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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1answer
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Can you add potentials if charge redistributes?

Let say we have charged conductor $M$ and we know its potential energy function $V_m(r)$ when $M$ is isolated from any charges. We also have charged conductor $N$ with potential energy function ...
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1answer
37 views

Twin paradox spacetime intervals

I've very recently started to try to understand special relativity. I want to get a decent understanding of the twin paradox. I'll post what I've done so far and highlight what's gone wrong for me. ...
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1answer
45 views

Infiniteness of a knot energy

I am going through the paper, Physical Knots, by Jonathan Simon. Initially, on page 10, he describes the electrostatic energy of two charged stick, X and Y in space as follows. $$ \int_{x \in X} ...
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1answer
49 views

Starting velocity by distance, time, and friction

I am writing a game in Javascript, and I just got a big math problem, where $\text{friction} = 0.97$. This is what is being looped every $1000$ / $60$ milliseconds, to make the projectile move all ...
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1answer
68 views

Pendulum with angular velocity

I have another pendulum problem again but this time it's with angular velocity. My question is: If a pendulum is initially at its unstable equilibrium position, then how large an initial angular ...
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2answers
39 views

Re-arranging variables

In physics, you can say that: $T-m_2 g = m_2 a$ And that $ m_1 g - T = m_1 a$ So this, when combined, should equal: $a = \frac{m_1}{m_1 + m_2} \cdot g$ How do they arrive at that conclusion? I ...
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0answers
38 views

Line Integral Problem best or easier solved using geometry?

Does anyone have any recommendation on a line integral problem involving vector fields (aka work) such that evaluating the resulting line integral using parameterization would be significantly ...
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0answers
34 views

Cross Product - Moments :: Dynamics 2

This problem is related to Cross Product - Moments :: Dynamics Please look at that link for the background on the problem I am faced with right now, I have linked a pdf of the book that I am using ...
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1answer
40 views

Linear algebra and special relativity

I'm going over an exam I had a couple months back, over the exercises I didn't manage to get right and I'm kinda stuck with the following subtask: Let $\xi$ be a 4-vector with the Minkowski scalar ...
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2answers
25 views

Finding the magnitude of a vector product between two vectors?

Vector $\overrightarrow{A}$ has magnitude $11.0m$ and vector $\overrightarrow{B}$ has magnitude $16.0m$ . The scalar product $\overrightarrow{A}\bullet \overrightarrow{B}$ is $79.0m^2$. What is the ...
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3answers
54 views

Boxes on a slope [closed]

A box with friction slides down a slope and takes 2 times longer than a similar box with no friction takes to slide the same slope. What is $ \mu $ (the coefficient of friction)? I'm pretty lost. I ...
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1answer
25 views

Trying to understand free body diagram [closed]

Please consider the following image: Now I'm just trying to understand how exactly this thing is rotated...I'm looking at it exactly like on the image of the car...So the normal force is slightly ...
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1answer
45 views

Physics Vector Problem - Airplane

Heres the question: A plane leaves the airport in Galisto and flies $140$km at $68.0^∘$ east of north and then changes direction to fly $255$km at $48.0^∘$ south of east, after which it makes an ...
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2answers
41 views

Modeling with First Order Equations [closed]

A ball with mass 015kg is thrown upward with initial velocity 20m/s from the roof of a building 30m high. There is air resistance of magnitude v^2/1325 directed opposite to the velocity , where the ...
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2answers
52 views

Fundamental roles that astronomy played in the development of mathematics

I'm currently a third year undergrad maths student, and am particularly interested in how astronomy changed maths as we know it today? Are there any particular sources that could be recommended? Or ...
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0answers
14 views

Using Invariance of Lorentz interval and constant speed of light to prove the Lorentz transformations

By the invariance of the Lorentz interval and the fact that the speed of light is the same in both frames we have \begin{align*} -c^2 dt^2 + dx^2 = -c^2 dt'^2 + dx'^2 \end{align*} By considering the ...
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1answer
26 views

1-D heat diffusion in a bar with fixed temperatures at the edges

I'm trying to calculate the temperature gradient in a bar of metal with a heater at either end. Initially, the bar is at room-temperature $T_0$, then at $t=0$ the heaters are turned on: $u(0,t)=T_1$ ...
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3answers
101 views

Interpretations of $\frac{\infty}{\infty}$

I am trying to understand the physical sense of the mathematical construct $\frac{\infty}{\infty}$ Suppose we have a function $f(x)$ representing some physical construct depending on a "quantity" $x$ ...
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0answers
58 views

Earnshaw's theorem

Proposition Suppose $U\colon\Omega\to\mathbb R$ is a non-constant harmonic function, i.e. $U\in\mathcal C^\omega$, i.e. analytic, and $\Delta U=0$, where $\Omega\subseteq\mathbb R^n$ is a region. ...
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1answer
49 views

Forces and line of action

A force $F_1 = i - 3j -2k$ at the point $r_1 = -2i + 9j$ another force $F_2 = 2i + j -3k$ at the point $r_2 = i + yj -k$ and a third force $F_3$ are equivalent to zero. Find y for this to be possible. ...
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1answer
46 views

Problem with friction [closed]

Imagine two boxes stacked on top of each other. The bottom box is larger than the top box and it rests on a surface. So: Between the boxes is a friction force constant $\mu_s$ and between the ...
0
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1answer
38 views

What is the most tension I could get [closed]

Look at the following picture: Imagine that mass "m" is very large. What is the maximum tension we can get on the rope? I'm not sure how to understand this. The rope is indestructible I guess, so ...
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1answer
26 views

How to determine the magnitude of a resultant vector?

I was able to determine a resultant vector based on the sum of two vectors and told to express them in vector units. Here is my answer that was correct: ...
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0answers
21 views

Dynamic flows on sphere

How to draw a vector field on $S^{7}$ in the evolution? My own answer to this question is placed in the book in Russian http://socionet.ru/publication.xml?h=repec:rus:gulthb:7 Let I want to draw a ...
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1answer
34 views

Angle that car is at after angular acceleration

A car starts from rest on a curve with a radius of $150m$ and tangential acceleration of $\displaystyle 1.5\frac{m}{s^2}$. Through what angle will the car have traveled when the magnitude of its ...
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2answers
3k views

Perfectly centered break of a perfectly aligned pool ball rack

This question is asked on Physics SE and MathOverflow by somebody else. I don't think it belongs there, but rather here (for reasons given there in my comments there; edit: now self-removed). ...
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0answers
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Plotting motion from velocity equations

I have limited knowledge of physics but enough to frustrate myself. On this webpage there are two equations for Vx dot and Vy dot. The equations are in the background of this page: ...
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2answers
88 views

Particle Motion

So this is a simple problem but I'm just getting stumped. The question is: A particle not connected to a spring, moving in a straight line, is subject to a retardation force of magnitude ...
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0answers
41 views

Derivatives of polar coordinates

I've got a problem for which I'm trying to calculate $\ddot r$. The problem is right here for the sake of reference. So far, I've got that: $$\ddot r=\frac{d}{dt}v_r=\frac{dv_r}{dr}\frac{dr}{dt}$$ ...
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2answers
86 views

Area under the Trajectory of a projectile

I may need some help with the following problem. We have $$ y(\omega)=a+\omega\cdot b - \frac{1}{2}\cdot\omega^2\cdot g $$ where $g$ is the gravity vector $g=\binom{0}{\lambda}$, $\lambda \approx ...
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1answer
44 views

Vector functions applied to a football game

A wide receiver is standing $40$ ft to the left ($x=-40ft$) of the quarterback who is standing at the origin. The receiver immediately accelerates at $\displaystyle 9.79 \frac{ft}{s^2}$ at an unknown ...
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0answers
81 views

Calculate uncertainty of the gradient

In my case I have a directly proportional relation between the dependent and independent variables, i.e. $y=mx$. I know the uncertainty of $y_i$ is $\Delta y_i$ and uncertainty of $x$ is $\Delta x$. ...
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1answer
37 views

How to find position of object on a parabola?

I'm making a computer game, where an object flies along a parabola curve. This object is 'thrown' by a 'robot' towards another robot. I know the vertex of the parabola, and also it's two ...
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1answer
61 views

How do derive equivalent complex versions of linear differential equations.

I've done this before and have forgotten some of the details. I will try my best to re-derive it. Please help fill in the blanks. In my Acoustics book it says: An alternating force may be ...
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3answers
64 views

Finding velocity in optimization problem

Given $s=-16t^2+192t+144$, what is the velocity when $s=0$? This is part of a larger optimization problem which I solved, except for this last part. The critical point occurs at $t=6$, so after ...
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2answers
35 views

Solve for time, given distance and acceleration

Two gangsters are flying down I-70 West at a constant 108 hm/hr. If they make it to Indiana, they will be safe. When they are 1 km away from the Indiana border, while still traveling at a constant 108 ...
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1answer
60 views

Solving for equipotential lines

First off, I apologize if this is in the wrong section of StackExchange, it's at the intersection of several different topics (mathematics, physics, and computer science), so I chose the section that ...
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3answers
73 views

How do you solve this differential equation?

Though I've read questions on this site and really appreciate the quality of the answers, this is my first question, so I hope it follows the site's guidelines. When working with potential energy ...
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1answer
29 views

When to use trig substitution?

I'm trying to solve this physics equation: $$E=\frac {\lambda y} {4\pi \epsilon_{0}} \int_{-\frac l 2}^\frac l 2 \frac {dx} {({x^2+y^2})^\frac 3 2} $$ However, my calculus is a little rusty and am ...
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1answer
61 views

Physics and calculus?

A box slides down a slope described by: $$y = 0.05x^2$$ where $x$ is the x coordinate of the slope and y is the y co-ordinate (both in meters). Find the $y$ component of acceleration at $0.4 m$ if ...
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1answer
78 views

Center of mass in a straight rod

I got an assignment to prove that in a straight homogeneous rod, you can always choose a coordinate system in such a way that $$\int_S x_1 \, dx_1 \, dx_2=0 $$ $$\int_S x_2 \, dx_1 \, dx_2=0 $$ ...
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0answers
59 views

Continuity in a physical context

I'm currently trying to solve an exercise for my quantum mechanics class and have run into a bit of a jam: Suppose we have the following potential : $V(x) = 0$ if $x > |a/2|$ but $V(x) = V_0$ if ...
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1answer
362 views

Calculate maximum velocity given accel, decel, initial v, final position

I'm trying to calculate the maximum velocity of an object given: acceleration deceleration starting position (0) ending position initial velocity I've been trying to use formulas from: ...
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2answers
73 views

Car acceleration with gear shifting

I'm making a web game that requires a player to change gears at the proper RPM zone to win the race. If the player misses the prime RPM zone he will be slowed down by a factor relative to the ...
0
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1answer
50 views

Physics problem - about a shell. Differential equation

Can you help me please, to write the differential equation for this problem, and give me an idea how to solve this equation. A shell of mass $2$ kg is shot upward with an initial velocity of $200$ ...
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0answers
30 views

How to calculate the following 3D ${\bf k}$-space integral?

I'm struggling to calculate$$ \sum_{a,b=\pm}\int\frac{\text d\mathbf{k}}{(2\pi)^3} ...
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2answers
126 views

calculation of Stefan's constant

In the calculation of Stefan's constant one has the integral $$J=\int_0^\infty \frac{x^{3}}{\exp\left(x\right)-1} \, dx$$ which according to Wikipedia is equal to $\frac{\pi^4}{15}$. In this page of ...
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1answer
40 views

Averaging cosine with a randomly varying argument

Suppose I have a function $y(t)=\cos (\delta(t))$. Here $y(t)$ and $\delta (t)$ are single valued functions but not necessarily continuous or differentiable. The function $\delta(t)$ is a "random ...
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1answer
54 views

Finding angle on an inclined plane

How can I go about finding the angle, theta, in this Physics problem? As you can tell, the right-most triangle is a simple 30-60-90 triangle, so above the right angle is a 60deg angle. Then the ...
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1answer
65 views

Elliptical polarisation

In physic context one find the curve with parametrisation in t, $x=x_0\cos(t)$ and $y=y_0\cos(t+\varphi)$ with is an ellipse with equation ...