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Questions tagged [physics]

Questions on the mathematics required to solve problems in physics. For questions from the field of mathematical physics use (mathematical-physics) tags instead.

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Special Relativity (Time Dilation) [migrated]

Determine the speed with which one object must move relative to another for its clock to be slowed by 1% as seen by the other?
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0answers
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How do we plot a domain wall between two strings?

Intuitively, an angular vector field $\theta(x)$ such as the following would describe a domain wall between two vortices/strings of opposite winding number. I would like to draw this on a computer ...
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2answers
18 views

Complex SUVAT help?

Two objects are dropped from the top of a cliff height $H.$ The second is dropped when the first has travelled a distance $D.$ Prove that the instant when the first object has reached bottom, the ...
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2answers
23 views

Find a potential energy function for the force function F(x) = k/x2 where U = 0 at x = Xo [on hold]

Find a potential energy function for the force function $F(x) = \frac{k}{x^2}$ where $U = 0$ at $x = x_0$
6
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0answers
110 views

Is this physical model exactly solvable?

There exists a popular model in the Physics of heavy quark bound systems, called the Cornell potential model, in which the inter-quark potential is modeled to vary with radial distance $r$ as $$V(r) ...
6
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4answers
114 views

Asymptotic behavior of the integral $H(\beta)=\frac{2}{\pi}\beta\int_{0}^{\infty}\exp\left(-x^{3/2}\right)\sin(\beta x)xdx$

I found the integral $H(\beta)$ (which is called Holtsmark distribution) in Holtsmark's theory of ion field in plasma. In a book there is its asymptotic representation at small and great $\beta$: $$ ...
1
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1answer
26 views

Maximum kinetic energy of a particle

I'm having difficulty solving the following SHM problem A particle executes simple harmonic motion with amplitude $A=20cm$. At one instant it is at $+\frac{1}{4}$ the amplitude, moving away from ...
0
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1answer
17 views

Torque about a Line in 3D space

given: Force Vector $F = 2i - 3j + k$ force acts on the point $(1,5,2)$ line $\frac{x}{2} = y = \frac{z}{-2}$ Known: $T = n * (r X F)$ 'n' is a unit vector in the direction of the given line r is ...
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1answer
18 views

Understanding the forces on a simple model

A light elastic string AB has natural length $1.25m$ and modulus of elasticity $24.5N$. Another light string CD has natural length $1.25m$ and modulus of elasticity $26.95N$. The two strings AB and ...
0
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1answer
39 views

Torque on a tetrahedron

A tetrahedron has its corners $A=(1,1,1), B=(2,0,-1), C=(0,1,-1), D=(3,1,2)$. There is a point mass of weight $G=(0,0,-mg)$ placed on all of its corners. What is the total torque $M$ from the weights ...
3
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1answer
88 views

Integral encountered in mean field theory calculation

The integral $$ \frac{3}{2U} = \int_{\Omega}\frac{\mathrm{d}^{2}k}{(2\pi)^{2}}\frac{1}{\sqrt{\epsilon^{2}(k) + \Delta^{2}}},\quad\quad \epsilon(k) = -2t\left(\cos k_{x} + \cos k_{y}\right)$$ (where $...
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1answer
26 views

Physics with Kinematics and Projectile motion

A $0.1$ kg nut is thrown by a squirrel off of the top of a $10$ m tall tree. It is thrown with an initial upward velocity of $4$ m/s and an initial horizontal velocity of $3$ m/s. a) How long till ...
1
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1answer
25 views

Distance to stop given initial velocity, initial acceleration, and maximum jerk

Given an initial velocity $v_0$, initial acceleration $a_0$, and a maximum (positive or negative) jerk $j$, what will be the final resting position $p$ (in relation to the initial position) when ...
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0answers
37 views

Fourier Transform of Dyson's Equation

I'm attempting to show that the Fourier transform of Dyson's equation for a constant potential V, \begin{equation} G(\mathbf{r},t,\mathbf{r}_0,t_0) = G^0(\mathbf{r},t,\...
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0answers
23 views

Common eigenfunctions of 0 eigenvalue for the angular momentum components

I need to demonstrate (considering the natural representation in $L^2(S^2)$) that if two non zero vectors in $H^2(S^2)$ satisfy $J_a\phi=0$$ \forall a \in {1,2,3}$ (where $J_a$ are the components of ...
1
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1answer
28 views

Interpretation of $\tilde{f}(\mathbf{0})$

Given a function in real space $f(\mathbf{r})$, what is the interpretation of the of the value $\tilde{f}{(\mathbf{0})}$? As an example, take the Fourier transform of \begin{equation} V(\mathbf{r}) ...
0
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1answer
59 views

What is $d$**k**?

Earlier today, I saw $d$k $f(k)= $ ... in what I believe was a physics integration problem involving spheres. I cannot find the original problem. My question is what $d$k means; it is not part of an ...
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2answers
55 views

Solving a physical problem involving electric circuits

Well, I've a series RL circuit that is powered by a voltage source. The input voltage is given by: $$\text{V}_{\text{in}}\left(t\right)=50+\frac{400}{\pi}\cdot\sum_{\text{n}=1}^\infty\frac{\sin\left(...
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0answers
16 views

Movement problems [closed]

The ratio of the velocities of two vehicles is $v_2/v_1 =3/2 $. After these vehicles take off from point A, simultaneously, on a circular track with a circumference of 75km, they meet. According to ...
0
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2answers
25 views

Percentage of volume of object above water

I'm having difficulty proving that the percentage of the volume of an object above the surface of a liquid is $$\frac{100(p_f-p_o)}{p_f}$$ given that buoyant force exerted by the liquid on the ...
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1answer
20 views

Word problem regarding finding torque of a shoulder

Question: What is the torque about the shoulder if the arm is held in an abducted position at 60 degrees from the body in the frontal plane while holding a 10 kg dumbbell? Assume that the mass of the ...
2
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1answer
86 views

Help with Difficult Integral - Green's Function and Finding the Potential

I'm tasked with performing the following integral. Specifically, the problem asks the following: Calculate the potential along the $z$-axis for the case where the upper hemisphere [of a sphere] is ...
1
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1answer
41 views

Taking moments of a fluid equation

I understand that this question is maybe better placed in the physics stack exchange but thought maybe I would find some help here as well. Given the following term that is taken from the Vlasov ...
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2answers
33 views

Solve k in this ODE: mv′(t)=mg−kv^2(t)

I have this question about finding the air resistance using the following differential equation: *mv′(t)=mg−k(v^2)(t)* where m is the mass of the downward-...
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0answers
19 views

Social Force Model for Pedestrian Dynamics by Euler Method

The social force model is a model using newtonian forces to describe the movement of individuals. As seens here : page 1 Each individual feel the following forces : ->a driving force towards the ...
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2answers
50 views

How is $v {{dv} \over {dt}} = {d \over {dt}} ({{v^2} \over 2})?$ [closed]

Can someone show me step by step how $$v \frac {dv} {dt} = \frac d {dt} \frac {v^2} 2? $$ I came across this equation from derivation of the relationship between work done and change in kinetic ...
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1answer
32 views

Problem related to three point charges

Given 3 point charges are located in a Cartesian Coordinate system where Charge 1 (having a charge of 2nC) is placed at the origin, Charge 2 is placed at $(0,5)$ and has a charge of 2nC as well, and ...
0
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2answers
48 views

When does the rocket hit the ground?

A rocket is fired from the ground and the speed is given by: $$-4.9t^2 + 49t + 155$$ When does it hit (return to) the ground? So first we did: $$9.8t = 49 \implies t = 5$$ So it hits the ...
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1answer
22 views

Liquid nitrogen freezer daily evaporation with regular draining

Suppose we have a liquid nitrogen tank hooked up to a freezer. The freezer is replenished with 37.2 L of LN2 every 5 days from the tank. Additionally, the tank loses LN2 at a rate of 1.5% per day. ...
2
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1answer
53 views

Does the Time Evolution Operator Satisfy the Schrodinger Equation?

I would just like to confirm my solution to the following question. I'm a bit hesitant on my solution because of a specific step. I would just like confirmation if that step, which I will point out, ...
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1answer
29 views

How to use operators on tensor products

This problem is from physics, but I have trouble understanding the math. I have some problem understanding how to use tensors. Let's say in Quantum Optics if I have the state in mode $b$ (where I can ...
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1answer
17 views

How do I find the coefficient of friction when given velocity, distance, and mass?

A skier, moving at 8m/s, slides to a stop on a level surface while moving 64m. Assuming her mass to be 60kg, what is the coefficient of friction between her skies and the snow?
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0answers
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Find forces on cables of the cable car

My Calc professor gave us a Physics problem. I'm absolutely awful at Physics. So here we go. Here's the problem, plus my work and guess. So I know my guess is wrong, but here's what I didn't get. I ...
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0answers
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Representation theory and symmetry in physical systems.

I've come multiple times across statements like these Representation theory remains the method of choice for simplifying the physical analysis of systems possessing (a high degree of) symmetry ...
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1answer
22 views

Finding weight in Megagrams (Mg) given circumference and density

Glaciers often deposit large rocks called erratics. The granite rock has a circumference of 9.5 m. Assuming it conforms to the shape of a sphere, what would be its weight in Megagrams (Mg), where 1 Mg ...
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0answers
21 views

How much force needed to keep this together?

Let's consider the following situation: There are 3 identical cylinders each with a weight of 20 tons. The 3rd one is put over the other 2 like in the picture (but the bottom 2 do touch each other). ...
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0answers
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Symmetry of a planar system and product of inertia

I read the following sentence here: "The products of inertia occupy the off-diagonal positions and measure the asymmetry of the mass distribution with respect to the planes of the inertia frame of ...
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2answers
29 views

Interpreting Volterra Series Correctly

I was reading this and found on page 6 was a description of a generalization of Taylor series to linear functionals. Reproduced below as $$ F[\phi + \lambda] = \sum_{n=0}^{\infty} \left[\frac{1}{n!} ...
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1answer
28 views

I need help solving this problem regarding charge conservation and electric current.

Problem I think that part (a) is asking "What can be inferred by applying conservation of charge to an arbitrary control volume? I found the following breakdown that I think helps answer part (a), ...
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2answers
46 views

How long does the ball take to reach half of its terminal velocity?

A ball of mass m = 0.1kg falls from rest under the influence of gravity (on earth) in a medium that provides resistance that is proportional to its velocity. For a velocity of 0.2 m/s, the resistance ...
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0answers
45 views

Reference Request: Getting from introductory PDEs to kinetic models, non-local aggregation, and mean field games

My background is in statistics/machine learning though I have been looking more and more at differential equation models to better understand the dynamics of social and economic systems. It seems like ...
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1answer
33 views

Can a light-year be represented as a ratio?

Would it be valid to say that a light year is a ratio between the distance that light travels and the elapsing of one year?
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2answers
36 views

Mechanical vibration: single degree of freedom model of wheel mounted on a spring

I think the author of my book has this solution wrong and would like some feedback on my thoughts (see Example 1.4.1). The solution states that the total energy of the system is represented by the ...
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0answers
16 views

Inverting the WZW Lagrangian to its Poisson bracket

Could someone give me a hint or how one should start for inverting the WZW Lagrangian or equivalently the Kirillov-Kostant 2-form: $$\Omega = \frac{K}{4\pi} \int_0^{2\pi} \mathrm d x \text{ Tr} (g^{-1}...
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2answers
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Projectile Motion, finding the optimal angle

I've been studying multivariable calculus the last 2 weeks, and I understand (I think) how to optimize 2 variable equations through normal optimization and constrained optimization via Lagrange. I ...
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0answers
32 views

Velocity of a point expressed by using rotation matrix between two reference frames

I'm trying to express the velocity of a point P by using a rotation matrix between two reference frames (see attached file please). Notation: the vertical bar with $O_1$ or $O_2$ means that the ...
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0answers
49 views

Find a conserved quantity of a dynamical system to reduce the dimension of this system

Let $x_{1} , x_{2}, x$ points which are forced to move on a line, the mass of $x$ is M and the mass of $x_{1} , x_{2}$ is m with $M>m$. The points $x_{1} , x_{2}$ are connected to $x$ via two ideal ...
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1answer
46 views

Deriving analytic expression for magnetic field & flow lines of bar magnet.

How can we analytically derive the flow-lines of a normal permanent bar-magnet? Physics context & own approach: In classical electromagnetics we have the legendary Maxwell's Equations: $$\begin{...
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0answers
37 views

Problems for a concrete example in representation theory

I am currently studying representation theory. In my courses notes, I face trouble understanding one step of a concrete example: three masses connected by springs. This is the same approach as in ...
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1answer
18 views

How to determine what direction an object will orbit another object.

In this universe lets say everything exists in a 2d plane. There exists a 2d planet and hurdling towards it (at some velocity), is a 2d asteroid. Luckily, the asteroid isn't going to collide with the ...