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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String problem with two equal particles

Two equal particles are connected by a string one point of which is fixed and the particles are describing circles of radii $a$ and $b$ about this point with the same angular velocity so that the ...
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8 views

Find an estimate for the separation distance between two plates squeezing a long line of oil

I was wondering if someone could give me some help on with this problem, I'm really struggling to get my head around it. A long line of oil is being squashed between two flat plates of length $L$ by ...
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23 views

Problem on vertical light elastic string

A mass of $4$ lbs suspended from a light elastic string of natural length $3$ feet extends it to a distance $2$ ft. One end of the string is fixed and a mass of $2$ lbs is attached to other. The ...
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1answer
25 views

Calc 3 Problem about work [on hold]

Find the work done by the force → F = −2k to move an object from the point P(2, 1, 1) to the point Q(−1, −1, 1).
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a spring pushes 50N into a 2kg block for 0.5m,velocity?

a force of 50N from a spring pushes a 2 kg block for 0.5m, what is the velocity as the block leaves the spring?
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0answers
16 views

a cart is placed against a spring that is released, velocity it shoots off at? [on hold]

A 2 kg cart is placed against the spring when it is compressed by 0.5m and then released. How fast will the cart move as it leaves the spring? I have a F-s graph for the compression of the spring in ...
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2answers
91 views

Paradox or error in design?

Currently I'm writing a homework for my school. I've made an experiment built this way: There is a laser pointed at a half reflecting mirror which reflects 50% at a wall. The other half cross the ...
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1answer
13 views

Particle's acceleration when it achieves maximum displacement in the +x direction

I'm not sure if this goes in the physics section or the mathematics section, but this question seems pretty math oriented, so I'll ask it here. $t\ge0$ and $v_x=24-3t^3$ I have to find the ...
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1answer
24 views

Limit in electric field far from a charged disk

Let $\sigma$ be the areal charge density $\frac{Q}{\pi R^2}$ of a disk of radius $R$; then the electric field on the line pependicular to the disk and passing through is centre, if we use its ...
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1answer
33 views

Simple Harmonic Motion under Periodic disturbing force

A particle of mass $m$ is executing a SHM in a straight line under an acceleration $n^2 \times (distance)$. If a periodic force $mk \cos{pt}$ be introduced and the time period of forced vibration ...
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1answer
34 views

Find the position function from the piecewise-defined velocity function

I am getting stuck on a position function problem in my Diff Eq class. Problem 22 is shown on the right in the picture below. On the left is the answer. My work below shows that I get stuck ...
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0answers
273 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. ...
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34 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 ...
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2answers
45 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 ...
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1answer
22 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 ...
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1answer
43 views

Calculating the resultant of two forces and angle? [closed]

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?
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0answers
24 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) ...
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1answer
24 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?
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26 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 ...
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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 ...
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2answers
35 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 ...
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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?
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3answers
44 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 $10\text{h}$? ...
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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 ...
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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= ...
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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 ...
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0answers
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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 ...
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32 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: ...
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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 ...
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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 ...
2
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1answer
43 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 ...
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1answer
78 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 ...
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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.
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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 ...
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1answer
71 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, $S$ = ...
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2answers
81 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 ...
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1answer
47 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 $\frac{m-M}{m+M}g$.
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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 ...
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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 ...
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2answers
95 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 ...
1
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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1answer
21 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: $$P=U_{x}=xy^2$$ $$Q=U_{y}=x^2y$$ $$\Longrightarrow U=\int P dx=\frac{x^2}{2}y+C(y)$$ $$ U_{y}=\frac{x^2}{2}+C'(y)=Q=x^2y$$ ...
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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 ...
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1answer
21 views

Finding the work from $(0,0)\to(1,1)$ of $\vec F(x,y)=xy^2\hat i+yx^2\hat j$

I need to find the work from $(0,0)\to(1,0)\to(1,1)$ of the following vector field:$\vec F(x,y)=xy^2\hat i+yx^2\hat j$ My attempt: $$\oint_{c}\vec F d\vec r=\int_{(0,0)\to (1,0)}\bigg(xy^2\; dx ...
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0answers
31 views

What does it mean to take the Laplace transform of a non-periodic position function?

What I'm trying to get through my head here is how taking the Laplace transform of a system with a position function like $X(t)=t$ is possible. To my current (admittedly incomplete) ...
2
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0answers
33 views

Vector/Tensor analysis, Elastic Waves

So I'm fairly confused at the moment. For reference, I'm reading this document, and the current area of interest is Section 7: Characteristic Surfaces for Planar Waves. I'm not gonna give too much ...