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
29 views

Finding total work by integration

The following tank is completely filled with water. Find the total amount of work done in pumping water out of the outlet. Note that the density of water is kg/m$^3$ I feel like I am headed ...
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0answers
14 views

HyperCube questions

I have three hypercube questions. 1) How many nodes does a d-dimensional HyperRing have (as a function of d) ? 2) How many edges ? 3)What is the degree of each node in a HyperRing with n nodes ? I ...
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1answer
13 views

Pressure and force used in equations [on hold]

A solid block, weighing 200 N, has the following dimensions: 0.1 m x 0.5 m x 0.3 m. What is the maximum pressure it can exert on a surface? What is the minimum pressure is can exert on a surface? ...
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1answer
52 views

Problem about Dirac delta function used in Ampère's law in physics [on hold]

This page uses the dirac delta function to explain why the function $\nabla \times B= 0$ is not $0$. I have tried to find how they justify this without any success mathematically. How was this ...
1
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1answer
14 views

Find the average acceleration

Find the average acceleration of the tip of the 2.4-cm long hour hand in the interval noon to 6pm. I found the average velocity is -2.2x10^6 but I'm not sure how to go about finding acceleration. If ...
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1answer
24 views

help setting up a velocity question

Standing on the ground from 3.0 m from a building, you want to throw a package from your 1.5- shoulder level to someone in a window 4.2 m above the ground. At what speed and angle should you throw ...
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0answers
26 views

Solution to Laplace's Equation in different coordinate systems

Find the general solution to Laplace's equation for spherical symmetry (everything can only depend on $r$, the radius), cylindrical symmetry (everything can only depend on $s$, the radius), and planar ...
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0answers
28 views

Jumping Flea acceleration and magnitude

A flea jumps by exerting a force of 1.07x10-5 N straight down on the ground. A breeze blowing on the flea parallel to the ground exerts a force of 1.14x10-6 N on the flea. Find the direction and ...
-3
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1answer
42 views

Simple harmonic motion $y=A \cos{\omega t} + B \sin{ \omega t} $ [closed]

Show that: $$ y = A \cos{\omega t} + B \sin{ \omega t} $$ is a solution of (†)
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0answers
24 views

Relative motion question

You wish to row straight across a 63-m-wide river. You can row at a steady 1.3 m/s relative to the water, and the river flows at 0.57 m/s. I know I need to draw a right triangle for the question but ...
0
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0answers
34 views

Physics Problem Help [closed]

Bob has just finished climbing a sheer cliff above a beach, and wants to figure out how high he climbed. All he has to use, however, is a baseball, a stopwatch, and a friend on the ground below with a ...
1
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1answer
32 views

List of well-known submodular function in physics, statistics, math?

Can you please share a list of well-known submodular functions (have the diminishing return property) that you know? In physics, stats, math, etc? I am searching for a submodular function for my ...
1
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1answer
24 views

The weight of a drilled out cylinder

Cylinder is $2.71$kg or $2710$g, diameter is $5$cm and $7.5$cm high. The volume is $147.18$cm$^3$ and the density is just the mass divided by the volume, I'm not sure if I need to convert it into ...
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0answers
20 views

Is the Moment of Intertia of A Thin Rod equal to The Moment of Intertia of a thin Strip? [migrated]

This is the Moment of Intertia of a Thin rod I am not aware of a formula for a thin strip (or if there is any such formula). I was imagining a thin rod does not have a radius in the formula (thin ...
1
vote
1answer
145 views

Work on Springs using Hooke's Law

I'm currently stuck on parts c and d of this problem. The problem says Suppose a force of 20 N is required to stretch and hold a spring 0.4 m from its equilibrium position (0). I found k constant to ...
2
votes
1answer
49 views

Quantum translation operator

Let $T_\epsilon=e^{i \mathbf{\epsilon} P/ \hbar}$ an operator. Show that $T_\epsilon\Psi(\mathbf r)=\Psi(\mathbf r + \mathbf \epsilon)$. Where $P=-i\hbar \nabla$. Here's what I've gotten: ...
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0answers
26 views

Giant leap of the space goat [migrated]

This problem was inspired by this one and similar problems involving tethered animals. A space goat is tethered to the north pole of a spherical asteroid of uniform density and radius $a$ by a rope ...
4
votes
3answers
159 views

Intuitively, how do you explain the concept of Flux?

Lately in my physics and mathematics classes, I've come across the concept of Flux. And although I've been able to define them mathematically and figure out how to use them. I'm still not entirely ...
2
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0answers
30 views

Liouville's theorem (Hamiltonian) [closed]

can some one give me a link for a rigorous proof for Liouville's theorem (Hamiltonian) thanks
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0answers
28 views

Calculate cost/kWh

I'm stuck on a question in my college class, the figures are in Swedish crowns so they might seem a bit weird for non-swedes: A wind power station costs 18 million swedish crowns to build and ...
0
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2answers
25 views

Why write the solution of the harmonic oscillator form 1 is equal to writing form 2?

Why write the solution of the harmonic oscillator form $$\psi=A\cos\omega_0 t+B\sin \omega_0t$$ is equal to writing form $$\psi=C_1e^{i\omega_0t}+C_2e^{-i\omega_0t}$$? I would like to see how one ...
0
votes
1answer
21 views

Quadratic problem

NASA launches a rocket at $t = 0$ seconds. Its height, in meters above sea-level, as a function of time is given by $h(t) = -4.9t^2 + 37 t + 101$. Assuming that the rocket will splash down into the ...
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0answers
21 views

Using differential equations vs general solutions

I was looking at Newton's Cooling Law with a student when he asked me why, for this particular case, do we use the ODE and not just the general solution to analyse data. I couldn't come up with an ...
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4answers
73 views

Products of Infinitesimals

In my physics class my professor was abusing the derivative, as per so many physics classes I've been in. This time, he took the quantity $(x+dx)(y+dy)$ and argued that the $dxdy$ term should ...
1
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2answers
15 views

Newton 2nd law for rotations: $\tau = I \alpha$ dimensions correct?

I have a really stupid question, which I can't figure out at the moment. I don't see why the following is correct when you check the dimensions: $\tau = I \alpha \;\;\rightarrow \mathrm{Nm= kg ...
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0answers
19 views

rabbit and Tortoise

A hare (rabbit) and a tortoise (turtle) are in a foot race. When the tortoise is 22 m from the finish line, he has a speed of 4.0 m/s but is 5.0 m behind the rabbit. The rabbit has a speed of 5.0 m/s. ...
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2answers
23 views

How to calculate the direction (of velocity of a ball) after collision with another ball?

Say I have two balls of same radius, in the 2-D Plane. So like a pool (billiard) game. I have the cue ball, moving with the velocity vector V, the magnitude is not important, so we only need an angle ...
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0answers
29 views

Forced oscillation in a pendulum and resonances

In a pendulum without the small angles approximation the equation describing the motion of the mass is: $$\ddot{\phi}(t)=-\dfrac{g}{l}\sin\left(\phi(t)\right)$$ Applying a sinusoidal force ...
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0answers
25 views

Solving the integral to calculate the electrostatic force between two tubes

Let's say we have two tubes with charges $q_1$, $q_2$, radii $b_1$, $b_2$ and lengths $l_1$ and $l_2$. They are placed along the surface of each other like in this figure: To calculate the ...
1
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1answer
64 views

Solving the equation of damped oscillator

I'm asked to prove that any solution of the equation $$\ddot\Phi+\Gamma\dot\Phi+\omega_0^2\Phi=0;\qquad \omega_0>\frac\Gamma 2$$ is $$\Phi=A_0e^{-\frac{\Gamma}{2} t}e^{i(\omega t-\beta)};\qquad ...
0
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0answers
34 views

Testing Divergence Theorem using Spherical Coordinates

I'm trying to verify the divergence theorem using spherical coordinates for the vector field $\vec{F}=r^2cos^2\theta(cos\theta\hat r-sin\theta\hat\theta)$ through the top half of the unit sphere. ...
4
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1answer
69 views

Show that the profile of the hill is a cycloid

I'm struggling with this problem: From George Simmons_ Differential Equations At sunset a man is standing at the base of a dome-shaped hill where if faces the setting sun. He throws a rock ...
3
votes
1answer
115 views

Find vector field given curl

I have an equation $\nabla \times \vec{B} = \mu_{0}\vec{J}$, where $\vec{J} = \left\langle f(x,y), g(x,y), 0 \right\rangle$ and need to solve for $\vec{B}$. I've looked elsewhere on here for how to ...
1
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3answers
259 views

Center of Mass in 3D object?

How would I find the center of mass in a 3D object (a "spinning top" or "dreidel") that consists of a cylinder welded on top of a box welded on top of an upside down cone? Assume building material is ...
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0answers
50 views

How can I calculate the force that is applied on a tube by an another tube?

Let's say there is two tubes (cylinders with no tops or bottoms) with charges $q_1$ and $q_2$, radii $b_1$ and $b_2$, lengths $\ell_1$ and $\ell_2$. These tubes are located along the axis of each ...
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2answers
67 views

Given the instantaneous value of current, find the amplitude, period, frequency, phase

The instantaneous value of current, i amp, at t seconds is given by: $i = 15 \sin(100\pi t + 0.6)$ Find the value of; amplitude period frequency initial phase angle value of i when t = 2.5s time ...
0
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1answer
19 views

How to find time it takes for an object to slide on an incline ramp [closed]

So I hope I am asking this question in the correct spot. Here is my question: if there is an incline at $70$ degrees, the object's friction is $\mu = 0.1$, and the incline is $1$ meter long, how long ...
2
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1answer
42 views

When does a particle with given acceleration change the direction of motion?

A particle moves along the x-axis so that its acceleration at any time $t\geq0$ is given by $a(t)=12t-4$. At time $t=1$, the velocity of the particle is $v(1)=7$ and its position is $x(1)=4$. ...
0
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2answers
21 views

Finding vertical displacement

I am being asked to find the distance a shuttle travels upward after a given amount of time. I know that time passed is 79s, the rate of acceleration is 6.244 m/s^2, and the speed at 79s is 493.276 ...
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0answers
37 views

Strange question about magnetic dipole in a plane at infinite distance

Please allow me to ask something rather unusual and perhaps completely naive. Suppose I have an electric current in a circular loop in a plane. Consider it just in a mathematical sense, i.e. an ...
3
votes
1answer
43 views

How to mathematically determine if the magnitude of a cross product is up/down(positive/negative?)?

So, I'm a newbie at complex vector math. I'm working on a 2D physics engine, and my issue is, with angular acceleration from torque, is it supposed to be positive or negative? I understand the right ...
2
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2answers
50 views

Find the work done by the force field in moving the particle from one point to another

Find work done by the force field F in moving the particle from $(-1, 1)$ to $(3, 2)$ This sounds good till we are given that $\textbf{F} = \dfrac{2x}{y}\textbf{ i }- \dfrac{x^2}{y^2}\textbf{ j }$ ...
0
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1answer
19 views

Simplifying $\frac1{gt}\sqrt{g/2h}\,dx$ in free fall equations

The relevant equation: $x(t) = \frac12 gt^2$ , $dx/dt = gt$ , $T=\sqrt{2h/g}$ $dt/T = (dx/gt)\sqrt{g/2h} = 1/(2\sqrt{hx}) dx $ I do not see how $(dx/gt)\sqrt{g/2h}$ turns into $1/(2\sqrt{hx}) dx $ ...
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2answers
69 views

Water Refraction and the depth of the water.

I'm not sure if this is the right place to ask my question! But I hope I will find some help!. Image distortion occurs by refraction of light at the boundary surface between air and water when a ...
1
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1answer
37 views

How do component wavelengths *add* to wavelength of light color?

Say you have 3 leds at frequencies (or wavelengths) $u_1, u_2, u_3$ in Hz (or nm). Then how do you calculate the apparent or center of, or blah frequency (I don't know what I want really) of the ...
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0answers
38 views

Using significant figures, what would the answer be?

I've been learning about significant figures and I have a few questions. When you multiply/divide, the number of significant figures in the answer should be the same as the term with the least number ...
2
votes
1answer
52 views

Why does a heating model work?

I am referring to: $T=T_0 e^{kt}$ where T=temperature,t=time and k=constant. It seems to work, I as just curios to why it works?
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1answer
62 views

How to calculate the area of a 4 dimensional curve?

I have been searching on Google about it, and I found that given a sample, 4 points, per example, I could find a function and use integral on it. I am sorry if it sounds silly, I am very dummy in ...
1
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1answer
88 views

Quantifier problems of equations in physics [closed]

Equations in physics are often written without quantifiers. For instance, from time to time we can see the equation $$E = mc^2$$ is casually written down. To assert that static energy equals mass ...
0
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1answer
51 views

Dirac Delta identity proof.

I was working on showing that: $$x \frac{\mathrm{d}(\delta (x))}{\mathrm{d}x} = -\delta(x)$$ using integration by parts. I arrived to a point where I had had as an answer the following: $$ -f(0) - ...