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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4
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1answer
61 views

What are super-translations?

There's been a lot of news lately about a possible solution to the black hole information paradox from a presentation given by Stephen Hawking to the KTH Royal Institute of Technology in Stockholm. ...
0
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0answers
30 views

Solving an integral that includes an exponential function and the error function

This question contains all the values needed to compute an equation. My question is, do you get the same result I get? Or do you get the result in the paper I've linked to? I'm trying to decipher ...
6
votes
2answers
43 views

Is it possible to distinguish rest and movement in hyperbolic universe?

Imagine a large body (for example, a planet) in 3D hyperbolic space. Now imagine the planet starts moving in a straight line at constant speed. In Euclidean space, all points would move along ...
0
votes
1answer
85 views

An integral expressing the resistance of a triangular region

Say there is an acute isosceles triangle (40,70,70 degrees) with a height of 75 units. I would like to take the surface integral over the function $f(w,l)=w/l$ where $w$ is the width and $l$ is the ...
0
votes
1answer
42 views

Calculating the resultant of two forces and angle? [on hold]

A force of $256 N$ and a vertical load of $537 N$. Trying to work out the resultant of the two forces and the angle at which it acts to the horizontal?
1
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2answers
21 views

Sketching a Graph of a Particle Trajectory

How can I sketch the trajectory of a particle of mass $m$ with a position vector $\mathbf{r} = \cos(\omega t)\,\hat{\mathbf{i}} + \sin(3\omega t)\,\hat{\mathbf{j}}$ ? Will this be a three ...
-6
votes
1answer
31 views

electrical circuits.dont understand the table,graph and conclusion part [closed]

Aim:to determine the equivalent resistance using an ammeter and voltmeter and compare with their theoretical values Method: 1)4 cells 1,5v each were placed in a cell holder and were connected in ...
0
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0answers
22 views

Euler-Lagrange equation of motion for tensegrity

I have read this paper “Dynamic equations of motion for a 3-bar tensegrity based mobile robot” (1) and this one “Dynamic Simulation of Six-strut Tensegrity Robot Rolling”. 1) ...
-2
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1answer
23 views

Mechanics question about energy

A body of 10 kg weight drops from a height of 60 cm upon a spring whose modulus is 60 kg/cm . What will be the speed of the block when the spring is deformed 2 cm?
1
vote
1answer
291 views

How to convert FFT magnitude of square wave to dBm?

I wish to convert the FFT magnitude of square wave into dBm. I use FFT to covert voltage of square wave to a complex number, then i absolute the complex number into magnitude. Then i divide the ...
0
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0answers
23 views

Population balance model

I have some experimental data and I need to make a population balance model to compare the experimental results with. The experimental results are from the bubble size distribution in a bioreactor. I ...
2
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1answer
35 views

How to correctly write definite time integration of this function?

Last time I saw an integral was something like 10 years ago, and I am having doubts about the notation I should use. I want to describe the evolution of the volume difference between two cylinders ...
1
vote
2answers
34 views

Engineering Mathematics Problem with Taylor's Series

This is a problem from Engineering Mathematics book by K.A. Stroud 7th edition, Exercise 18, Chapter 12 Further problems. It has been given in a physics manner, but it just requires manipulation of ...
2
votes
2answers
80 views

Numerical solution to a system of secon order differential equations

I'm writing a sort of physical simulator. I have $n$ bodies that move in a two dimensional space under the force of gravity (for instance it could be a simplified version of the solar system). Let's ...
0
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0answers
22 views

Fourier methods and a conductor bar

I was doing this question bellow: I tried: Could you help me in the 3 (second Picture) and how to solve the problem?
0
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1answer
29 views

Gaussian optics

We are given $\frac{n_1}{l_0}+\frac{n_2}{l_i}=\frac{1}{R}(\frac{n_2s_i}{l_i}-\frac{n_1s_0}{l_0})$ $l_0=\sqrt{R^2+(s_0+R)^2-2R(s_0+R)cos(\phi)}$ $l_i=\sqrt{R^2+(s_i-R)^2+2R(s_i-R)cos(\phi)}$ $h= ...
0
votes
3answers
43 views

calculating you weight if you $100\text{Km}$ above the earth etc.

Qualitatively, how would your weight be different if you weighed yourself: $100\text{Km}$ above the earth? $100\text{Km}$ above the moon? near the equator if the earth's rotation were $10\text{h}$? ...
1
vote
1answer
62 views

Finding Equations of Motion

A package is dropped from an aeroplane travelling horizontally at speed $U$ at time $t_0$ and height $z_0$. The package experiences acceleration due to gravity $ \boldsymbol{F_g} = $ $m$ $\boldsymbol ...
0
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1answer
41 views

Finding angular acceleration

Given: $\mu_B=0.52$ $\theta=30^{\circ}$ Weight- $25$ lb $\omega=0$ $l=6$ ft $1/\kappa=3\sqrt 2$ radius of curvature. Find $\alpha$ My Equations of motion are the following: $\xleftarrow{+}\sum ...
1
vote
3answers
887 views

Velocity vectors and trigonometry

I am trying to learn about velocity vectors but this word problem is confusing me. A boat is going 20 mph north east, the velocity u of the boat is the durection of the boats motion, and length is ...
1
vote
1answer
1k views

Calculating time taken to get down a slope

I'm doing my homework for a Physics class and trying to get ready for a quiz. I encountered this question: Two ramps of equal length are situated such that ramp #1 has a slope (with respect to ...
6
votes
1answer
719 views

Damped Harmonic Oscillator and Response Function

This is another one of those questions that I feel like I am almost there, but not quite, and it's the math that gets me. But here goes: For a driven damped harmonic oscillator, show that the full ...
1
vote
0answers
30 views

Collision of Inelastic ball above the ground [migrated]

An inelastic ball of mass $m$ is dropped from a height $h$ above the ground and at the same time a second ball of mass $m_1$ projected vertically upwards to meet the former. Show that in order that ...
0
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0answers
30 views

Solve for initial velocity - trajectory of projectile, must hit target

This has been bothering me for weeks now so I thought it was time to ask for expert help! I'm trying to develop this code for use in a game but it should still be a simple physics equation. Q: ...
2
votes
0answers
36 views

Behaviour of an infinitely jointed pendulum

as seen by some animations at (for example) the wikipedia page on double pendulums, the behaviour of a a pendulum with a single joint is already somewhat 'complicated.' Some quick googling seems to ...
0
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0answers
40 views

Is there a mathematical theory of physical (or other) quantities?

Please try to be lenient with me since I have a hard time formalizing this question. I'm not even a physicist. Many people are probably familiar with Newton's second law: $F = ma$ Like other ...
0
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1answer
71 views

Hookes Law, Calulus and Bungee Jumping

A rope is specially designed and its modulus of elasticity is known from specifications. For the purpose of this problem, assume that the rope is stretched to twice its natural length by a person of ...
0
votes
1answer
681 views

Acceleration and Tangential Velocity Vector? <Completely Lost>

Find the resultant acceleration of a particle moving on a circle of radius 0.70 m, if its angular speed is 37 rpm and its tangential acceleration is 2.9 m/s2. Express the angle with respect to the ...
2
votes
1answer
42 views

Proof of the law of reflection without calculus

I am working on some optimization problems, and I am aware of the method of proving that the "angle of incidence equals the angle of reflection" using Fermat's principle and calculus. However, my ...
0
votes
1answer
31 views

Sphere intersecting a triangle

I'm studying "game physics" programming, and in this article, at page 14, I don't understand how is the author right. ... if the sphere does indeed collide with the inside of the triangle then a ...
-3
votes
0answers
26 views

Thermodynamics about turbines [migrated]

1.A turbine is rated at 650 hp when the flow of water through it is 0.85 m3/sec. Assuming an efficiency of 84%, what is the head acting on the turbine.
0
votes
1answer
44 views

Why would integrating acceleration give the following solution?

Suppose I have a mass with equation of motion described by: $x^{''}(t) = F(t) - 1$, $0<t<T$, all initial conditions equal to zero $F(t)$ is some unknown force My text claims that the equation ...
1
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1answer
69 views

Rigorous treatment of expressions with differentials in physics books

The question is rather general, but let me give a specific example. In thermal physics we have the following identity involving differentials: $$T\,dS = dE + p\,dV$$ where $T$ = temperature, $S$ = ...
2
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2answers
29 views

Positive entropy of system of mixed substance (mathematical viewopoint)

If two substances respectively having mass $m_1$ and $m_1$, constant pressure specific heat capacities $c_{p1}$ and $c_{p2}$, and temperatures $T_1$ and $T_1$ are mixed at constant pressure, reaching ...
-2
votes
1answer
46 views

Unable to understand a solved problem: Impulse & Impulsive force. [closed]

Why the acceleration $f$ of $m$ to the attached solution of the problem has been taken as $\frac{m-M}{m+M}g$.
1
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2answers
88 views

A problem on Impulse & Impulsive Forces [closed]

A jet of water leaves a nozzle of $1$ inch diameter at a speed of $50$ ft/sec and impinges on a plate fixed at right angles to its direction. What pressure is exerted on the plate? If the ...
0
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1answer
41 views

Another problem on Impulse & Impulsive Forces

A bullet of mass $125$ gms strikes a fixed block of wood horizontally with a velocity of $100$ metres/seconds. The resistance of the wood is $500$ kg-weight. Show that the distance through which ...
1
vote
1answer
33 views

Scale change properties in $R^n$ for a kinetic energy functional

I'm working on a project and for it I needed to read and understand a paper by Berestycki-Lions about the existence of Nonlinear Scalar Field equations. (If someone has it or is further interested in ...
1
vote
2answers
67 views

A problem on the chapter: Work, Power and Energy

An engine of $150$ Kilowatt is drawing a train of total mass $1.5\times 10^5$ Kg up an incline of $1$ in $50$. The frictional resistance is $4$ Kg-wt per ton. Show that the maximum speed of the ...
-1
votes
1answer
32 views

How to apply Zernike polynomials for circles with radius bigger than one?

In optics usually Zernike polynomials are used to represent the aberration of a lens. As you know Zernike polynomials are defined in the unit disk and there they are orthogonal. The problem is that ...
13
votes
4answers
3k views

Can this gravitational field differential equation be solved, or does it not show what I intended?

This is the equation I'm having trouble with: $G \frac{M m}{r^2} = m \frac{d^2 r}{dt^2}$ That's the non-vector form of the universal law of gravitation on the left and Newton's second law of motion ...
0
votes
1answer
22 views

Notation regarding linearization near equilibrium point of dynamical system

Suppose we have $\frac{dx}{dt} = \dot{x} = f(x)$ with equilibrium point $x_e$ such that $f(x_e) = 0$. Then for the linearized approximation of the differential equation near $x_e$ we hope to use the ...
0
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0answers
55 views

A problem on Constrained Motion

Q. A particle is moving in a smooth curve under gravity and its velocity varies as the actual distance from the highest point. Prove that the curve is a cycloid. Attempt: The eq. of motion is ...
1
vote
1answer
67 views

A problem on collision of two elastic spheres

Two elastic spheres, each of mass $m$ collide directly. Show that the energy lost during the impact is $m(u^2-v^2)/4$, where $u$ and $v$ are their relative velocities before and after impact. ...
1
vote
1answer
36 views

Impact of two bodies problem

A body of mass $M$ moving with a velocity $u$ collides with another of mass $m$ which rests on a table. Both the balls are perfectly elastic and smooth and the the body of $m$ is driven in a ...
19
votes
7answers
3k views

Does Gödel's Incompleteness Theorem really say anything about the limitations of theoretical physics?

Stephen Hawking believes that Gödel's Incompleteness Theorem makes the search for a 'Theory of Everything' impossible. He reasons that because there exist mathematical results that cannot be proven, ...
1
vote
2answers
69 views

From the perspective of the multiverse theory, would maths “work the same” in every possible Universe?

I've had an interesting discussion with a friend recently and I was arguing that in every possible Universe, mathematics would always have to work the same, i.e. $1 + 1 = 2$ would have to be true for ...
0
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1answer
336 views

Velocity depending on position

Let $v(x)$ be the velocity of a point on a line. Find the acceleration $a(x)$. I found the following relations: $$x(t)=\int v(t) dt$$ $$v'(t)=v'(x)v(t)$$ but now I'm stuck.
1
vote
1answer
20 views

Finding potential function of $\vec F =xy^2 \hat i +y x^2 \hat j$

$$\vec F =xy^2 \hat i +y x^2 \hat j$$ My attempt: $$P=U_{x}=xy^2$$ $$Q=U_{y}=x^2y$$ $$\Longrightarrow U=\int P dx=\frac{x^2}{2}y+C(y)$$ $$ U_{y}=\frac{x^2}{2}+C'(y)=Q=x^2y$$ ...
1
vote
1answer
30 views

Can anyone answer this with the steps of Assumption > Given > Formula > Solution?

The height in feet of a bottle rocket is given by the function $h(t)=160-16t^2$, where $t$ is the time in seconds. How long will it take for the rocket to return to the ground? What is the height of ...