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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15 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 ...
1
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1answer
46 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
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1answer
46 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
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2answers
130 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 ...
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1answer
41 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 ...
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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
153 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
29 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. ...
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5answers
261 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
119 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
603 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. ...
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1answer
45 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 ...
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1answer
38 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
105 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 ...
0
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0answers
33 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
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1answer
82 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 ...
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0answers
26 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 : ...
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1answer
38 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 ...
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0answers
38 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
57 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
votes
2answers
67 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 ...
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1answer
49 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
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1answer
67 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 ...
13
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2answers
232 views

Is it possible to use physics or other form of non-canonical reasoning to study functions?

It is well-known (see, for example, the books New Horizons in geometry, Maxima and minima without calculus and The Mathematical Mechanic) that it is possible to use some forms of "physical reasoning", ...
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1answer
228 views

Can someone identify the following key equations in physics? [closed]

I need help identifying the following equations in physics. Most equations are related to quantum mechanics, a few is from relativity and electromagnetism. Thanks
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1answer
24 views

Charge given to the electroscope

The question is: What is the charge given to the electroscope? Also each ball has a weight of 25g. Here's how I started. First I draw the scheme on the forces acting one one ball (I took the one ...
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0answers
38 views

Finite difference scheme for the continuity equation

I am currently trying to solve a system of PDE's numerically, one being the equation; $$ (1)\quad \partial\rho/\partial t + \partial(\rho v)/\partial x = 0 $$ I have been reading up on ...
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votes
3answers
65 views

How to show that show that $\frac{v+u}{1+ uv/c^2}=c$ when $u=c$?

I am trying to show that $\dfrac{v+u}{1+\dfrac{uv}{c^2}}=c$ when $u=c$. Context It's needed for a physics proof that I'm working on. This is the formula for relative velocity, $u$ represents the ...
3
votes
1answer
28 views

Simulating elastic collision

I wrote a simple program where i can move around some objects. Every object has a bounding box and I use hooke's law to apply forces to the colliding objects. On every tick, I calculate the forces, ...
0
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1answer
25 views

Physics differential equations problem

I am told that a torpedo is fired and has an initial velocity of 60 km/hr. After 1 km travelled, its velocity falls to 30 km/hr. We know that the drag force acting on the body is proportional to the ...
3
votes
3answers
167 views

General Solution for the Gravity Between Two 3D Triangles

I would like to find the general solution for the gravity between two (flat) triangles in 3D, including the location $(x,y,z)$ where this force should be applied (in order to later account for ...
2
votes
3answers
117 views

It takes 80J of work to stretch a spring 0.5m from its equilibrium position. How much work is needed to stretch it an additional .5m?

It takes $80\,\textrm{J}$ of work to stretch a spring $0.5\,\textrm{m}$ from its equilibrium position. How much work is needed to stretch it an additional $0.5\,\textrm{m}$? Here's what I have: ...
2
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0answers
63 views

Equipartition of energy

Let $u$ solve the initial-value problem or the wave equation in one dimension: $$\begin{cases}u_{tt}-u_{xx}=0 & \text{in } \mathbb{R} \times (0,\infty) \\ u = g, u_t = h & \text{on } ...
0
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1answer
32 views

Not locally flat space

In physics, and particularly in general relativity, we use the notion of manifold to describe space-time. In this way we have a space that locally looks like $\mathbb{R}^n$, a "flat" space. Are there ...
2
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3answers
206 views

“Methods of Theoretical Physics for Mathematicians”

I read in the Princeton Companion to Mathematics that even pure mathematicians should know some theoretical physics. However, I see that there are many reference books of mathematical methods for ...
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1answer
158 views

Solving Collision Problem (Momentum conserved) Systematically in more than 2 dimensions

I know that the equations for conservation of momentum and energy $m_1v_{i1}+m_2v_{i2} = m_1v_{f1}+m_2v_{f2},\;\frac{1}{2}\epsilon(m_1v_{i1}^2+m_2v_{i2}^2) = \frac{1}{2}(m_1v_{f1}^2+m_2v_{f2}^2)$, ...
5
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1answer
176 views

How to find the integral curves that are orbits of one-parameter groups?

Consider $\mathbb{R}^2$ with standard symplectic structure and inner product. Consider a Hamiltonian $$H=(x,y)A(x,y)^t$$ where $$A=\begin{pmatrix} \alpha & \beta \\ \beta & \delta ...
2
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0answers
38 views

Stress Volume of Revolution

A bar with circular cross-sections is supported at the top end and is subjected to a load of $P$ as shown in Figure below. The length of the bar is $L$. The weight density of the materials is $ρ$ ...
1
vote
1answer
62 views

Help with a 3-body problem

If I have three particles with masses $ m_1, m_2, m_3$ with their respective position vectors $ x_1, x _2, x_3 $ and their speeds $ v_1, v_2, v_3 $ how could I find a parametric function that would ...
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2answers
67 views

How to solve for multiple unknowns using substitution?

$R_1$, $R_2$, $R_3$, $R_4$, $R_5$ and $V_6$ suppose to be 'known' values. $$\frac{V_{n_1}}{R_1} + \frac{V_{n_1}-V_{n_3}}{R_2} + i_6 = 0$$ $$ \frac{V_{n_2}-V_{n_3}}{R_4} + \frac{V_{n_2}-V_{n_4}}{R_3} ...
2
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2answers
234 views

I want to learn math from zero

I finished high school 2 years ago and now I'm stuck in a university in Turkey. I am interested in learning precalculus, discrete mathematics, physics and chemistry. Question: I need to learn math ...
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1answer
37 views

Objects sliding on a frictionless surface

An object with the mass 2 kg slides on a frictionless surface. When the velocity of the object is h, the object is subjected to a force (air resistance) that's $5v^2$ N. Apparently the equation is ...
0
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0answers
40 views

Stadium billiard reflection angles

Given a boundary and a massless particle with constant velocity with a certain direction, a billiard consists of an experiment where the particle collides with the walls conserving its velocity ...
0
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1answer
49 views

Partial Differentiation in Statistical Mechanics

I am damn struggling with basics in here. I know that $U=U(N,V,T)$ and $z=z(N,V,T)$ so that $N=N(z,V,T)$. Now, I want to do partial differentiation using chain rule involving three variables so that I ...
2
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1answer
151 views

Physical or geometric meaning of the trace of a matrix

The geometric meaning of the determinant of a matrix as an area or a volume is dealt with in many textbooks. However, I don't know if the trace of a matrix has a geometric meaning too. Is there ...
9
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3answers
302 views

Examples of useful, insightful, and interesting hand-waving [closed]

It seems to me that some hand-waving (by which I mean some arguments that aim at giving some form of intuition on the problem even at expenses of complete rigour [and not mnemonics for high-schoolers ...
0
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1answer
61 views

Interchange of derivatives

Given Euler-Lagrangian equation $$\frac{d}{dt}\frac{\partial L}{\partial \dot q}-\frac{\partial L}{\partial q}=0$$ Can I equivalently write as $$\frac{\partial \dot L}{\partial \dot q}-\frac{\partial ...
1
vote
2answers
91 views

How much thrust is required to move a boat of 120 kg / 265 pounds to a speed of … [closed]

How much thrust is required to move a boat of 120 kg / 265 pounds to a speed of 10 km / 6 miles per hour in 7 seconds. I found the following: http://en.wikipedia.org/wiki/Thrust-to-weight_ratio ...
0
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3answers
229 views

Work done to fill up a spherical tank

A spherical tank of radius $12$ feet is $40$ feet above the ground. How much work is done in pumping water into the tank until it is full? I obtained $$ w= \int_{16}^{40}[12^2-(40-y)^2y] \, dy. ...
4
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1answer
78 views

mechanics piston problem involving rotational motion.

The above figure shows a piston driving a crank OP pivoted at the end $O$. The piston slides in a straight cylinder and the crank is made to rotate with constant angular velocity $ \omega $. Find ...