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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5answers
76 views

Assumptions in Word Problems (Calculus)

I just had a small question about assumptions in mathematical word problems. Suppose you are given a calculus problem (related-rates), "A spherical balloon is inflated with gas at the rate of 800 ...
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1answer
36 views

Dirac Delta identity proof.

I was working on showing that: $$x \frac{\mathrm{d}(\delta (x))}{\mathrm{d}x} = -\delta(x)$$ using integration by parts. I arrived to a point where I had had as an answer the following: $$ -f(0) - ...
0
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0answers
11 views

How the Jacobian is connected to the movement of particle from one domain to another? [on hold]

I am dealing with the proof of Reynold-Transport Theorem. There the Jacobian is used for the changing position of particles from one domain to another. Can anyone help me to understand what does ...
-3
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0answers
22 views

using Lagrange on a double pendulum with a motor and an impeller [on hold]

how do we use Lagrange on a double pendulum with a motor and an impeller(adding thrust) connected to L2 provided the theta 1 or the angle to L1 is maintained/constant.
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0answers
51 views

Symbolic manipulation inside integral

I'm an undergrad who has just completed the standard calculus sequence (1, 2, and multivariable). I've done well in the courses, however, things like the following, which is a derivation of kinetic ...
3
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1answer
246 views

Complex parametrization of Airplane wing?

I read once about complex parametrization with fluid-dynamics objects such as airplane wings, something related Rieman Zeta function. What are the mathematical models this kind of things such as ...
37
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15answers
6k views

Why learn to solve differential equations when computers can do it?

I'm getting started learning engineering math. I'm really interested in physics especially quantum mechanics, and I'm coming from a strong CS background. One question is haunting me. Why do I need ...
0
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4answers
40 views

Integration, ball throw simple example

I thought that I could do it like this. Given that $$g=9.8m/s^2$$ $$\int -9.8 \, dt=v_0-9.8 t$$ Setting it equal to zero we have: $$t=\frac{v_0}{9.8}$$ $$\int \left(v_0-9.8 t\right) \, dt=-4.9 ...
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2answers
162 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
30 views

Calculate launch angle of projectile

I'm creating a game and am having trouble designing aiming system for AI. How do I calculate all angles at which the projectile can be launched from point $T_0(x_0,y_0)$ with launch velocity $v_0$ to ...
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0answers
20 views

Ternary balance with unknown weight

Main references: Ternary (Wolfram MathWorld) Balanced ternary (Wikipedia) Weighing scale: Balance (Wikipedia) <quote> Balanced ternary has other applications besides computing. For example, a ...
1
vote
1answer
49 views

I need some help understanding the tensor algebra done this problem.

I often see equations rearranged across an equal sign and I have no clue what tricks and reasoning they are using to arrive at these solutions. The only resources I can find on tensor algebra only ...
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0answers
24 views

Anomalous effect on friction. [on hold]

A 1kg wood cube. This cube is affected by friction i reverse. Instead of decelerating it will accelerate at an equal rate. Placed in the middle of a concrete room where it has 0.63 coefficient ...
3
votes
3answers
131 views

Explanation of line element formula $dl^2 = dx^2 + dy^2$

I found this in a physics textbook without justification: $$dl^2 = dx^2 +dy^2,$$ where I presume that $l = \sqrt{x^2+y^2}$. Why is this so? By my calculations I obtain $$ dl = \dfrac{\partial ...
4
votes
1answer
41 views

What exactly are the curves that are a best fit to the Harmonic Cantilever?

Let's start with a few references to get an idea: Daniel Goldwater: Harmonic Cantilever Book Stacking Problem Block-stacking problem Harmonic Series and Bricks Interesting related issues: Maximum ...
1
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3answers
37 views

By how much should the distance from the source be increased to reduce the surface illuminance to 30 lumens?

This is my problem and I have no idea how to solve it: The illuminance of a surface varies inversely with the square of its distance from the light source. If the illuminance of a surface is 120 ...
7
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0answers
134 views

How to solve a time-dependent Schrodinger equation in periodic Dirac delta potential

I'm trying to solve a 1D time-dependent Schrodinger equation: $$ i\frac{\partial \psi(x,t)}{\partial t}=\left[-\frac{1}{2} \frac{\partial^2}{\partial x^2}+V(x)+F(t)*x\right]\psi(x,t) $$ where $V(x)$ ...
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0answers
29 views

What is the absolute side of every material coin? [closed]

Besides relative head and tail, does every coin have absolute side?
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1answer
19 views

Setting Up an Integral (depends on displacement vector from a long line)

The following is a physics problem, but I don't actually care about the physics right now. I just want to set up the integral, which I'm having a difficult time doing (the problem is from the book ...
6
votes
2answers
142 views

Line Spectra in Hydrogen atom

Suppose you have a collection of large amount of Hydrogen atoms in $n$th state($n-1$th excited state). They have to go to their ground state($n$=1). Going from $n_1$ to $n_2$ makes a unique spectral ...
2
votes
2answers
244 views

Calculating the linear output force a threaded rod and nut would produce based on the input torque

I would like to calculate the amount of linear thrust a threaded rod combined with a rotationally static nut would be able to produce based on the rotary force applied to the rod. The information ...
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5answers
52 views

Vector field ${\bf F}$ with $\int_S {\bf F}\cdot{\bf n}\ dS=c$

Find a vector field ${\bf F}$ on $ {\bf R}^3$ with $$\int_S {\bf F}\cdot{\bf n}\ dS=c > 0 \tag{1} $$ where $S$ is any closed surface containing $0$ and ${\bf n}$ is normal Here there is a ...
6
votes
1answer
104 views

Why do objects that are farther away look smaller?

What is the reason, mathematical and/or physical, that the further away something is the smaller it looks? We know stars are humungous, but they look like tiny dots in the sky.
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1answer
36 views

The motion of the particle satisfies $\textbf{v} = \textbf{c}\times \textbf{r}$

Why is the path is contained in a circle that lies in a plane perpendicular to $\textbf{c}$ with centre on a line through the origin in the direction of $\textbf{c}$
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1answer
587 views

A Ferris wheel has a radius of 20 m. Passengers get on halfway up on the right side.

A Ferris wheel has a radius of 20 m. Passengers get on halfway up on the right side. The direction of rotation is counter clockwise. The bottom of the Ferris wheel is 2 m off the ground. It rotates ...
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1answer
18 views

Sound and decibels at distance

If I have an object that is 53 decibels at x distance, how many decibels would y objects be at the same distance x, assuming they all created 53 decibels.
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2answers
47 views

Constants for anti-derivatives

Hey StackExchange I'm diving into integral calculus for the first time and I have a few questions about this problem. A steel ball bearing at rest is accelerated in a magnetic field in a line with ...
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2answers
29 views

Calculating velocity of an object moving at 12m/s north, with 5m/s wind from the west

An object moving 12m/s passes north and hits an object. Due to the wind from a west direction, it is pushed sideways at 5m/s. Find the resultant velocity. I don't know where to start with this one, I ...
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1answer
766 views

Angular Velocity of a Pulley

I am having trouble with this questions about angular velocity. Could you please show me the solution? I keep getting $\approx 41.9$ cm/sec but my friend gets $\approx 419$ cm/sec. Question: A ...
5
votes
2answers
83 views

Why is the integral of $\|\nabla f\|^2$ called the energy of $f$?

Let $\Omega$ be a region in $\mathbb{R}^2$ with $f:\Omega \to \mathbb{R}$ a smooth function. Why is the quantity, $$ \tfrac{1}{2} \iint_{\Omega} \|\nabla f\|^2 $$ Called the "energy" of $f$? I am ...
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1answer
26 views

Trigonometry in projectile motion

I initially posted this question on Physics SE but got no responses probably because it's more related to maths than physics. A plane surface makes an angle $\bf X$ with the horizontal. From the ...
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1answer
23 views

How to prove the Hubble law is the unique expansion law compatible with homogeneity and isotropy?

In the book physical foundations of cosmology, it saids that Hubble law is unique and a problem seems to be a hint of proving that. In order for a general expansion law,v=f(r,t), to be the same ...
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0answers
35 views

Setting up the Lagrangian for a pendulum with a circular weight

A pendulum consists of a light inextensible rod $OA$, length $b$, freely pivoted at $O$, attached at $A$ to the rim of a uniform disc of radius $a$ and mass $m$. The disc is free to rotate about $A$. ...
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0answers
40 views

Angular displacement/speed of a rotating sphere from 3d points

I have 3d points on the surface of a unit sphere that describe every minute its rotation. I want to know angular velocity of this sphere. The sphere center is fixed and the axis of rotation can change ...
0
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1answer
36 views

force of magnetic fields [closed]

Can anyone help me with this question ? The force F of a magnetic field B on an electric charge Q moving with velocity V is given by $$\vec F=q\,\left(\vec v\times \vec B\right)$$ If Q is positive, ...
2
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1answer
74 views

How would you prove $E = -\vec{\nabla} V$ from the electric potential's line integral?

Basically, we were given an equation: $$V_1 - V_2 = \int_{r_1}^{r_2}\vec{E}\cdot d\vec{r}$$ where $\vec{E}$ is the electric field distribution and $d\vec{r}$ is the displacement vector of the charge. ...
2
votes
1answer
52 views

Question regarding combinatorics of resistance network. [closed]

If you have $N$ $1$Ohm resistors, how many distinct equivalent resistances can you create? Assume that only parallel and series and mixture of them is allowed and no bridging between two parallel ...
3
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0answers
61 views

My orbiting body is orbiting about the wrong focus of it's elliptical orbit… why? [closed]

I am coding in c++ and am computing the position of an orbiting body as a function of time. Everything is almost working. I have a nice elliptical orbit. Except, my orbiting body speeds up as it ...
1
vote
1answer
177 views

Determining the minimum angle of a baseball trajectory to get a home run

This is a homework question: The skydome in Toronto has a center field fence that is 10 feet high and 400 feet from home plate. A ball is hit 3 feet above the ground with an initial velocity of ...
0
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1answer
77 views

Help with polar coordinates for physics problem

I need to solve a physics problem but don't know about polar coordinates properly, can anybody help with it? Suppose a curve which is a current carrying wire: $$r=\frac ...
2
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2answers
142 views

How to calculate the mass of a layer of an atmosphere?

In a problem I'm working on, I need to derive what fraction of molecules in the Earth's atmosphere are found in the troposphere (the bottom layer extending from the surface to approx. 12 km). I have ...
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3answers
2k views

How can I calculate the time two people will meet if they are paddling towards each other on a lake?

Here's the question I'm having trouble with. Ken and Kara are 30 miles apart on a calm lake paddling towards each other. Ken paddles at 4 mph, while Kara paddles at 7 mph. HOw long will it take them ...
1
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1answer
35 views

How to find the total distance traveled, given the position function?

A particle moves in a straight line according to the rule $x(t)=t^3-2t+5$, where $x(t)$ is given in meters and where $t$ is given in seconds. Determine the position, velocity, and acceleration of ...
10
votes
2answers
2k views

What is the optimum angle of projection when throwing a stone off a cliff?

You are standing on a cliff at a height $h$ above the sea. You are capable of throwing a stone with velocity $v$ at any angle $a$ between horizontal and vertical. What is the value of $a$ when the ...
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0answers
35 views

What is the density of a homogeneous disk with mass $m$ and radius $a$?

Could someone help me understand why the density of a homogeneous disk is $\dfrac{m}{(\pi a)^2}$? I am trying to understand an example about finding the moment of inertia of an object. The question ...
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0answers
28 views

translating vectors in polar coordinates to the complex plane [duplicate]

These equations model circular motion. Equation R is the position vector given in polar coordinates. What I've done is represent this vector onto the complex plane via equation (1). Equation (2) and ...
12
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5answers
747 views

In what ways has physics spurred the invention of new mathematical tools?

I came across this comment: Mathematical rigor is not a criterion that physicists have for evaluating their theories. From a mathematical perspective, the non-rigorous theories are far more ...
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0answers
32 views

Derivation of the equations for non-uniform circular motion using complex analysis.

Here http://farside.ph.utexas.edu/teaching/301/lectures/node89.html They use complex analysis to derive the equations of non-uniform circular motion. My confusion is this: In the derivation they ...
3
votes
2answers
131 views

Gödel's incompleteness theorems

In the last paragraph of Stephan Hawking's speech "Godel and the End of the Universe", he mentioned "... I'm now glad that our search for understanding will never come to an end, and that we will ...
3
votes
1answer
57 views

A question in application of derivatives and vectors

Consider a skier who is sliding without friction on the hill ${y = h(x)}$ in a two dimensional world. The skier is subject to two forces. One is gravity. The other acts perpendicularly to the hill. ...