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
18 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: ...
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3answers
30 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 $V - \frac{dq}{dt} R - \frac{q}{C} = 0$ <== ...
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1answer
45 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
25 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 ...
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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 ...
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1answer
36 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
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1answer
38 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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0answers
19 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
39 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
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3answers
27 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
41 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
26 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
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. ...
0
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1answer
24 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
44 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
24 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
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 ...
1
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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
36 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
27 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
143 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 ...
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
15 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 ...
0
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0answers
37 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
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1answer
31 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
59 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
36 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
33 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
30 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
93 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
36 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 ...
1
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1answer
33 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
13 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
37 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 ...
9
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1answer
96 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 ...
1
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2answers
88 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
31 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
votes
1answer
95 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 ...
1
vote
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
36 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, ...
3
votes
2answers
61 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 ...
1
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1answer
36 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 ...
4
votes
1answer
130 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 $\pi^2\approx9.86\dots$ ...
2
votes
3answers
136 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 ...