$ ...
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2answers
33 views

Two trains and a fly using the series

I'm having some difficulties dealing with this problem: A train starts travelling from A towards B. It's velocity is v. Simultaneously train starts travelling at the same velocity from B to A. The ...
2
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1answer
43 views

Pendulum loss/gain of time per day given : $\ddot{\phi}+\frac{g}{l}\sin{\phi}=0$ and max displacement $5^{\angle}$

Here is what i am given: The oscillations of a pendulum are described by the equation: $$\ddot{\phi}+\frac{g}{l}\sin{\phi}=0$$ where $\phi$ is the angle between the pendulum and the vertical axis, ...
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0answers
77 views

A version of Ampère's law

The most common proof that I have found of the fact that Ampère's law is entailed by the Biot-Savart law uses the fact that, if $\boldsymbol{J}:\mathbb{R}^3\to\mathbb{R}^3$, $\boldsymbol{J}\in ...
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1answer
23 views

What direction would a hinge's reaction force point?

In my homework question there is a ladder with the bottom touching the smooth floor and the other end is attached to a hinge. I need to draw a force diagram and use that to find the normal. There is ...
2
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1answer
37 views

Vortex flow - Surface Integral

Consider the vortex flow of a fluid of density $\rho$ where the fluid rotates with an angular velocity $\omega$ about the $z$-axis. Determine where a unit square $S$ on the $yz$-plane should be placed ...
3
votes
1answer
518 views

How to convert FFT magnitude of square wave to dBm?

I wish to convert the FFT magnitude of square wave into dBm. I use FFT to covert voltage of square wave to a complex number, then i absolute the complex number into magnitude. Then i divide the ...