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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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 ...
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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 ...
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22 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 ...
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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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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 ...
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0answers
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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 ...
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0answers
27 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. ...
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1answer
25 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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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
27 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
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 \...
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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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2answers
56 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
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: $$ \begin{align*...
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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 ...
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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
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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
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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 ...
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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 ...
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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 ...
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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 ...
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1answer
62 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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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 ...
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2answers
82 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....
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0answers
34 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 ...
3
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2answers
110 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 t}(x,t)=\left(-\dfrac{\hbar}{2m}\nabla^2-\frac{e^2}{x+\alpha}-...
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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
19 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
40 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 (0,1)\...
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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
39 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 T+y_i\...
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1answer
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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
104 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
114 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
57 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
106 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
72 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
47 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 $g=...
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1answer
133 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
141 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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0answers
37 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
64 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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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?