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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3answers
342 views

How long would it take for light to go through a human eyeball and back to the other side

I couldn't find any TAGS that fit my question... I don't know if I'm doing this correctly. I want to know how long a "twinkling of an eye" would be. A twinkling of an eye is the time it takes from ...
1
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1answer
62 views

Units of ODE solution don't match

I have to solve the differential equation: $v\,'=g-cv$. Sorry in advance for lack of latex. I will learn it soon, please let me make a question using the common programming notation for my ...
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0answers
45 views

How can I use the Bullet-Physics's ray-cast normal to calculate angles for a object to lay on a surface?

[Give the normal of a surface in XYZ format, how do I calculate rotations (also in XYZ format) needed to set an object parallel to the surface?] I have a collision library that uses the bullet ...
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3answers
3k views

How do you calculate kw from kwh?

A family spent \$235.25 in the month of February to heat their house. a) Calculate the kilowatts of energy they consumed given that the price of electricity is \$0.09/kWh (kilowatt hour). Assume ...
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1answer
39 views

Significance of 'faces' in Stress tensor components?

I am trying to understand what the significance is of the face for which a force is acting on when talking about a stress tensor. Say we consider the components $T_{xx}$ and $T_{zx}$ of the stress ...
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1answer
12 views

How to divide a vector on a sphere into northern and southern components?

Suppose we have $S^2$ and a vector $\vec{A}$ pointing at a random direction. Let us divide the sphere into $S_N$ for $0 \leq \theta \leq \frac{\pi}{2}$ and $S_S$ for $\frac{\pi}{2} \leq \theta \leq ...
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2answers
34 views

Solving for the resonant frequencies of a mass-spring system

Given 3 masses ($M_1, M_2, M_3$) connected linearly with 2 springs ($K_1,K_2$), let $X_1,X_2,X_3$ be the displacement of the masses relative to their rest positions. Using the Lagrangian I can write ...
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0answers
12 views

Modeling smoke cloud as expanding Gaussian / ellipse

I am making a simplified model of smoke coming from a train's smokestack. You can imagine that if you want an accurate model you have to think in 3D and use computational fluid dynamics and stochastic ...
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3answers
52 views

kinetic energy approximation

If a pitcher throws a pitch at a velocity $v_0$, then the kinetic energy is $E_0=\frac 12mv_0^2$. If the pitcher releases the pitch from x feet higher, then we will suppose that he can readjust his ...
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6answers
1k views

What Mathematics questions can be better solved with concepts from Physics?

Over the years, I've seen several questions in mathematics that can be solved using concepts borrowed from Physics. Having seen these question, I'm interested to find out what other mathematics ...
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1answer
42 views

How can we explain energy (or intensity) distribution mathematically? [on hold]

We have the following scene: We can see that in this scene, there are places which are very bright and there are places which are dark (shadows). I want to know, how can we explain this energy (or ...
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3answers
53 views

potential energy

Let $t_1$ be the time it takes an object to fall $x$ feet. The kinetic energy of a ball of mass m dropped vertically $x$ feet is $E_1=\frac 12mv_1^2$, where $v_1=h'(t_1)$. Find the formula for $E_1$ ...
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1answer
48 views

Triple Integral Using Cylindrical Coordinates

Find the total mass of the solid defined by the inequalities $x^2 + y^2 + z^2 \ge 1, \hspace{.1cm} x \ge 0,\hspace{.1cm} y \ge 0$ with mass density $z^2$. I know I have to use triple integrals to ...
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0answers
47 views

Integrate $\int_{-\infty}^{+\infty} \frac{1}{\sqrt{P(x)}}e^{-ax^2 - bx - c}dx$ where $P$ is a polynomial of degree $6$

From a physics problem I'm interested by a closed form of this integral : $$\int_{-\infty}^{+\infty} \frac{1}{\sqrt{P(x)}}e^{-ax^2 - bx - c} dx$$ where $P(x) = \lambda_6 x^6 + ... + \lambda_0$ I ...
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0answers
11 views

Question about Spring mass damping system ?? [on hold]

I have a spring mass damping system with mass = 6 gram, spring constant = 157000 N/m, damping co efficient = 6.7 N/m, input y(t) = 20 um. is it necessary that doubling mass from 6 to 12 gram would ...
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1answer
252 views

derive an equation for this mass spring damper

derive an equation to represent this mass spring damper in terms of input fore $F$ and relates to output displacement $(x)$ when springs $K_1=3$ , $K_2=5$ damper $C=6$ and mass $M=1$ , $F$ is a step ...
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1answer
75 views

All $f(x)$ on $[0,1]$ such that center of mass of the function (uniform density) is on its graph

So, as the title describes, I'm trying to find a way to express all $y=f(x)$ differentiable on $[0,1]$ such that the center of mass of the function, assuming it has uniform density, will be a point on ...
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1answer
42 views
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0answers
19 views

How do I find the angular momentum and the energy of a central force?

I've been studying classical mechanics with Symon's book and I'm having trouble when I have to find the energy and angular momentum for a given potencial if the particle moving in a circular orbit, ...
1
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1answer
58 views

Heat equation — Modelling a real-life situation

I have read through a lot of books and lecture notes that cover the heat equation and I am still not sure how I would model the easiest real world situations. For example, take a rod at constant ...
2
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1answer
32 views

Defining a partial derivative with respect to an antisymmetric tensor/matrix

I'm looking at some nonlinear electrodynamics, and have been following a textbook which contains a primer on some of the stuff I'm interested in following up. However, I seem to have fallen at the ...
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1answer
52 views

A problem on collision of two elastic spheres

Two elastic spheres, each of mass $m$ collide directly. Show that the energy lost during the impact is $m(u^2-v^2)/4$, where $u$ and $v$ are their relative velocities before and after impact. ...
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1answer
29 views

Impact of two bodies problem

A body of mass $M$ moving with a velocity $u$ collides with another of mass $m$ which rests on a table. Both the balls are perfectly elastic and smooth and the the body of $m$ is driven in a ...
0
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1answer
13 views

Curvature at a point in a vector valued function

I am trying to determine the curvature when $t=2$ of the function $r(t)=<t^3,3t^2,8t>$ So I found $v(t)=<3t^2,6t,8>$ and $a(t)=<6t,6,0>$. So now that I have these two functions, I ...
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2answers
446 views

Index notation for tensors: is the spacing important?

While reading physics textbooks I always come across notation like: $$J_{\alpha}^{\quad\beta},\ \Gamma_{\alpha \beta}^{\quad \gamma}, K^\alpha_{\quad \beta}.$$ Notice the spacing in indices. I can't ...
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2answers
48 views

If you flip a quarter, what are the odds that you will land on that little piece on the edge? [duplicate]

If you were to flip a quarter what is the probability you will get the quarter to land on it's little edge? How would you calculate this? Assuming the probability is not $0$ and is instead a really ...
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1answer
25 views

How do I calculate the gravitational force exerted by a thin ring of uniform mass M?

I'm working on a problem and can't seem to get it. Find the gravitational force exerted by a thin uniform ring of mass M and radius a on a particle of mass m lying on a line perpendicular to the ...
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0answers
26 views

Find the wrench pitch

A system of forces consists of a single force ${\bf F} = 2{\bf i} − {\bf j} + 2{\bf k}$ acting at the origin together with a couple of torque ${\bf G} = 9{\bf j}$. Describe the equivalent wrench ...
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1answer
19 views

unit vectors: solving with component method and graphical method

P and Q are vectors in the X , Y plane, have the same magnitude, and are perpendicular to each other. If Q=3.0i+4.0j. What is P?
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1answer
179 views

How to write $SO(2n)$ characters in terms of rotation angles?

Say one is working in a representation of $SO(2n)$ such that it has the highest weights $(h_1,...,h_n)$. And let $\{H_i\}_{i=1}^{n}$ be a basis in the Cartan of $so(2n) = Lie(SO(2n))$. Now one says ...
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2answers
153 views

Well-posed problem

In the definition of a well-posed problem it states that a problem is well posed if: 1.A solution exists. 2.The solution is unique. 3.The solution's behaviour changes continuously with the initial ...
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1answer
667 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 ...
2
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1answer
52 views

Stuck on computing distance travelled from velocity and yaw rate.

I am somewhat stymied on what appears to be a simple formula. Here is the problem statement: Assume that a rigid body is traveling with constant velocity $v$, and is rotating with a constant yaw rate ...
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1answer
40 views

Methods of Calculating Position

Suppose we have the following code (Euler Method?) to determine Position versus Velocity, Acceleration and Time: ...
3
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2answers
58 views

Functional Derivative ${\delta q_a(t)}/{\delta q_b(t')}$

$\newcommand{\fdv}[2]{\frac{\delta #1}{\delta #2}}$ $\newcommand{\dv}[2]{\frac{\mathrm{d} #1}{\mathrm{d}#2}}$ $\newcommand{\pdv}[2]{\frac{\partial #1}{\partial #2}}$ I'm from a physics background and ...
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0answers
24 views

Sphere intersecting a triangle

I'm studying "game physics" programming, and in this article, at page 14, I don't understand how is the author right. ... if the sphere does indeed collide with the inside of the triangle then a ...
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1answer
18 views

How to generate the icosahedral groups $I$ and $I_h$?

The icosahedral groups $I$ with 60 elements and $I_h = I \times Z_2$ are also three dimensional point groups. However, ever unlike other point groups, it seems there is rarely reference to give their ...
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1answer
30 views

Finding constant acceleration required to hit a target where mag(a) = n

I am currently using the equation: $$ \vec p=\frac12\vec at^2+\vec vt+\vec x$$ to find the acceleration I need to move from one point to another. where: $\vec p$ = target position (point 2d) ...
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3answers
62 views

Figure out the component of a value in X and Y coordinates using trigonometry.

Alright. It's been long that I studied trigonometry and did Laws of Motion and Free Body Diagrams, and I was decent good at them, but somehow I am having trouble in understanding the following. Note ...
1
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1answer
23 views

Mechanics: Projectiles involving a ball shot out of a cannon, moving in the opposite direction of the shot

A child is playing with a toy cannon on the floor of a long railway carriage. The carriage is moving horizontally in a northerly direction with acceleration $a$. The child points the cannon ...
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1answer
63 views

The real equation of a pendulum

In physics I never solve the equation $\ddot\theta = \sin(\theta)$. Instead, we used the approximation $\theta = \sin(\theta)$ for small angles and then it was easy to solve. I didn't do any physics ...
6
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1answer
445 views

Studying quantum mechanics without physics background

I am a PhD math student, and I am wondering if I should study quantum mechanics while I don't have an undergrad background in physics. I posted this question in physics stackexchange, but there ...
7
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1answer
121 views

What is the generalization of Gauss's Theorem to a manifold?

In a (pseudo-)Riemannian manifold with constant basis vectors, one certainly has that the integral of the divergence of a tensor field $T$ over a submanifold $\Omega$ is equal to the integral over the ...
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1answer
65 views

What's wrong with my math in this function to update the position of a planet near a star?

Initially the code seems to work as the planet curves toward the star, but then as it should either get pulled into the star or make an orbit, it just gets pushed away in the opposite direction. What ...
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0answers
49 views

A problem on Constrained Motion

Q. A particle is moving in a smooth curve under gravity and its velocity varies as the actual distance from the highest point. Prove that the curve is a cycloid. Attempt: The eq. of motion is ...
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0answers
65 views

Why do people prefer cosine to sine when speaking of harmonic oscillation?

In almost all of the physics textbooks I have ever read, the author will write the oscillating function as $$x(t)=\cos\left(\omega t+\phi\right)$$ My question is that, is there any practical or ...
6
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1answer
697 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 ...
0
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1answer
29 views

solving equation in terms of $w_1$ and $w_2$

I have a a physics problem involves the following equation $$\tan(\alpha) = \frac{(w_1 + w_2)^{1/2}}{w_3}$$ from a certain set of equations that I use I derive the following equation: ...
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2answers
60 views

Practical use for negative $dt.$

I am writing a section of notes for Calculus 1 on related rates. In the section where I discuss differentials, I write that the quantity $dt$ must be nonnegative. I imagined the only reason it would ...
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1answer
68 views

What is the ratio of the intensities of the two sounds?

1. Suppose that a jet engine at 50 meters has a decibel level of 130, and a normal conversation at 1 meter has a decibel level of 60. What is the ratio of the intensities of the two sounds? we ...