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
12 views

Find the speed required for a boat to “catch” a key dropped from a bridge.

So I'm doing a simple Physics homework problem, and I'm honestly unsure if I'm using the proper formulas for each step. The problem is as follows: A key falls from a bridge that is 47 m above the ...
1
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0answers
14 views

Projection operator is Hermitian

Use Dirac notation (the properties of kets, bras and inner products) directly to establish that the projection operator $\mathbb{\hat P}_+$ is Hermitian. Use the fact that $\mathbb{\hat ...
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0answers
15 views

Intercept planet following an elliptical path (i.e. interplanetary space travel)

So, just as in this question (Intercept path to object following an elliptical path) I have a simple game where I want spaceships to intercept planets, which follow elliptical paths (in my case ...
0
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0answers
9 views

Express Kirchoff's first law using power flow.

If we just know the power flow in and out of a junction node, can we say that $\sum\limits_{p: e\in p, i\in e^-} f_p = \sum\limits_{q:e\in p, i\in e^+} f_q, \forall i$, where $f_p$ is the power flow ...
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0answers
10 views

Proving that the derivative of the LRL vector $=0$ [on hold]

How to prove that the derivative of the Laplace–Runge–Lenz vector $=0$? $$A=\dot{x}\times(x\times\dot{x})-\dfrac{k}{\mu}\cdot\dfrac{x}{||x||}$$ $$\dot{A}=0$$
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0answers
8 views

Convert position and velocity vector to TLE for propagation

I have a set of position and velocity vector for a satellite at time t0. I want to propagate position and velocity of the satellite at time t (t>t0) I converted these vectors to Keplerian Elements ...
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0answers
25 views

What is the root structure of the Diffeomorphism Group?

Being a physicist, I think it'd be cool to have Coxeter plane projections of the root systems of the symmetry groups associated with the fundamental forces hanging on my walls (example for E8: ...
0
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1answer
25 views

Calculate how long a ball will be in the air after being thrown

So I'm doing some online homework, and have done this specific problem 3 different times and gotten the same answer, but the answer I get seems to be wrong? The problem is as follows: (a) With ...
0
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0answers
23 views

Stiffnes tensor, Hooke's law

Let's have a deformed body of an isotropic homogenous material. How is it possible that we can write the free energy in the form $$F=F_0+\frac12\lambda\left(\sum_i ...
2
votes
1answer
63 views

Differentiating position with respect to 'modified time'

I've been reading a book on orbit determination, and I've hit a block with the calculus. Why do this and is the resulting value even acceleration? This differentiation is very odd to me. He defines ...
0
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1answer
23 views

Effective Acceleration for Non-Constant Acceleration Motion

This question uses the same symbols as "Effective Acceleration" is Distance-Averaged Acceleration?. One of the kinematics formulas for constant acceleration is: $\Delta x=v_0*\Delta ...
4
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1answer
114 views

Finding $\mathbf{10}\otimes \mathbf{8}\otimes \mathbf{8}\otimes \mathbf{8}$ in $SU(3)$

I know that in $SU(3)$ $$\mathbf{8}\otimes \mathbf{8} = \mathbf{27}+\mathbf{10}+\mathbf{\bar{10}}+\mathbf{8}+\mathbf{8}+\mathbf{1}. $$ How can one use this to compute $$\mathbf{10}\otimes ...
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2answers
33 views

Significance and physical meaning of diagonalization of linear maps and bilinear forms, eigenvalues and eigenvectors

In linear algebra, I have studied the diagonalization of a linear map and of a bilinear form; and also the concepts of eigenvalues and eigenvectors. However, the importance of diagonalizing a linear ...
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0answers
30 views

Ship A and ship B distance problem [closed]

A ship leaves port at 1:00pm and sails in the direction N$34^\circ$W at a rate of $24$ mi/hr. Another ship leaves port at 1:30pm and sails in the direction N$56^\circ$E at a rate of $18$ mi/hr. ...
0
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1answer
25 views

Second order differential equation, physics.

I need your input on this exercise I'm doing: "A 2-kg mass is suspended from a string. The displacement of the spring-mass equilibrium from the spring equilibrium is measured to be 50 cm. If the mass ...
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0answers
13 views

How can i Plot Laguerre-Gaussian mode vortex by Mathematica? [closed]

I've been using Mathematica for a few years. I couldn't plot the Laguerre-Gaussian vortex vawefron by using the Mathematica. I know i should use the Laguerre-Gaussian function in coding, but i ...
1
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1answer
46 views

“Effective Acceleration” is Distance-Averaged Acceleration?

My question involves simple math, but to be precise on what I'm asking, I need to write a lengthy description. Let us define the following symbols: $t$: time $x(t)$: distance as a function of time ...
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0answers
13 views

Probability - Wind speed calculation

I've been asked to find the probability of wind speed exceeding 15 m/s in a certain area. The question states that a bridge must be shut down if the wind exceeds that value and so my challenge is to ...
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0answers
13 views

Issues Calculating Average Acceleration?

So I'm doing a Physics problem here and I'm down to my last answer and I honestly can't figure out where I'm going wrong. The problem is as follows: From t = 0 to t = 4.22 min, a man stands ...
0
votes
2answers
49 views

What are the degrees of freedom of $F=ma$ and $F =mdv/dt$? [closed]

I read in http://en.wikipedia.org/wiki/Degrees_of_freedom, the definition of "degree of freedom" for equations. However, I am consfused about what is the degree of freedom of the two known physical ...
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1answer
27 views

How can I take the derivative of $Q=C \cdot \Delta T$

How can I take the derivative of $$Q=C \cdot \Delta T$$ with respect to time $t$? note: $C$ is heat capacity and $T$ is temperature
0
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1answer
13 views

Shifting Velocity and Position functions

I'm given a function $A(t)$ that defines the acceleration of an object w.r.t. time $t$ and am tasked with finding the position function and velocity function for that object. Finding the functions ...
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0answers
14 views

Computing the angular momentum in spherical coordinates [migrated]

How to compute the angular momentum of a particle in spherical coordinates? It's given by: $$x_1=r\cdot\cos(\phi)\cdot\sin(\theta)$$ $$x_2=r\cdot\sin(\phi)\cdot\sin(\theta)$$ ...
0
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0answers
12 views

Trouble converting $m^3$/hr to kg/sec

So I'm doing a physics problem on conversions, and having a bit of trouble with the intermediate steps (since I keep getting the wrong answers. The problem is as follows: Suppose that it takes 18.2 ...
0
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0answers
9 views

Lift force formula

Hello! I'm creating a (simple) flight simulation game, and to simulate the aircraft physics up and down movemet as realistically as I can, I'm going to use the Lift force formula. I found the formula ...
1
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1answer
39 views

Characteristic of a ring: intuitive explanation

I know the following definition of characteristic of a ring: it is the smallest positive $n$ such that $$\underbrace{a+\cdots+a}_{n \text{ summands}} = 0$$ for every element a of the ring, if $n$ ...
2
votes
1answer
37 views

Find Distance Function from Acceleration Function

The (non-constant) acceleration as a function of time, $a(t)$, is defined and known over $[t_0, t_2]$. It is also known that $a(t)$ is integrable. Also, $a(t)=\frac{dv(t)}{dt}$ and ...
4
votes
2answers
103 views

Why $F(\mathbf q,\dot{\mathbf q},t)$ and not $F(\mathbf q,t)$?

In beginner classical mechanics, which I've just started learning, a particle with coordinates $\mathbf q\in\mathbb R^n$ has its equation of motion specified by $F(\mathbf q,\dot{\mathbf ...
1
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1answer
27 views

Relationship between proper orthochronous Lorentz group $SO^+(1,3)$ and $SU(2)\times SU(2)$, or their Lie algebras

I have seen sources claim that $SO^+(1,3) \cong SU(2) \times SU(2)$, but have seen others claim that only their Lie algebras are isomorphic. Is it true that $SO^+(1,3) \cong SU(2) \times SU(2)$? If ...
1
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0answers
28 views

Verify solution to $\frac{i R}{L}+i'=\frac{U_m \sin (\text{$\omega $t})}{L}$

Show that this is a solution $$i(t)\text{:=}\frac{U_m \sin (t \omega -\varphi )}{Z}$$ to $$i'+\frac{i R}{L}=\frac{U_m \sin (t \varphi )}{L}$$ given: $$\varphi =\tan ...
3
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0answers
97 views

“The All-Purpose Calculus Problem” [closed]

Taken from "The Futility Closet" which, in turn, took it from Math Horizons, Spring 1994. The illustration and text are here: ...
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0answers
9 views

Another box sliding up a ramp question

This is the problem: A woman exerts a horizontal force of 9 pounds on a box as she pushes it up a ramp that is 6 feet long and inclined at an angle of 35 degrees above the horizontal. ...
4
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0answers
50 views

Tricky question (physics) [migrated]

I know this may not be the place for this question, by stackexchange physics has banned homework questions :( A piece of hair taken from a goat has a radius of $3.1\times 10^{-5}\text{ m}$. What is ...
5
votes
5answers
238 views

What really are units? And why is it valid to ignore them (once you have dimensional homogeneity), as is done in class?

All my life the approach has been as follows: In math class I learn the rules and almost always deal with purely numerical problems. In physics class I apply the things learned in math class but ...
2
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0answers
94 views

Classical perturbation theory + KAM theory

In classical canonical perturbation theory of many degrees of freedom we encounter the problem of small divisors when attempting to find a solution for the generating function of the canonical ...
6
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2answers
588 views

Why can't a perpetual motion polyhedron exist?

I've been thinking about polyhedrons, when placed on a table on a certain face, will tip over and keep tipping over infinitely. I'm trying to prove mathematically that such a polyhedron doesn't exist. ...
0
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0answers
20 views

Find center of mass and moment applied on beam structure. [migrated]

I have a simple mathematical problem to solve but it is giving me a slightly difficult time to figure out. The problem: I have a beam structure with same cross section. It consists of three beam. ...
0
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1answer
22 views

Railway track and Cyclist crossing, Motion Problem.

A railway track runs parallel to a road until a turn brings the road to railway crossing. A cyclist rides along the road everyday at a constant speed 20 km/hr. He normally meets a train that ...
1
vote
1answer
36 views

Problem with average velocity.

A particle moving in a straight line having acceleration which varies with velocity as $a=-kv^n (n\ne1,2)$. Here k is a constant. For what value of $n$ the average velocity of the particle averaged ...
4
votes
1answer
87 views

A doubt about Differential Geometry Books.

I intend to read "Physics for Mathematicians" by Spivak, and he says that vols. 01 and 02 of "A Comprehensive Introduction to Differential Geometry" are necessary to understand the book. Are those ...
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0answers
48 views

Calculus. Physics

i am here with a question I tried a lot to solve this question but can't able to find the answer. I hope someone will help me to find out the solution. Thanks in advance.. Here is my question: You ...
0
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0answers
24 views

Finite Difference Approach for the 1D Conservative Advection Equation with Spacially Varying Velocity

I am attempting to numerically solve the following conservative advection equation in 1D, using a finite difference method. $\frac{\partial}{\partial t}u(x,t) + \frac{\partial}{\partial ...
3
votes
1answer
62 views

Math or Physics

I'm a Master Math Student And I'm very interested in Some fields in Physics Like Cosmology. I even Considered Changing my field and Apply for physics(Cosmology) but wasn't really possible (my ...
0
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0answers
24 views

Derivatives : trouble to understand formulas

My teacher gave us some useful formulas, but honestly I don't know how to understand it. gradient of a scalar field : $d_{x}i{V^{i}}f(M)\varepsilon ^{i}$ gradient of a vector field : ...
1
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1answer
37 views

Pouring shampoo into a bottle at 16.5 cm³/s [closed]

Here's a photo of the question from my book: How can you find the rate without knowing the shape of the bottle? do you just assume it is a perfect sphere at the top half, and as if it is shaped ...
0
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0answers
19 views

Find the maximum safe allowable bending moment.

A rolled steel universal I-section beam with a serial size of $406\times178$ has a mass of $60$kg/m. What is the maximum safe allowable bending moment this beam can sustain,given that the maximum ...
3
votes
1answer
33 views

Total thrust on the face of a vertical dam

"A vertical dam is a parabolic segment of width $12m$ and maximum depth $4m$ at the center. If the water reaches the top of the dam, find the total thrust on the face." Is it possible to answer this ...
0
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2answers
40 views

Coordinate geometry reflection of point

I have point in $1st$ octant($ x, y, z$ all positive). Now I take the mirror image of that point about $xy$ plane. I guess that new point will be simple $ (x, y ,-z)$. Verify if I am right. Further ...
0
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1answer
25 views

Conversion of the Gauss law $\nabla \cdot E = \frac{\rho } {\epsilon_0}$ into integral form

This may be physics related but I think it belongs here because I have some doubt about mathematical operators we have gauss law in differential form as $$\nabla \cdot E = \frac{\rho } {\epsilon_0}$$ ...
2
votes
1answer
34 views

With picture: convert angular velocity to linear velocity of bicycle wheels and sprockets

Find the angular velocity of the pedal wheel of a stationary bike whose main wheel is moving at 320 ft/min. The diameter of each wheel is: main wheel 2 feet, pedal wheel 1 foot, wheel ...