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

learn more… | top users | synonyms

1
vote
0answers
34 views

Group theory argument

I'm reading Group Theory in Physics by Wu-Ki Tung and on page 69 in the proof of Theorem 5.3 he makes a group theory statement that I don't get. Let me try give some notation and explanation ...
-4
votes
1answer
25 views

calculus II with physics application [on hold]

can someone help me with question 32? It has a physics application and I am completely stuck The question is screenshoted below http://imgur.com/mXldL7b
0
votes
0answers
16 views

Quantum Harmonic Oscillators [migrated]

I'm having trouble with quantum harmonic oscillators and I'm not sure how to approach these questions: . I'd really like to get my head around these concepts but I'm struggling to understand fully. ...
0
votes
0answers
20 views

determining the fermi velocity via density of states

The problem is to determine the Fermi velocity for a fermion gas at absolute zero. the problem using integrating a function that looks like $$ v = \frac{4\pi V}{h^{3}} m^{3} \int_{0}^{\infty}{ ...
0
votes
0answers
22 views

How does the Schrodinger's potential transformer if the metric conformally transformers?

Given Schrodinger's equation $$ (-\nabla^2+V)\psi=E\psi $$ and the conformal transformation $\tilde{g}_{mn}=e^{2\phi}g_{mn}$, how does the Schrodinger's potential $V$ transformer if the metric ...
1
vote
1answer
39 views

Coordinate systems in physics problem (damped pendulum)

A simple pendulum of lenght $\ell$ is vibrating freely (with small oscillations). The pendulum is set into forced vibration by moving its point of suspension horizontally with a Simple Harmonic ...
0
votes
0answers
42 views

Dealing with negative work [migrated]

Dumb question, I'm working with vector fields right now, and one question on here tells me to assume an object can take on three paths from a to b. (paths not listed here) for times in [0,1] Now ...
0
votes
0answers
25 views

How to solve an overconstrained system of equations?

What is the easiest codeable way to solve an overconstrained static model? How does Force Effect https://forceeffect.autodesk.com do it? Given a 10m long bar angled as the hypotenuse of a 3, 4, 5 ...
0
votes
0answers
23 views

Differential of Gibbs free energy (dG) in terms of dT and dV [on hold]

The heat capacity, isothermal compressibility, and thermal expansion coefficient can be in the answer. A hint is to use the upstairs-downstairs-inside-out rule to help.
0
votes
0answers
7 views

Calculating line of motion based on turn-rate acceleration

Given initial time, velocity, position, forward acceleration, and (uniquely to my question, it seems) turn acceleration; and given max forward and turn acceleration; and given the time that has ...
-5
votes
2answers
47 views

deceleration question [on hold]

You are Driving. Is it possible to decelerate from 35mph to 15mph in less than 1/10th of mile?
-1
votes
0answers
22 views

Find T when l=20 cm and g is acceleration due to gravity (9.8m/sec2) [closed]

The time period of a pendulum is given by T=2π √l/g Find T when l=20 cm and g is acceleration due to gravity (9.8m/sec2)
1
vote
1answer
72 views

Proving that $\int \delta \dot{x} dt = \delta x$

Everytime I've seen this I've assumed it was true. It seems plausible. But I would like to rigorously prove it. I think this is correct, but I would like another opinion because my mathematics is very ...
-1
votes
2answers
23 views

Determine the resultant force of the inclined plane

So I was given this problem for my statics subject. I'm just having problems getting the x and y components of the force $120$ lb. I know that $60$-lb Force $$F_x = (60\mbox{ lb})\cos20^\circ$$ ...
0
votes
1answer
16 views

Pendulum tension force

I realize this is physics related, although the problem is really about math so I thought it would be a good fit for this site. My illustration is supposed to depict a pendulum and the forces ...
1
vote
2answers
49 views

How to verify how good my data is?

I'm in an undergrad physics lab right now and I have taken some data. The theoretical curve should be proportional to $\cos^2(\theta)$. How can I quantify how close my data values are to this ...
0
votes
3answers
36 views

Prove that if the speed of a particle is constant, $\vec a$ is perpendicular to $\vec v$

My train of reasoning (well, not even that, more like "translating") so far: Let $C$ be some constant. $\|\vec {v(t)}\|=C$, so $\frac {d\|\vec {v(t)}\|} {dt}=0$. But, where to go from here? I don't ...
0
votes
1answer
25 views

How to derive velocity out of acceleration in a circular motion?

A car starts moving in a circle with a radius of 200 meters. It has a constant tangential acceleration of $1{\text{m}\over {\text{sec}}^{2}}$. a. What is the angular acceleration? b. What is the ...
1
vote
1answer
24 views

If a velocity vector $\vec {v(t)}$ has constant length, must its acceleration also have constant length?

I'm not really sure how arbitrary acceleration is (like, if I can just choose an acceleration that makes the velocity vector erratically change directions while still keeping its length the same, or ...
0
votes
0answers
18 views

Questions about the mechanics of a spinning CD.

A CD is spinning counterclockwise with a radial velocity of $\omega=30\text{rad}/\sec$. The preface of what I did manage to solve and further details: I was asked what is the period time (12 seconds), ...
3
votes
1answer
50 views

What is a good reference for rigorous Electromagnetism and Electrodynamics?

Is there any good book on Electromagnetism from a more mathematical point of view? By this I mean a book which makes use of differential forms and maybe De Rham cohomology. I was also searching for ...
0
votes
0answers
12 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
votes
1answer
19 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 ...
0
votes
1answer
25 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 ...
1
vote
1answer
19 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.) ...
4
votes
2answers
83 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 ...
0
votes
0answers
8 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 ...
0
votes
0answers
14 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 ...
0
votes
0answers
17 views

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 ...
0
votes
2answers
46 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, ...
0
votes
1answer
40 views

Connection between Functional Analysis and Quantum Physics [closed]

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.
1
vote
0answers
21 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 ...
0
votes
1answer
29 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 ...
-1
votes
2answers
44 views

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

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 ...
1
vote
0answers
21 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 ...
0
votes
0answers
28 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 ...
0
votes
0answers
13 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 ...
0
votes
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 ...
0
votes
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 ...
2
votes
4answers
55 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 ...
0
votes
2answers
26 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
votes
2answers
79 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
votes
0answers
43 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 ...
0
votes
0answers
50 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 ...
0
votes
1answer
25 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 ...
1
vote
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? ...
-1
votes
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 ...
0
votes
1answer
46 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 ...
0
votes
2answers
37 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 ...
0
votes
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 ...