Questions tagged [physics]

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

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Interfering higher frequency waves to create a lower frequency one

Once I saw a demo where multiple speakers were outputting inaudible sounds (I assume very high frequency) that would interfere at certain locations to be audible. It has fascinated me for some time ...
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Statistical mechanics partition function from probability distribution

I am curious about the mathematical background of something I came across while working on a problem in statistical mechanics. As an example, I am going to use the classical canonical ensemble, though ...
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How many vectors do I need to span the vector space for Velocity, Distance, Angles, Acceleration, Position, and Time?

I am working on a Robot Arm simulation project and trying to get those 6 varibles, in my question, coming from the Robot Arm. The robot arm has 6 joints and each joint can run the motor inside to ...
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Overdetermination of the Maxwell-Equations

I‘ve heard people talk about the overdetermination of the Maxwell equations, which are of course: $$ \nabla \cdot E =\frac{\rho}{\epsilon}\\ $$ $$ \nabla \cdot B=0 \\ $$ $$ \nabla \times E=-\...
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Mechanics | Use the work-energy principle to find the speed of the book as it hits the floor. [closed]

Problem A small book of mass $m$ is held on a rough straight desk lid which is inclined at an angle $\alpha$ to the horizontal, where $\tan\alpha=\frac34$. The book is released from rest at a distance ...
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Calculate stopping time based on force acting against object. [closed]

I have a force of 17065N acting against a 70kg object, which has is moving at 7.7 m/s. How would i calculate the stopping distance?
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Calculating true airspeed: Horseshoe Heading Technique

This question relates to calculating the speed of an aircraft relative to the air, based on GPS measurements (i.e. groundspeed measurements). Specifically it is about David Rogers' Horseshoe Heading ...
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What is the difference between $\int v_i\,dt$ and $\int v_f\,dt$?

I'm starting physics, and for a simple exercise, I wanted to derive each of the kinematic equations with calculus. I want to go from $v_f = v_i + at$ to $\Delta x = v_0t + 1/2at^2$, so I just ...
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Difference between heat capacity at constant pressure and volume

Define $C_V=T (\partial{S}/\partial{T})_V$ and $C_P=T (\partial{S}/\partial{T})_P$. Prove that $C_P-C_V=T(\partial{V}/\partial{T})_P (\partial{P}/\partial{T})_V.$ This is equivalent to proving $(\...
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Is my solution acceptable if I use a different sign convention?

Problem: A ball of mass 0.15 kg is moving with a velocity of 12 m/s and is hit by a bat so that the ball is turned back in the complete opposite direction with a velocity of 20 m/s. The force of the ...
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2 answers
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Is the component of a vector along another vector also a vector?

I will surmise what I've learned from a couple of Wikipedia articles below: Vector projection: The vector projection of a vector $\vec{a}$ onto a vector $\vec{b}$ (also known as the vector component ...
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How to derive the following approximation for a set of coupled equations?

Background I have the following set of coupled equations $\frac{d}{dt}\rho_{ab} = -i\omega A - \frac{1}{2}\Lambda B$ with $\omega, \Lambda$ parameters that are real and $A, B$ 4x4 matrices that are ...
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How can I calculate the right obit period of planets with python?

...
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Dimensional Analysis - Simple Pendulum

For a simple pendulum consisting of a spherical mass $m$ anchored to a fixed point $O$ via a mass-less rod of length, perform dimensional analysis on the problem to find the period of oscillation τ (i....
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3 votes
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Find the equation for the angle in which the particle abandons the hemicircle. No friction.

I think I missed something in this mechanics problem. We're given a polish and homogeneous hemicircle which has mass $M$ and a particle of mass $m$ laying on the top of it. There is also no friction ...
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How to add shadow effect to 2D fractals?

My question is simple: how do you add a shadow effect (like the one in Kalles Fraktaler 2)? I have tried distance estimation, but have failed at creating it reliably. I would like a relatively fast ...
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1 answer
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Given $[A,B]=0$ then $[A,f(B)]=0$

Given $A$ and $B$ two operators that commute ($[A,B]=0$) then $A$ commutes with an arbitrary function of $B$ I recently saw this property of the commutators on a quantum mechanics course. We didn't ...
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Explanation of trick used to prove the work energy theorem in 1-D

The proof of the Work energy theorem for 1-D starts with $$F(x)=\frac{dv(t)}{dt}$$ Then, they integrate with respect to the position x in both sides of the equation(even though v doesn't depend on x!):...
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The material point M (m=1-mass) in the Oxy plane moves on the effect of a force field which components are Fx=y,Fy=x.

Can someone help me with this exercise? The material point M (m=1) in the Oxy plane moves on the effect of a force field which components are $F_{x}=y$,$F_{y}=x$. Is there a power function and if so, ...
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How to calculate the new position at time t of bodies with variable acceleration?

Intro For an N-body simulation of calestial bodies I need to calculate on the one hand the accelerations of the calestial bodies based on the received gravitational forces [done] and on the other ...
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Can $x^{\mathrm{cm}}$ ($x$ to the power $\mathrm{cm}$) be defined?

We all know that $x \cdot \mathrm{cm}$ is "$x$ times $\mathrm{cm}$" but I was wondering about what is $x^{\mathrm{cm}}$ ($x$ to the power $\mathrm{cm}$) can be define this $x^{\mathrm{cm}}$ ...
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Integral measure quantum fields

In many physics books (especially QFT), the integral measure for a quantum field is written down as \begin{equation} \phi(x)=\int\frac{d^{3}p}{(2\pi)^{3}}.... \end{equation} It is a summation over the ...
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Newtons second law for fluid resistance

I am trying to follow Zemansky's derivation of a particles speed in a body of fluid described by the following eq: $$ m \frac{dv_y}{dt} = mg - kv $$ Replacing $ mg/k $ by $ v_t $ (the terminal speed) ...
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What initial velocity is required for a bullet to enter orbit?

I need some help for a school assignment. I'm trying to make a differential equation to solve in Comsol. The part I'm having trouble with is the fact that air resistance and gravity changes based on ...
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2 answers
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Where this $2\pi$ came from?

In this link there are this equation (12.3.2): $B = \frac{\mu_0}{4\pi}\int_{wire}\frac{I\sin{\theta}dx}{r^2}$. And is said to substitute $r$ by $\sqrt{x^2+R^2}$ and $\sin{\theta}$ by $\frac{R}{\sqrt{x^...
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How to write the Lagrangian of a cyclic tri-atomic molecule?

I'm familiar with Lagrangian of a $\bf{linear}$ tri-atomic molecule moving only on 1-dimension.like this The kinetic energy is written as $$ T = \frac{1}{2}(m\dot{x}_{1}^{2} + M\dot{x}_{2}^{2} + m\dot{...
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1 answer
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Please first use equation (3) and solve θ(𝑡) ,𝜃̇(𝑡) , ℎ𝑐(𝑡) of roly-ploy toy model

Question:Please first use equation (3) and solve θ(𝑡) ,𝜃̇(𝑡) , ℎ𝑐(𝑡) By definition: let a=second derivative of theta b=first derivative of theta Here, ℎ𝑐 is the y-coordinate of 𝐶 ...
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3 votes
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Compressible Navier-Stokes vs Incompressible, which is 'Easier' or usually has shorter computation times for finding numerical solutions?

This is a broad question which might not have a clear answer. I am aware that the incompressible NS equations can be used to approximate the compressible when the Mach number is low, and that this ...
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Change orientation of turns of a trajectory

Consider a robot following the dynamical system $R_B'=R_B\exp(\omega_B^{\times}), v_W'=R_B\alpha_B + g_W$, where $R_B\in SO(3), v, \alpha, \omega, g \in \mathbb{R}^3$, and $\omega^\times$ is the skew ...
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Projectile motion science 9 [closed]

A foot ball is kicked at a certain angle above the horizontal. The vertical component of its initial velocity is $40 \ m/s$ and the horizontal component is $50 \ m/s$. Determine: a. its time of ...
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2 answers
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Question on angular acceleration in OCR A Level further maths textbook

OCR A Level Further maths: mechanics, Year $1.$ Chapter $4$ Section $2$: Acceleration in horizontal circular motion. $\omega$ is angular speed and is defined as $\frac{d\theta}{d t},$ sometimes ...
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1 answer
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Distribution of Mass Due to Centripetal Accel.

Short Question: So, let's say that hypothetically I were to spin pizza dough in the air. Would the outer ring of the pizza dough have a greater volume/mass due to centripetal acceleration? And how ...
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1 answer
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Hermite polynomials for non-integer degree

I have solved an eigenvalue problem using Mathematica and the answer is in terms of Hermite polynomials. Now, for integer degrees $H_n(z)$, I can find a nice definition. However, in the solution to ...
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2 answers
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Given the period lengths for the orbits of $n$ different planets around the sun, how long until they all align?

Say you have $n$ planets orbiting around the sun, where the $i$th planet takes $t_i\in\mathbb{R}_{>0}$ days to complete one full cycle. Assume at $t=0$, all the planets are aligned with the sun. ...
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-2 votes
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How to remove gradient from algebraic expression

So, I found the Schrödinger's Equation (shown below), and I found out I can expand it into two or three dimensions, as well, by simply adding another term $\frac{\partial^2\psi}{\partial z^2}$, for ...
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Is there a unique solution to: $ay(x)y'(x)+by(x)+c=0$? I have found one (for the purposes of modelling particle motion) but is that one the only one?

I would like to ask about the uniqueness of solutions to the ODE: $$ay(x)y'(x)+by(x)+c=0$$ Given a condition $y(0)=k$. Contextual motivation: A vehicle of mass $M$ kilograms is travelling in a ...
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Using "Maxwell's curl equations" to get $H_y = \dfrac{j}{\omega \mu} \dfrac{\partial{E_x}}{\partial{z}} = \dfrac{1}{\eta}(E^+ e^{-jkz} - E^- e^{jkz})$

I am currently studying the textbook Microwave Engineering, fourth edition, by David Pozar. Chapter 1.4 THE WAVE EQUATION AND BASIC PLANE WAVE SOLUTIONS says the following: The Helmholtz Equation In ...
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2 votes
1 answer
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Does the electrostatic potential have a local maximum on the sphere?

Let $$M=\{(x_1,x_2,x_3,x_4) \in \mathbb{S}^2 \times \mathbb{S}^2 \times \mathbb{S}^2 \times \mathbb{S}^2 \, |\,\, \text{ all the } x_i \, \text{ are distinct}\} $$ $M$ is an open subset of $( \mathbb{...
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5 votes
2 answers
132 views

How to place optimally four electrons on a sphere?

$\newcommand{\S}{\mathbb{S}^2}$ Let $x_1,x_2,x_3,x_4 \in \mathbb{S}^2$ be points on the unit sphere, that minimizes the quantity $$ E(x_1,x_2,x_3,x_4)=\sum_{i < j}\frac{1}{\| x_i - x_j \|}, $$ ...
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1 vote
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Describing acceleration in terms of limits [closed]

I am not sure how to answer this question I am unsure how to represent a particular notation in terms of equations (2) and (3) as described in the link above. If $$a=\frac{dv}{dt}=\frac{d}{dt}(\frac{...
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A horizontal beam is attached to a wall by a cable. Find the force of the cable and the force exerted by the wall.

A 5.00m long horizontal beam weighing 315N is attached to a wall by a pin connection that allows the beam to rotate. Its far end is supported by a cable that makes an angle of $53^o$ with the ...
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Simple Harmonic Motion in case of periodic force

A particle is execution SHM in a straight line under the acceleration $kx$. If a periodic force of $ml$ cos $pt$ be introduced and time period of forced vibration increased to $1.5$ times then show ...
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4 votes
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How to derive the Sommerfeld radiation condition from the resolvent?

Suppose the resolvent $R_0(\zeta)$ for an operator $P_0(\zeta)$ is known to satisfy a limiting absorption principle at $\lambda \in \Bbb R$. For some perturbation $P(\zeta)$ of $P_0(\zeta)$ with $V (\...
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1 answer
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Atwood system of two pulleys

A light string passes over a light fixed pulley carrying a mass P at one extremity and a light pulley at the other. Another light string passes over this second pulley and has masses Q and R at its ...
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When it's better choose an specific Dx than calculate the Derivative?

I was thinking about this problem: a car that moves as x(t) = t^3 in t=0 if i calculate the derivative in that point is 0. But in the reality the car near the time 0 its accelerating. If i choose ...
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1 answer
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Differential equation of cycloid

I have a problem where I study the brachistochrone curve which is described by the following differential equation: $$(1+(y')^2)y = k^2 ,$$ where $k$ is the appropriate constant I have to explain why ...
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2 votes
2 answers
62 views

Solving system of three equations in three unknowns for electric circuit analysis problem

My electrical engineering circuit analysis textbook presents the following problem: Find the currents and voltages in the circuit shown in Fig. 2.28. Answer: $v_1 = 6 \ \text{V}$, $v_2 = 4 \ \text{V}...
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Calculate Projectile flight time based on Gravity

Hey I want to calculate the flight time of a Projectile in 3D Space based on Bullet's speed, Velocity, Acceleration and Gravity or a custom downward force. I already have a formula that calculates the ...
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1 answer
60 views

At what point of the pole should the rope be tied so that the man can turn the pole upside down easily?

Question: One end of a $20m$ long rope is tied to a telegraph pole standing perpendicularly on the ground and its other end is being pulled by a person with a definite force. At what point of the pole ...
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1 vote
1 answer
43 views

Geometry: path length in atmosphere ("round" Earth)

I'm having trouble obtaining this physics formula. Since it's mostly about geometry, I hope it isn't out of place here. I'll paste the text from the book: Considering the curvature of the Earth (R is ...
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