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
26 views

How to make vector from azimuth and speed?

I don't know how to make $3$D vector of speed from azimuth and speed. Azimuth is in degree and speed is in m/s. Azimuth is angle on $X$ and $Y$. Thank you for your help!
2
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2answers
41 views

Least squares regression with two predictor variables (exponential functions of time)

Question cropped from textbook (Apologies for the link- I don't have enough rep to post the actual image.) [Now pasted below. Ed.] I've come across a question in a textbook (linked above) requiring ...
3
votes
3answers
455 views

Find equation for mass in gravity

A satellite is moving in circular motion round a planet. From the physics we know that $$\Sigma F_r = ma_r = \frac{GMm}{r^2}$$ So I wanted to find the equation for $M$ knowing also that $$v = \...
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2answers
21 views

Normalizing the Simple (Quantum) Harmonic Oscillator for $n=2$

I am trying to find the constant for the second excited wave state that will normalize it. The equation for the second excited state is $$\psi_2(x)=A_2(1-\frac{2m\omega x^2}{\hbar})e^{-\frac{mwx^2}{2\...
2
votes
2answers
35 views

Find an function that oscillates between a given upper and lower envelope

Suppose I'm given two real, continuous functions $f(x)$ and $g(x)$ such that $f(x)\ge g(x)$ for all real $x$. I'd like to determine an oscillating function $h(x)$ that has $f(x)$ as its upper-envelope ...
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0answers
13 views

Simulation missiles - initialization vector

I'm trying to implement a simple simulation of the trajectory of bullets. Only for school project. I am using formula: ...
0
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1answer
21 views

How to calculate work done on standing a rod upright with arbitrary mass distribution m(x)

I was way overthinking how to calculate calories that you would do performing a pullup, which is a straightforward mgh. But with a sittup, you have some non-uniform torso that's being lifted to ...
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0answers
53 views

Hydrostatic force on a dam

A dam is inclined at an angle of 30° from the vertical and has the shape of an isosceles trapezoid 200 ft wide at the top and 100 ft wide at the bottom and with a slant height of 160 ft. Find the ...
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1answer
40 views

Rocket simulation. Are my equations correct?

I am simulating a rocket launch (two dimensions) and I am a little unsure about my implementation of Euler Forward. I will only give the $x$ component since $y$ is done the same way. I first ...
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3answers
68 views

Having trouble simultaneous trigonometric equations

I'm racking my brain trying to solve some formulae that I will need to implement into a program I'm making. The program is based around statics of a particle, as in that all forces acting on the ...
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0answers
22 views

Solving the finite square well graphically (Transcendental Equations)

I am attempting to comprehend how they are solving these transcendental equations here. The equations they derive are $\tan(ka)=\frac{\alpha}{k}$ which gives the even solutions and $-\mbox{cotan}(ka)=\...
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2answers
27 views

Find distance as function of time.

A car starts from rest and accelerates in $a = \frac{2\cdot m}{3\cdot s^3}t$, After $3$ seconds, The car will be $27$ metres from beginning. Find distance as function of time. I know i have to ...
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3answers
52 views

Free fall of 2 water drops

Cloud is showering 2 water drops from 1000 meters above the ground in 1 second difference. Let be Gravitational acceleration = $10\frac{m}{s^2}$, and Air resistance is negligible. What will be the ...
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0answers
14 views

Energy Conditions

Hi guys im trying to solve the energy conditions for a specific stress energy tensor but have come up at a stumbling block. How would i calculate the energy conditions for the following stress ...
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0answers
11 views

Entropy fix for 1-d conservation law with convex flux functions

Consider the following Riemann problem for a convex function $f$ \begin{eqnarray*} \partial _t q + \partial _x f(q) &=& 0 , \\ q(x,0) &=& q_0(x) =\left\{\begin{array}{ll} q_l &\...
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0answers
33 views

Modelling diffusion in composite media (PDEs)

I have to construct and solve a system of PDEs for drug delivery through a transdermal patch. I have been given that the epidermis has thickness ${\delta}_1$ and coefficient of diffusion $D_1$, the ...
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0answers
8 views

Greens Function for poisson equation in cartesian along boundary

I am tryng to solve $$\nabla ^2 \phi = -\rho(\vec x)$$ Where $\phi(0) =0$ and $\phi(L)=\phi_0$ and $\rho$ is an arbitrary functionAccording to wolfram we can write G in terms of spherical harmonics, ...
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0answers
53 views

Angular moment (Hibbeler's book question)

This question's from the book HIBBELER, R. Engineering Mechanics: Statics; chapter 4. The curved rod lies in the x-y plane and has radius $3m$. If a force $F=80N$ acts at its end as shown, determine ...
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1answer
30 views

Einstein Summation Convention Minkowski Metric

Picked up a book on General Relativity for Mathematicians, but I'm a bit unclear on some of the tensor notation. For example, the Minkowski Metric $$\eta_{\mu \nu} (\Delta x^\mu)(\Delta x^\nu)$$ ...
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1answer
20 views

Showing that the integral of one equation yields another.

Background: The equations are derived from a Physics 2 Lab circuit that has a resistor and a capacitor Problem: Show that the integral of equation 5 yields equation 2. I'm given: $I(t) ...
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3answers
33 views

Showing that one physics equation 'satisfies' another

Background: This is from a Physics 2 Lab. The equations come from a circuit that has a resistor and a capacitor I'm given these two equations $V - \frac{dq}{dt} R - \frac{q}{C} = 0$ <== Eqn(2) ...
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1answer
52 views

Simulating a rocket in Matlab

I want to simulate a rocket. I found this code in a book. For the past two days I have been trying to understand it. For instance there is a line: ...
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0answers
37 views

Neumann condition and Dirichlet condition at the same point

I am studying heat equation on a 1-D bar. We now that Neumann conditions at both ends leads to a singular matrix (for finite element methods) in equilibrium. Adding an initial condition can lead to ...
2
votes
5answers
76 views

Let $\ddot x=2x$. If $\dot x$ is $0$ when $x=1$. Find $\dot x(x=3)$.

I was given this problem in a physics class, and below is the answer by the professor. ($x$ is position, $v=\dot x$ is velocity, $a=\dot v=\ddot x$ acceleration). Let $a=2x$. If $v$ is $0$ when $x=...
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1answer
67 views

Projectile Motion Question [closed]

A ball is thrown towards a vertical wall which is a horizontal distance $d$ from the point of projection. The initial speed is $u > 0$ and the angle of projection is $0 < \alpha < \pi/2$. The ...
1
vote
1answer
42 views

Moving oil out of a conical shaped tank

I need some help finishing out a Calculus problem. I'm not sure how $d$ works (single value, or integral) at the end. A conical shaped tank, with its apex pointing upward is one fourth full of ...
2
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0answers
23 views

Probability distribution obtained by repeatedly sampling $S_x,S_y$ on a spin-$S$ system

While trying to rework an upcoming quiz problem for a quantum physics course, I came up with the following question which turned out to be harder than I expected. (Note: I take $\hbar =1$ in all ...
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4answers
40 views

Airplane decelerating as a function of speed

So, I have a problem where an airplane is decelerating as a function of speed. The acceleration is described as $a=dv/dt=-0.0035v^2-3$ as a function of time. For $t=0, v=83.3$ m/s. Can someone help me ...
2
votes
3answers
29 views

Is the following derivation of how to find $v$ given $a=v'$ wrong?

My physics professor did the following: Let $a(t)=v'(t)$ be a given function. Suppose $v(0)$ is known, then $$ \int_{v(0)}^{v(t)} dv=\int_0^ta(t)dt \iff v(t)=v(0)+\int_0^ta(t)dt $$ I believe ...
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vote
3answers
70 views

How to solve ODE

Solve the DE: $$2y^2y''+2y(y')^2=1$$ Is it possible to solve this by implicit substitution i.e. let $v = y'$ and thus $$\frac{dv}{dy}v = \frac{1-2yv^2}{2y^2}$$ by the chain rule. And then from ...
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3answers
43 views

Calculation of the velocity of an object

I have the position function $$s(t) = -4.9t^2 + v_0t + s_0$$ for free falling objects. The question is what is the velocity of an object after $5$ seconds with initial velocity $120$ m/s. I tried to ...
2
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0answers
38 views

elastic strings and springs mechanics problem.

This is an example given in Edexcel M3. In question below length =1m and λ=10N but the given answer(Circled in red) it looks like the value of λ multiplied by 2. I couldn't figure it out why? Need ...
2
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0answers
28 views

Schrödinger's equation denumerable eigenvalues

The Schrödinger's equation can be written in this form: $-u''(x)+V(x) u(x) = E u(x) $ $V(x)$ is a function that is defined on the real line. We know ${u}^{2}$ is integrable on the whole real line. ...
0
votes
1answer
26 views

normalisation constant of SE for infinite square well

we fix arbitrary constant A by normalizing wave function $\displaystyle \int_{0}^{a}|A|^2sin^2(kx)dx = 1$ by using identity $sin^2(x) = \displaystyle \frac{1}{2}-\frac{1}{2} cos{2x}$ we can ...
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0answers
59 views

Problem with 4-body Matlab code

I'm trying to model the 4 body problem to see how Jupiter, Earth and Mercury orbit the Sun. I found a two body script and adapted it as accordingly to modify my problem, but for some reason the ...
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2answers
35 views

Proving That Even Potential Leads to Even or Odd Wavefunction

if the potential $V(x)=V(-x)$ (is even), then $\psi(x)$ can be taken as even or odd $\displaystyle -\frac{\hbar^{2}}{2m}\frac{d^{2}\psi(x)}{dx^{2}}+V(x)\psi(x)=E\psi(x)$ is the same as $\displaystyle ...
4
votes
1answer
41 views

Situations in which interchanging the order of integration fail.

Suppose that our underlying space is $\Bbb R^2$ and $f:\Bbb R^2\to \Bbb R$, for concreteness. It is not hard to artificially construct such a function $f$ such that $$ \int_Y\int_X f(x,y)dxdy\ne \...
1
vote
1answer
57 views

Finding the Velocity of a Particle after an Impact

If a particle of mass $m$ has velocity $v$, its momentum is $p=mv$. In a game with balls, one ball of mass $2g$ springs with velocity $2m/s$, it hits two balls, both of which have mass $1g$, and ...
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votes
2answers
60 views

Find the rate of change of the speed of sound with respect to time.

The speed of sound, v, in air is a function of the temperature T, of the air... $v=331.4+0.6(T-273)$ with v in meters per second and T in kelvins. Suppose the rate of change of air temperature is -0....
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1answer
29 views

Finding time with unknown acceleration

Assume an object moves from $0$ m to $a$ m with an unknown constant acceleration $c$ m s$^{-2}$. The moment it gets to $a$ m we know that its velocity is $b$ m s$^{-1}$. So basically: $$ \begin{align*...
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vote
1answer
147 views

Very confused on fluid flow question

I am very confused on how to solve the following problem: If $2 \pi m$ represents the volume that is ejected per unit of time per unit length of the $z$ axis, obtain the velocity $v(r)$, ie the line ...
-3
votes
1answer
21 views

Kinematics initial velocity [closed]

A grape is tossed straight up in the air and caught in the mouth. if the mouth is 1 foot higher than the point where the grape is released in the grape enters the mouth at 25 ft./s what was the ...
2
votes
1answer
34 views

How do I represent this in terms of m and x

This is the problem: Let $t$ be the time it takes an object to fall $x$ feet. The kinetic energy of a ball of mass, $m$ dropped vertically $x$ feet is $E = {1 \over 2} m v^2$, where v = $h'$, and $h =...
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vote
0answers
19 views

Identity in continuum mechanics

For a problem in the textbook I am reading, I need to prove that $\int_Vw_{i,j}v_jdV = \int_Sw_iv_jn_jdS$, where $S$ is the boundary of the volume $V$, $v_i$ is the velocity vector field of a ...
3
votes
3answers
74 views

Falling objects - finding the speed [closed]

I am trying to work out how fast water will be falling by the time the water hits the ground. If it starts 100m high how fast would it be travelling and why? With the acceleration because of gravity ...
0
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0answers
39 views

Result from derivatives seem inconsistent

I'm working on a physics problem that looks like this For some context we have a person on his sled represented in our first term. The second term represents the velocity of a stone thrown backwards ...
1
vote
1answer
35 views

Questions on energy conservation of the wave equation

I'm reading this book. In Ch. 3.4, it studies the wave equation $u_{tt}=c^2u_{xx}$ with BCs $u_x(0,t)=0,\,u_x(L,t)=0$, and ICs $u(x,0)=f(x),\,u_t(x,0)=g(x)$. The total energy of a string is the ...
3
votes
2answers
65 views

On the existence of a point in the plane where repulsive central forces exerted by $ n $ fixed points cancel

This is a physics-inspired question. In what follows, $ \alpha \in (1,\infty) $ is a fixed constant, $ n \in \mathbb{N} $ a fixed integer $ \geq 2 $, and $ [n] \stackrel{\text{df}}{=} \mathbb{N}_{\...
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votes
1answer
39 views

What is the meaning of arc length in this physical scenario?

Let's say a particle's velocity is modeled by $v(t)=\sin(t)$. Therefore, assuming the particle starts at position $0$, it's position $x$ can be modeled by $x(t)=\cos(t)$. The total distance traveled ...
2
votes
2answers
101 views

A motorboat going downstream overcame a raft at a point A (Kinematics question)

A motorboat going downstream overcame a raft at a point A. $T$ = $60$ min later it turned back and after some time passed the raft at a distance $l$ = $6$ km from the point $A$. Find the flow velocity....