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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51 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
26 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 ...
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1answer
40 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 ...
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1answer
56 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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2answers
41 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 ...
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1answer
28 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: $$ ...
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1answer
146 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 ...
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1answer
20 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 ...
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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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0answers
16 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
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3answers
70 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 ...
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0answers
38 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 ...
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1answer
33 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
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1answer
60 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}}{=} ...
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1answer
37 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
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2answers
63 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 ...
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0answers
31 views

What do these variables mean in regard to the wave equation and spherical waves?

https://en.wikipedia.org/wiki/Wave_equation#Spherical_waves Before it states ''where K=w/c'', there is an equation that has the following variables: d,r,w,c,l. It also has f_lm(r) What do each of ...
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2answers
104 views

How to solve Schrödinger equation numerically with time dependent potential

How to solve the Schrödinger equation with time dependent potential in 1D or 3D (if it is easier): $$i\hbar\dfrac{\partial \Psi}{\partial ...
4
votes
1answer
53 views

Evaluate $\int _0^{\infty}d\lambda \left(\lambda ^2 + 2b\lambda + c\right)^{-\frac{\epsilon}{2}}$

Evaluate $\int _0^{\infty}d\lambda \left(\lambda ^2 + 2\lambda b + c\right)^{-\frac{\epsilon}{2}}$ with $b<0,\epsilon>0$ and $\epsilon$ is very small $\epsilon\to 0$. I see this in the book ...
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1answer
17 views

How do I determine the significant figures of a derived uncertainty?

I have been given an arbitrary set of values with their respective (absolute) uncertainties. I am to perform an arbitrary amount of arithmetic operations upon these values in order to ultimately ...
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1answer
38 views

Interpretation of a reaction diffusion equation

I have a reaction-diffusion equation in 1-dimensions of the typical form: $$\frac{\partial }{\partial t} u(x,t)= \frac{\partial^2 }{\partial x^2} u(x,t)+ \alpha(x) u(x,t), \,\qquad (x,t)\in ...
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1answer
36 views

Damped Harmonic Oscillator

I'm trying to find the solution to the differential equation for a damped harmonic oscillator, i.e. $m\ddot{x}+c\dot{x}+kx=0$ but using that the damping force can be represented by the frictional ...
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0answers
14 views

If a ball is projected into a hole, then do the extremas necessarily occur when the equator of the ball is parallel to the surface?

I was asked this question earlier and was unable to provide a definitive answer because I wasn't sure if the assumption was valid. The question is asking for what values of $u$ will the ball fall ...
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2answers
38 views

How would you find the kinematic range using the position function?

Knowing that the range is: $$ R = \frac{v^2\sin2\theta}g $$ Taking the integral of the velocity function we have: $$ R(T) = (V_i \cos\theta T + x_i)X +\left(-\frac{1}2gT^2+V_i\sin\theta ...
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1answer
99 views

Intuition behind the “infinite velocity” of a falling ladder

In Calculus there is a "classic" related rates problem involving a falling ladder. Say the ladder is $25$ ft tall and is leaning against a wall. The bottom edge of the ladder is pulled away from the ...
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1answer
103 views

Finding the force on a charge

I am trying to do the following problem; A uniform surface charge lies in the region $z=0$ for $x^2+y^2 \gt a^2$ and $z=\sqrt{a^2-x^2-y^2}$ for $x^2+y^2 \le a^2$, Find the force on a unit charge that ...
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2answers
103 views

Collision of two particles: constant velocity, constant acceleration

In the figure, particle $A$ moves along the line $y = 25~\text{m}$ with a constant velocity $v$ of magnitude $3.0~\text{m}/\text{s}$ and directed parallel to the $x$ axis. At the instant particle A ...
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0answers
45 views

Length and width of shadow of rectangular plane

A book that I've read shows how to find the area of the shadow cast by a sphere and ellipsoid. The spherical shadow makes sense; its simply the area of a circle (which would be the sphere's shadow) ...
4
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1answer
97 views

A commutation between curl and integral

I have been struggling to understand the only derivation of Ampère's law from the Biot-Savart law for a tridimensional distribution of current (which, needless to say, is not the case of a linear ...
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1answer
30 views

Precision of Manual Vector Addition

I learned the fundamentals of vectors and basic (e.g. addition, dot product) vector operations in a Trigonometry course, and they're being reintroduced in the Physics I course I just began. My ...
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1answer
37 views

Is there a unique solution to this upstream/downstream canoe rowing proposition?

A man jumped into his canoe and paddled upstream for one mile. After this, he continued for another fifteen minutes. Having arrived at his destination, he then turned around and paddled downstream, ...
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2answers
68 views

Understanding Eigenvalues, Eigenfunctions and Eigenstates

Please could somebody explain the meaning and uses of Eigenvalues, eigenfunctions and eigenstates for me. I have taken 3 years of physics and math classes at university and never fully grasped the ...
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1answer
43 views

Motion in 3D Space: Finding Velocity from Distance, Launch Angle

The question asks: A bullet is fired from the ground at an angle of $45°$. What initial speed must the bullet have in order to hit the top of a $130 m$ tower located $190 m$ away? (Recall that ...
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1answer
131 views

Why is “$\pi^2= g $” where $g$ is the gravitational constant?

Some months ago a professor of mine showed us a 'proof' of why $g\approx 9.8 ~\text{m}/\text{s}^2$ (the gravitational acceleration at the surface of the Earth) is 'equal' to $\pi^2\approx9.86\dots$ ...
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3answers
137 views

Learning mathematics for physicists from scratch

i am a freshman physics student and naturally my curriculum includes math-classes. The thing is, that -at least for the time being- teachers cover only the surface of topics so as to have only a ...
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34 views

virtual work and potential energy

I was just going through the thermal and elastic buckling of bars & plates ,I found some researchers use virtual work to derive the equations, another researchers use potential energy in other ...
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2answers
63 views

Mechanics - Motion round a vertical circle [closed]

A ball of mass 100 grams is hanging from a fixed point by a string 2.5 metres long. It is struck with a bat so that it starts to describe a circle in a vertical plane. When the ball reaches a height ...
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2answers
39 views

Physics Velocity Correction

So, been up all night working on getting the velocity/angle of arrow simulations perfect. Running into an issue with the physics engine I'm using is ever so slightly off (probably a rounding issue) ...
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0answers
29 views

Averaging speeds

I read the answer to this question: http://stackoverflow.com/questions/34794664/how-should-i-calculate-the-average-speed-by-road-segment-for-multiple-segments/34795821#34795821 Can anyone please ...
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2answers
43 views

Is velocity a function of displacemnt?

The velocity $\displaystyle\vec{v}$ of a particle $=\frac{d\vec{x}}{dt}$. So surely this means that $\vec{v}$ is dependent on the position of the particle?
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0answers
47 views

Acceleration of an air bubble under the sea

An air bubble arises from the bottom of the sea. Find its acceleration if the resistance force is proportional to $\rho$*A*$v$ where $\rho$ is density of water, A is cross section area and $v$ is ...
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1answer
49 views

Examples of physical motivation for integrals over scalar field?

I'm looking for good examples of physical motivation for integrals over scalar field. Here is an example I've found (source): A rescue team follows a path in a danger area where for each position ...
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4answers
102 views

How does computing the determinant of a matrix with unit vectors give you the Cross Product?

Say you had $(a_x,a_y,a_z)\times(b_x,b_y,b_z)$, you would set up a matrix like the following: And the resulting would be your Cross Product or the coordinates of an orthogonal vector. My question ...
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1answer
16 views

Cartesian State Vectors → Keplerian Orbit Elements

So, I've been working my way through the following as I'm messing about with programming some helper functions for orbital mechanics: ...
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1answer
36 views

More equations than unknowns for maxwell equations?

I had one curiosity regarding maxwell equations in 3-D From the curl equations, you get 6 unknowns, with 6 equations. The divergence equations add 2 additional equations. When these are combined, we ...
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1answer
17 views

Momentum change in an inelastic collision

Hello fellow stackexchangers, this is my first post, so sorry if this is too vague or violates guidelines. I am studying Physics and this problem came up, I will type it verbatim A small object ...
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0answers
16 views

Gauss-Green cubature in 2d

Hello friends of maths, I've given an arbitrary polygonal cross section (in cartesian coordinates $y$ and $z$). On this cross section, there acts an arbitrary stress-field $\sigma = f(y,z)$ as ...
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1answer
33 views

PDE Von Neumann Problem- Physical Interpretation

The Von Neumann Problem is as such: $\Delta u = f(x,y,z)$ in $\ D$ $\frac {\partial u} {\partial n} = 0$ on bdy $\ D$. Using this you can prove that for there to be a solution to this Von Neumann ...
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1answer
46 views

Do we have $\frac{1}{a} - \frac{1}{b} = b - a$?

I am attempting to prove that $$\frac{1}{E'} - \frac{1}{E} = \frac{1}{m_e c^2} \cdot (1-\cos\theta)$$ can be derived from $$E + m_ec^2 - E' = c^2(p^2 - 2pp'\cos\theta + p'^2) + m_e^2c^4 $$ where ...
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0answers
49 views

Davenport's Q-method (Finding an orientation matching a set of point samples)

I have an initial set of 3D positions that form a shape. After letting them move independently, my goal is to find the best rotation of the original configuration to try to match the current state. ...