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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10 views

Integration of $dR/(d{\alpha}R_0)=-\tan (\pi/N)$

i was doing a physics problem (circular motion's problem) where i had to deal with an object in motion approaching to the center over a regular N-agon and i end up having to integrate this function: ...
3
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1answer
13 views

Differential length of a logarithmic spiral

I am working on a problem that asks to find the magnetic field at the origin of a logarithmic spiral $r = e^\theta$ from $\theta = 0$ to $\theta = 2\pi$, where the angle $\theta$ is measured ...
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0answers
14 views

Finding the range of a cannonball- proof verification.

I asked such a question before but I do learn best by mistakes and corrections.(I didn't fully understand it yet.) I could really use your verification: A cannonball is being fired with a velocity of ...
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1answer
18 views

How to get a range of a body being shot\thrown? Theoretical question.

I already asked a similar question here, but the answers were technical, leading me to no genuine comprehension of what I am doing.(I am not complaining or anything, I really thanked you then.) ...
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2answers
65 views

What are some tips/techniques that might help me solve this (brutal) differential equation?

I've been working on a certain physics problem involving differential equation for two years. I've made some progress on it recently, but I've come across another roadblock, namely an integral that I ...
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0answers
7 views

Moment of inertia of lower dimensional bodies and limits

I have noticed that the moment of inertia of an $n$-dimensional body having uniform density $\rho$ is at least sometimes identical to the limit of the moment of inertia of a $(n+1)$-dimensional body ...
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0answers
9 views

Express 3 dimensional movement by using 2 vectors?

I have a system that can be described in 3 equations(Lagrange Euler equations) for each coordinate. $L_x, L_y, L_z$: $$\frac{d}{dt} \frac {\partial \mathcal{L}}{\partial \dot{L_x}} = \frac ...
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0answers
8 views

A collective spin motion, related to differential equations. - - how to prove y component of the field is zero throughout the motion?

This is a pure mathematical question, here is a little background for the interested reader, you can jump directly to the mathematical part if you are not interested. background Imagine we have ...
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2answers
39 views

How to calculate the force of tension?

"Three masses are connected by wires and hung vertically. Draw a Force Body Diagram for each mass and determine the tensions in the three wires." I know there are forces only in the y-direction, ...
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0answers
16 views

How can i generate energy using only a kite? [on hold]

So I have this homework and basically what I need to do is a kite using biodegradable materials. The kite must be able to generate enough energy to light a led.
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0answers
16 views

A pendulum 10cm in length is diplaced through an angle $\theta$ with the vertical? [on hold]

a) Express the vertical displacement, $d$, as a function of the angle $\theta$. b) What is the vertical displacement of the end of the pendulum when $\theta=\pi/3$?
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1answer
34 views

Connection between Functional Analysis and Quantum Physics [on hold]

Hi does anyone have an idea of which specific areas of Functional Analysis and Topology have a strong connection with the study of Quantum Mechanics and Quantum Field Theory? Thanks.
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0answers
20 views

How are 2D collision forces calculated?

Between 2 circles of the same radii, how can I calculate the collision forces to apply to each of the 2 circles? I have position, mass, and velocity for each of the circles. Here's what I have ...
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1answer
23 views

How to calculate solid angle of a rectangular detector of 20cm x 10cm?

I have an detector of $20cm*10cm$, how can i calculate the solid angle subtended by the detector if the detector is placed at $30$cm apart? Because directly i cannot use the formula ...
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2answers
34 views

Integrating to find deceleration, and finding ball height? [on hold]

1) A ball is thrown straight up from a height of 8 ft with an initial velocity of 40 ft/sec. How high will the ball go? (Take g = 32 ft/sec2.) How would I do this? Wouldn't I need to find a velocity ...
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0answers
20 views

Problem with center of mass in polar coordinates

When we calculate center of mass using rectangular coordinates, we find the average values in each coordinate. Obviously we can't do this very same thing in polar coordinates: if we integrated a ...
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0answers
27 views

Can't replicate solution to a non-linear PDE ($- \square \varphi + \lambda \varphi^3 = 0$)

I am trying to replicate the solution of this paper : http://arxiv.org/pdf/0807.2179.pdf Which is, roughly, for the quartic scalar field theory, $- \square \varphi + \lambda \varphi^3 = 0$ a set ...
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1answer
44 views

Finding work done by a force [closed]

Find the work done by the force field $\overrightarrow{F}(x, y) = xy > \hat{ i} + 3xy^2 \hat{j}$ in moving an object along the line segment from $(0, 1)$ to $(2, 4)$.
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0answers
12 views

Source sound position mutiple point

i want find sound source position like this picture : ![find source][1] But i just konw the delay I know the delay for position 2 and 3 (or more) from source after hits the first point. I don't ...
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1answer
20 views

Computing relative directions

I'd like to ask your help for this problem: I have two bearings. These bearings are angle of direction from $-180$ to $+180$ degrees. One is between my current position $(A)$ and a target $(T)$. One ...
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0answers
11 views

Selective substitution of parameter

I came across some solutions to a problem which states: $$V_1=V_2e^{j\theta}=V_2\cos{\theta}+jV_2\sin{\theta}=V_2\cos{\theta}+jI_2Z_0\sin{\theta}$$ In this case they just replace the $V_2$ with its ...
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4answers
54 views

Physics based trigonometry question

I am working on solving the problem stated in this image: I understand almost everything about this problem. I solved for the magnetic field along the axis of a circular loop, and now I need to ...
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2answers
25 views

How to find the range of a cannon ball?

A cannon is positioned with a direction of 60 degrees between the ground and itself. (Sorry, again, for my poor English. I hope you understood that sentence.). The shooting velocity is ...
3
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2answers
74 views

How are these definitions of the inertia tensor the same?

I'm looking for some help in understanding the inertia tensor (not the physics, just the math). I'm trying to figure out how to convert between the wedge product and tensor product definitions. ...
2
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0answers
39 views

Question related to the ballistic motion

A point mass will move in the gravitational field of the Earth according to the equation $$\ddot R =-\frac{GM_eR}{|R|^3},$$ where $R$ is the position vector of the point mass measured from the ...
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0answers
49 views

how to solve this integral involving any square root

how to solve the integral $\int\sqrt{\alpha+\beta e^{\gamma t}}dt$ i got this integral from the problem Given that the velocity $v$ of a body $t$ segonds after passing a point $O$ is found by ...
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1answer
22 views

Simple Harmonic Motion Formula

The SHM general formula is this: $y(t) = A\sin(\omega t + \alpha) +B$ I have two questions about it As far as I know, there is the cosine formula for when the particle starts at P and sine for ...
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3answers
55 views

Where have I gone wrong? A basic question in physics (Mechanics)

A stone is dropped vertically in a velocity of $15$ minutes per second, from a point $40$ meters above the ground (excuse my poor English.). a. How long will it take to the stone to hit the ground? ...
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1answer
17 views

Is $Cr^a\hat r$ always a conservative vector field?

Is the vector field $\vec r(r, \theta, \phi) = Cr^a\hat r$, where $C, a\in \Bbb R$ are constants and $r \in \Bbb R^+ \cup \{0\}$ is the radial component, always a conservative vector field? I really ...
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votes
1answer
13 views

Matlab, given data in matrix form 550x2, need to find the period of signal [closed]

By using Matlab, I have adata in matrix form 550x2, need to find the period of signal by finding two maximas and finding difference between their x-axis location.
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1answer
44 views

Finding speed of snowballs given initial velocity and angles

You and a friend stand on a snow-covered roof. You both throw snowballs from an elevation of $14$ m with the same initial speed of $12$ m/s, but in different directions. You throw your snowball ...
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2answers
35 views

is there any mathematical model how the guitar strings are related?

I'm just curious to know the mathematical relationship between guitar strings and how their frequency changes with the variation of guitar's string length and thickness. Say, I'm vibrating some node ...
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1answer
23 views

When should I recalculate starting values for my physics engine's multistep integration?

I'm writing a physics engine that uses an Adams-Bashforth and Adams-Moulton predictor-corrector pair for integration, and Runge-Kutta 4 to calculate starting values for their initialization. I am ...
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3answers
324 views

Solve for velocity, if acceleration is a function of velocity?

Yes, this is a canned question, because canned questions are simply solvable to understand ideas. No, this is not homework. For simplicity, let's assign values. A given object weights 1000 kg, it ...
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3answers
24 views

A $1.00 m^3$ volume of iron has a mass of $7.86 \cdot 10^3 kg$, find the length of one side with a mass of $200g$

So this is a relatively simple physics problem, but I'm sort of stumped and need some help finishing this off. The full problem reads: Iron has a property such that a $1.00 m^3$ volume has a mass ...
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1answer
23 views

Acceleration vector at highest point of accelerated projectile [closed]

A projectile is thrown at an angle of $60$ degrees with horizontal with initial speed $20 m/s$,with H being the highest point of its trajectory.Another particle P is now forced to move along the same ...
2
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2answers
26 views

Strange formula for radar horizon, does anyone know where it comes from

I am in Electronics Technician "A" School in the Navy and we are learning the basics of radars. In one module, we were exposed to this formula which confuses me. If someone has an inkling as to why it ...
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1answer
27 views

Spaceship transit times [closed]

I want to travel X km. My ship can accelerate at 1 G for half the distance, then needs to decelerate at 1 G for the second half. What's the formula for determining the transit time?
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1answer
19 views

Expression for $dW$ for a 3D position dependent force $\vec{F}(\vec{r})$.

I was looking at the derivation of the infinitesimal element of work done for a 3d position dependent force and I couldn't get over the switching of $\text{d}\vec{v}$ and $\text{d}\vec{r}$ in the ...
0
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1answer
16 views

Little mistake with Levi-Civita symbol property

I have this equation $ \varepsilon_{ijk}B_k = \partial_iA_j - \partial_jA_i $ and I was asked to prove $\mathbf{B}=\nabla\times\mathbf{A}$, where $\mathbf{B}=B^i\mathbf{e}_i$ and ...
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1answer
48 views

Planetary Motion: A comet describe a parabola about the sun [closed]

A comet describe a parabola about the sun, show that the sum of the squares of the velocities at the extremities of a focal chord is constant. I have no idea how to solve. Please help. I only ...
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0answers
38 views

Energy conservation $\iff \frac{dE}{dt} = 0\ $? [migrated]

If I'm asked to prove that a system is/ isn't conservative and compare it to whether or not the Hamiltonian is conserved, does that mean I need to compute the time derivative of energy $(T+U)$? Doing ...
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1answer
15 views

Rearrangement of harmonic oscillation formulae

Can anyone show me why the following identity is true? $$A\cos(\omega t) + B\sin(\omega t) = \sqrt{A^2+B^2}\cos\left(\omega t + \arctan\left({ \frac BA}\right)\right) $$ I ask this is relation to ...
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2answers
20 views

Calculate work done using integral

A chain lying on the ground is 10m long and its mass is 80kg. How much work is required to raise one end of the chain to a height of 6m? So im working in MKS system since its m and kg so the work ...
3
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1answer
26 views

Inequality involving sums and products (related to multi-stage rockets)

Let $a_i$ and $b_i$ be strictly positive real numbers for $i=1,\ldots, n$. I wonder whether the following inequality holds in general or does not:$$\frac{\sum_{i=1}^n a_i+\sum_{i=1}^n ...
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1answer
27 views

A Problem On Vectors-Forces

A particle is subjected to two equal forces along two different directions.If one of them is halved,the angle which the resultant makes with the other is also halved.The angle between forces is ? Ok ...
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2answers
29 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
32 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 ...
0
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2answers
56 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
33 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} ...