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
3
votes
3answers
57 views
What is the relation between vectors in physics and algebra?
Vector math is something I find very interesting. However, we have never been told the link between vectors in physics (usually represented as arrows, e.g. a force vector) and in algebra (e.g. ...
0
votes
1answer
45 views
Finding a gravitational potential
A uniform thin straight rod of length $2a$ and mass per unit lenth $p$ lies along the $z$-axis for $-a\le z\le a$. Find the gravitational potential of the rod, letting $r^2=x^2+y^2$.
Also check that ...
2
votes
1answer
44 views
Show that the SU(2) group is a Lie group
How can I prove that the SU(2) is a Lie group with the Pauli matrices as generators?
0
votes
1answer
21 views
Parabolic projectile equation demonstration question
I was looking at a book of physics and, it will sound dumb, but while I know that the maximum height equation of a projectile is max=(v·senα)/2g, I can't understand how do you get there from ...
7
votes
1answer
144 views
Mathematicians conceived of black holes long before astronomers actually found any?How?
I read this statement in Lockhart's - "A Mathematician's Lament". But how could mathematicians figure out something like black holes even before astronomers noticing any of them?
2
votes
0answers
44 views
Circular Motion
A car is driven in a flat circular curve of radius $r$ m. The car’s engine supplies a
constant tangential driving force. The car experiences a friction heading towards the centre of the circle.
By ...
0
votes
1answer
37 views
Finding the Extremals of a Functional J.
The functional $J$ is defined on smooth functions $y \colon [a,b] \to \mathbb{R}$ satisfying $y(a) = u$, $y(b) = v$ and is given by
$$J[y]=\int_a^b \sqrt{y} \sqrt{1+(y')^2}\, dx.$$
I have found ...
1
vote
1answer
36 views
Efficiency physics problem
84 An internal combustion engine consumes 1 gallon of diesel fuel per hour. It provides a
constant 10 hp. One gallon of diesel fuel has potential energy of about 115,000 Btu. Remember
that 1 hp × ...
1
vote
1answer
49 views
Math question efficiency
A solar collector has 1000 Btu/min of radiant energy available on a clear sunny day. The collector can transfer 450 Btu/min to a storage tank. What is the efficiency of the system?
I used n= ...
1
vote
1answer
58 views
What kind of equation is this?
I saw a book on my brother's bookshelf and I decided to look through it and to me it looked pretty complicated (it's physics). On the first page I encountered the Rayleigh-Jeans formula:
$$u(v) ...
3
votes
1answer
51 views
Quadratic Equation with “0” coefficients
Let's say I have two objects $x$ and $y$ whose position at time $t$ is given by:
$$
x = a_xt^2+b_xt+c_x \\
y= a_yt^2+b_yt+c_y
$$
And I want to find which (if any) values of $t$ cause $x$ to equal ...
2
votes
2answers
47 views
Faulty velocity question?
If a ball is thrown vertically upward with a velocity of $160 \text{ ft/s}$, then its height after t seconds is $s = 160t − 16t^2$.
a) What is the velocity of the ball when it is $384 \text{ ...
1
vote
1answer
27 views
Differential equations basic problem
I know this is a basic Physics problems but somehow I can't solve it.
We have the differential equation: $2x''x^2 - 4 x^2x' - 2 x^3 = 0$
We have to conclude that the system:
$x' = y $
$y' = 2y + ...
1
vote
3answers
60 views
How can you show that $\delta′=f(0)\delta′−f′(0)\delta$ for a function f that is infinitely differentiable?
Assume that $f$ is infinitely differentiable. Let $\delta$ be the (Dirac) delta functional.
I know that $f\delta = f(0)\delta$, but I'm not sure how to derive the equation ...
0
votes
0answers
51 views
A theoretical problem on Mechanics [closed]
Two particles with masses $m_1$ and $m_2$ are moving in 3D space with some Cartesian coordinate system. There are known the laws of motion of these particles, i.e. the position vectors $\vec{r_1}(t)$ ...
2
votes
2answers
37 views
To use the two-point formula to find the linear equation relating $C$ and $F$:
I've tried to solve a problem which I'm going to give below. What I don't understand is that which variable is dependent and which is independent among $C$ and $F$. I think we can relate $C$ and $F$ ...
1
vote
3answers
88 views
Thermodynamics for math majors
I'm about to wrap a course in partial differential equations. We've discussed the heat/wave equations and introductory Fourier Analysis.
I'd like to do some reading into the field of thermodynamics. ...
1
vote
1answer
77 views
Describe a sine wave of known frequency with only two points
This is my first post on math.stackexchange (sorry if meta people remove the Hello (sometimes we do that over on stackoverflow ;P)!
I have a system wherein I know that the output is a sine wave, with ...
0
votes
2answers
42 views
Work done by a force Field
Homework for Calc III includes a problem about computing the work done by a force field (defined by a specific vector equation) on a moving particle. I was attempting to compute this using the ...
2
votes
1answer
62 views
Trouble understanding a common vector calculus example
I have difficulty understanding the following vector calculus example. Text can be found here. It is the 5th Q&A -- starting with equation (31.1035).It concerns finding the vector potential of a ...
1
vote
1answer
23 views
Minimum Ejection Velocity
PROBLEM:
Calculate the minimum ejection velocity with which a shell must be fired to strike a target 1000ft high and directly overhead.
QUESTIONS:
I use integration to work back from 32ft/sec and ...
3
votes
2answers
34 views
Up and Down Motion (Two objects meeting in time?)
PROBLEM:
Suppose than an object is thrown upward with an initial velocity of 200ft/sec and that another one is thrown upward 5 seconds later with an initial velocity of 300ft/sec. When and where do ...
3
votes
1answer
115 views
Self-learning; Physics and Mathematics
My fields of interest are Physics and Mathematics. Gerard t'Hooft, 1999 Physics Noble Prize Laureate, has suggested a better scheme to study physics online. I can't wait for the university, so I've ...
5
votes
0answers
90 views
Where do I go from Linear algebra past Calc III to try to learn complex physics (relativity and quantum group theory)?
I'm mainly a programmer, but I have a love for Mathematics that's been, well, insatiable. I've had my eye on learning Quantum Groups and Relativity, but I want to stay in something I can do with ...
-1
votes
0answers
34 views
Chain Rule Problem [closed]
Newton's Law of Gravitation asserts that the magnitude of force between objects of masses $M$ and $m$ is $F = GMm/r^2$ where $r$ is the distance between them and $G$ is a universal constant. Let an ...
0
votes
0answers
32 views
Differential Rocket Probem
Can someone explain to me how I can find the solution with the variables provided? I understand that I need to figure out the rate of which the rocket burns fuel by working out it's "force", but i've ...
-1
votes
1answer
62 views
Moment of inertia of a circle
A wire has the shape of the circle $x^2+y^2=a^2$. Determine the moment of inertia about a diameter if the density at $(x,y)$ is $|x|+|y|$
Thank you
5
votes
1answer
78 views
Degree of maps on the 3-sphere
I am currently in the process of going through Ticciati's Quantum Field Theory for Mathematicians, which states the following (Theorem 13.7.11):
"Let $g$ be a differentiable function from $S^3$ to a ...
1
vote
2answers
80 views
Resonance Frequencies of Oscillator
I understand that resonance is when the force term increases the natural oscillation of the system.
In the next equation the oscillator has a natural frequency $\omega_0=\sqrt{\frac{k}{m}}$. But I ...
1
vote
1answer
82 views
Coordinate Transformation on Local coordinate system
I am having a point $P(x,y,z)$ in $3D$ with respect to global coordinate system. I want to create an another Local Coordinate System by picking three points $N1, N2, N3$ in 3D. Now I want to know the ...
2
votes
1answer
82 views
Geometry brain teaser (Candle in the room with mirrored walls)
King wants 2D room with smooth walls and columns (second derivative exists) that reflects light. King asks you to build it in such way that there exists a spot, where you can place a candle and there ...
0
votes
1answer
211 views
Electrostatic Potential Energy
How is the boxed step , physically as well as mathematically justified and correct ?
Source:Wiki http://en.wikipedia.org/wiki/Electric_potential_energy
As work done = $- \Delta U $. for Conservative ...
0
votes
1answer
46 views
Find the time at which a particle projected up an inclined plane, comes to rest?
A particle of mass $m$ is projected up a plane that is inclined at an
angle $\alpha$ to the horizontal. At $t=0$, its velocity is $v_0$ and
the coefficient of dynamic friction of the slope is ...
0
votes
0answers
18 views
Velocity and Distance; Functions of Time
$s(t)$ = distance a particle travels from time $0$ to $t$. If in this case, the distance $s$ is only the function of time then its necessary that the velocity should be constant. Likewise, $v(t)$ = ...
0
votes
2answers
24 views
Distance of a particle; a function its time
Force is a function of mass and acceleration. Here mass is a fundamental quantity, and acceleration is a derived quantity OR $F(a, m) = ma$.
I want to ask that why the distance traveled by a ...
-1
votes
1answer
45 views
Particle of unit mass subject to a force find the potential energy [closed]
A particle of unit mass moves in the xy plane subject to a force
$F = −(4x,16y)$.
(a) Find the potential energy $P(x, y)$ of the particle assuming it has zero potential at the origin.
(b) Suppose ...
6
votes
6answers
865 views
What is this physicist saying?
I do not want to poison this forum with politics. But I want to understand, precisely, what is meant by the bolded statement. It is made by a physicist who used to work at Harvard regarding the ...
1
vote
1answer
46 views
Let $F(x,y,z) = -c(r/||r||^3)$ be the force resulting from the inverse square law…
$c$ is a constant and $r = (x,y,z)$. Show that $\displaystyle f(x,y,z) = \frac{c}{\sqrt{x^2+y^2+z^2}}$ is a potential function for $F$. What can be concluded from any path from point $A$ to point $B$ ...
0
votes
1answer
52 views
Calculating the angular velocity
I have an inverted pendulum with a accelerometer mounted on the top that at rest gives me a vector up opposite to gravity, which is used to calculate the angle of the pendulum. Is it possible to ...
3
votes
1answer
184 views
Derivative of a bra?
I understand that
$$ \frac{\mathrm d}{\mathrm dt} \langle\psi|\psi\rangle =\left[\frac{\mathrm d}{\mathrm dt} \langle\psi|\right]|\psi\rangle + \langle\psi|\left[\frac{\mathrm d}{\mathrm ...
8
votes
1answer
250 views
Physics - Problem
Hi I am stuck with an integral problem trying to show $$ -\int \frac{d^{3}p}{(2\pi)^3}p\frac{\partial f(p,t)}{\partial p}=3F$$ where $F=\frac{1}{(2\pi)^3}\int d^{3}pf(p,t)$ I have read in many books ...
0
votes
1answer
95 views
Nonlinear Second-order ODE BVP with 4 boundary conditions
My Lagrangian comes out in this form when I impose spherical symmetry:
$$ φ''(ρ)+{3\overρ} φ'(ρ)+{4μ^4\over M^2} φ(ρ)-{4μ^4\over M^4} φ^{3}(ρ)-{μ^4\over2M} ϵ=0 $$
The following boundary conditions ...
1
vote
1answer
28 views
Are there solutions when the boundary conditions are particle positions at 2 different times instead of positions and speeds at an initial time?
Is it possible to find solutions for a dynamic system when the boundary conditions are particle positions at 2 different times instead of positions and speeds at an initial time?
The question is ...
2
votes
2answers
87 views
Generally covariant Klein-Gordon equation
Consider a 4-dimensional smooth manifold $M$ on which there is a Lorentzian metric $g_{ab}$ and a function $\phi$ satisfying the following two equations (in abstract index notation):
\begin{equation}
...
0
votes
0answers
27 views
Using the integral equation, find the eigenvalues and eigenfucntions
The integral equation:
$$
\int_{-\frac{T}{2}}^{\frac{T}{2}}dt' \phi (t')e^{\Gamma\left | t-t' \right |} =\lambda \phi(t)
$$
for $(-\frac{1}{2}T< t < \frac{1}{2}T)$
is useful in photon ...
0
votes
1answer
37 views
Consider a pendulum that that has a length of $50$cm …
I am trying to do a simple pendulum problem but for some reason my answer is different from the book's answer and I don't know what I am doing incorrectly.
The question is:
Consider a simple ...
1
vote
1answer
23 views
Is this a set of generators for the conformal group of Minkowski space?
My physics textbook asserts that the group of maps $f: M \rightarrow M $ ($M$ is the Minkowski space, i. e. $\Bbb R^4$ with the pseudonorm $||x||=x_0^2-x_1^2-x_2^2-x_3^2$ and scalar product $x\dot{} ...
1
vote
2answers
42 views
Units in this problem: velocity or distance?
I know this is slightly off-topic here, but it's really bothering me.
My class was given the following immensely simple problem today:
A bird flies due south at a constant speed of ...
0
votes
2answers
86 views
Give a physical explanation for why the Neumann Problem has no solution?
Give a physical explanation for why the Neumann Problem
$$
U_{xx}+U_{yy}=q(x,y)
$$
$$
\nabla U(p)\cdot n(p)=g(p) \quad \forall p\in C
$$
on $D$ for Poissons equation, has no solution, unless we ...
6
votes
1answer
169 views
Is it better to learn math before physics?
It seems that a persons ability to understand physics at a high level is limited primarily by their understanding of math.
It also seems to be more efficient to learn the underlying math for a ...
