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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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A simple proof of this equality: $\det_{\mu\nu}\left(\frac 1 2 \text{Tr}\left[A\sigma_\mu A^\dagger \sigma_\nu \right]\right)=1$

Question Let $A\in \text{SL}(2,\mathbb{C})$, so $\det(A)=1$. Define the following (Pauli) matrices: $$\begin{align} \sigma_0=\begin{pmatrix}-1 & 0 \\ 0 & -1 \end{pmatrix} & &\sigma_1=...
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0answers
33 views

Tautochrone and Brachistochrone problems are equivalent

It is a well known fact that the brachistochrone (the problem of finding the curve of quickest descent in a uniform gravitational field) and the tautochrone (the problem of finding a curve from which ...
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1answer
24 views

Time-dependent manifolds

I'm studying Classical Mechanics, and in some cases the particles in the study are constrained to move in a certain manifold, which changes with time. I've looked for bibliography about time-...
2
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1answer
30 views

How to find a function that is defined by its integral and its derivative?

I was trying to solve a physics problem. The question is: "How long will it take for a boat to cross a river if its velocity is always directed towards a fixed point on the opposite side of the river ...
0
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1answer
23 views

Finding distance by knowing velocities and acceleration [on hold]

An object moves with constant acceleration 4m/s^2 and over a time travel reached a final velocity of 12 m/s 1) If it’s initial velocity is 6 m/s what is its displacement during the time interval? 2) ...
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0answers
17 views

Nonlinear Pendulum integral section

$\sin \frac{\alpha}{2} = \sin \frac{\alpha_0}{2}\sin \alpha$, where $\alpha_0$ is a constant. How is this possible?
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1answer
45 views

Asymptotic behavior of the Coulomb logarithm

In transport theory in plasma physics, there's an important integral called the Coulomb logarithm, which relates to the scattering cross section off the Yukawa potential. It can be written as $$ \ell(\...
3
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1answer
54 views

How to show the trace relation: $\text{Tr} [A\not x A ^{\dagger} \not x]\geq0$

A speaker from a talk/lecture I attended recently quoted the following inequality without proof, and for no good reason I have taken it upon myself to prove it: Let $A\in SL(2,\mathbb{C})$, so $\det\...
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0answers
19 views

Finding force from a decelerating car (not stopping)

Driving home from school one day, you spot a ball rolling out into the street. You brake for 1.20 s, slowing your 950-kg car from 16.0 m/s to 9.50 m/s. (a) What is the average force exerted on your ...
0
votes
1answer
16 views

Distance required to stop a truck on a ramp (Kinetic energy and Friction)

Truck brakes can fail if they get too hot. In some mountainous areas, ramps of loose gravel are constructed to stop runaway trucks that have lost their brakes. The combination of a slight upward slope ...
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0answers
22 views

Projectile motion A level mechanics [on hold]

A ball is thrown from a point 4 m above horizontal ground. The ball is projected at an angle 𝛼 above the horizontal, where tan 𝛼 = 3/4. The ball hits the ground at a point which is a horizontal ...
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0answers
26 views

Silly doubt about a particular tensor product

In physics we have a particular tensor called inertia tensor. In abstract notation, this tensor can be written as: $$ \textbf{I} = m [\langle \textbf{r},\textbf{r} \rangle \textbf{Id} - \textbf{r} \...
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1answer
15 views

Question on Laplace Transform of a Bessel Integral of the First Kind

I am trying to understand an integral I saw in a book. The book is "Earth Resistances" by G.F. Tagg. Unfortunately it's difficult to get a hold of this book, but I am confused by equation 3.9 is in ...
0
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1answer
19 views

Equivalent resistance between points K and M

The equivalent resistance between K and L is given $3\Omega$. How do I evaluate the equivalent resistance between K and M? I couldn't think of anything so far. Could I get your dear assistance? ...
0
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1answer
45 views

Calculating the potential generated by a specific distribution of charge

I have been asked to calculate the Electric Potential ($V$) in the two planes $z=0$ and $z=1$ produced by a linear distribution of charge given by: $$\lambda=(\cos{\phi})^2$$ whose shape is a ...
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1answer
57 views

Analytical solutions to integrals

While calculating the magnetic field at an arbitrary point due to a charged sphere rotating about the z-axis, I came upon the following integral, $$\iiint\frac{x^3\cos^2{\theta}\left[\left(c-x\sin{\...
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0answers
10 views

What is the mean displacement in one dimention for a single step? [on hold]

An ammonia bottle is opened briefly in the centre of a large room releasing many ammonia molecules into the air. The molecules diffuse on average 10 microns between collisions with other molecules, ...
2
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0answers
18 views

Constrained equilibrium for inflated sheet

I am trying to figure out the shape that a disc of uniformly elastic material makes if you fix its circumference firmly to a flat table and slowly fill the interior with air. So far, I've determined ...
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0answers
29 views

If the time of 0.5 amplitude is 2 second calculate the time of complete oscillation [on hold]

If the time of 0.5 Amplitude is 2 second calculate the time of complete vibration
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0answers
184 views
+50

Proving a Mathematical hypothesis using Physics

We know that mathematical models of physical phenomena need to becomes more and more sophisticated as our observations become more precise and comprehensive by utilizing more advanced instruments that ...
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2answers
39 views

Is there a closed form expression for the first zero of the first Bessel function?

$j_{1,1}$ denotes the first zero of the first Bessel function of the first kind. (That's a lot of firsts!) It's approximately equal to $3.83$. My question is, is there any closed form expression ...
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0answers
22 views

Proof of the Law of the Lever [on hold]

Is there an accepted proof of the Law of the Lever? I know of several attempted proofs, such as Archimedes's, but these either are incomplete or do not transfer to the setting of Newton's Laws. (It ...
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25 views

Newton ring by Mathmatic [closed]

enter image description here Newton ring by Mathmatic
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28 views

Finding the resultant of these forces: $300$N at $50^\circ$, $60$N at $240^\circ$, $200$N at $180^\circ$ [closed]

Using the trigonometric component method, find the resultant of the following forces. Check the direction with a rough scale drawing. $$300\text{N at } 50^\circ \qquad 60 \text{N at } 240^\circ \...
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0answers
29 views

How to calculate acceleration [closed]

An object is moving with an initial speed of $5 \, m/s$ for $8\, s$, then its speed is uniformly increased to $10 \, m/s$ in $5 \, s$. Use the equations of motion for uniformly accelerated motion to ...
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2answers
25 views

Finding the range of launch speeds for which water shot from a hose will enter a tank a distance away

A water hose is used to fill a large cylindrical storage tank of diameter $D$ and height $2D$. The hose shoots the water at $45^\circ$ above the horizontal from the same level as the base of the tank ...
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1answer
24 views

Finding Ratio from Quadratic Equation?

In this question I encountered the quadratic equation Q1^2 + Q2^2 - 6(Q1)(Q2) = 0 How can I find the ration of Q1/Q2 ? How is the answer coming C please help .
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3answers
35 views

finding angular acceleration given the angular velocity and the radius of the circle

Problem: A woman is running at 8m/s in a circular motion, the radius of the circle is 100m. What is her acceleration in m/s/s? I don't have a clue how to start! I wanted to use this: \begin{align}\...
0
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2answers
32 views

Iterative solution for algebraic equation with small parameter

I am a bit confused. I don't understand what iterative solution is. In my solid state book it is written that from equation: $$\frac{2}{3}\mu^{3/2}+\frac{\pi^{2}}{12}\frac{\left(k_{B}T\right)^{2}}{\...
0
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1answer
22 views

Hankel Transform with Bessel function of the first kind

I am trying to understand a substitution in a paper I am reading. The paper is "The Application of Linear Filter Theory to the Direct Interpretation of Geoelectrical Resistivity Sounding Measurements" ...
0
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3answers
43 views

Using wrong physics formulas

We were given a couple formulas, but the one that immediately stood out to me was the Vfinal = Vinitial + at so we know the patrol will constantly accelerate "until he pulls next to the speeding car" ...
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1answer
11 views

Minimal force F to keep the block from moving if…

The question is: Determine the minimal F necessary to keep the block from moving if the coefficient of friction is $\mu=.3$. I know the horizontal force to the left is $cos (70)(50)=17.1 lbs$ My ...
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0answers
15 views

Tensor fields or operators of order $\geq 2$ being diffused by tensor fields of order 2?

Background: I am aware that in for example physics tensor fields can be used to describe things like properties of materia. Like heat conduction in macroscopic media (imagine a thermos, heat can flow ...
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2answers
47 views

Motion of an object that always has an acceleration perpendicular to its velocity

Consider an object whose position vector $x$(changes with time) satisfies the condition $$ \dot{x}\cdot\ddot{x}=0 $$ i.e. the object is always accelerating in the direction perpendicular to its ...
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1answer
47 views

Displacement at any given moment given total displacement, time and velocity

I want to compute the displacement of an object at a certain moment in time, given the values for: Initial velocity vStart (m/s) Target velocity vEnd (m/s) Total distance traveled sTotal (meters) ...
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0answers
32 views

Find max velocity given initial velocity, final velocity, acceleration and time

I am trying to find the maximum velocity in a trapezoidal-like motion profile given the initial velocity, the final velocity, the acceleration, the total time and distance traveled. If the initial ...
0
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1answer
18 views

Conjugate Momentum using Generalized Coordinates of Two Infinitesimally Close Points

I'm a bit stuck with the tensor analysis for the following problem. It was just introduced to me and I've never seen this before. All I'm looking for in a place to start, because I'm unsure where to ...
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0answers
39 views

What is the connection between these two notions of a “vector field”?

I'm reading a physics text which dives into some mathematical concepts that are new to me. Consider a function $F(q,\dot q)$ (dynamical variable) where here $q$ and $\dot q$ represent sets of local ...
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1answer
61 views

Help With Difficult Integration

I'm working through a homework problem and came to the point where I needed to evaluate this integral. $$\int_{-(z^2 - 2z)}^{z^2 - 2z} \dfrac{-1}{\alpha z} \dfrac{1}{\sqrt{ \dfrac{2}{m} \bigg (E -...
2
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1answer
34 views

Proving a function is quadratic?

In Physics, an object of mass $m$ can be said to have a certain amount of kinetic energy $T = T (v)$, which is a function of its speed $v$. Let's presume that we do not know in advance the canonical ...
3
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1answer
69 views

Physics formula proof for height of a building

I am having difficulty proving this physics formula. It states: If a physics student drops a watermelon from the roof of a building and hears the watermelon going "splat" on the ground after time $\...
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1answer
53 views

Is it possible to prove that the speed of a falling object in a quarter of a circle is $\sqrt{\frac{3Rg}{4}}$ given these parameters?

The problem is as follows: A bronze cube is let slide from rest situated in the left corner labeled as position 1 of a quarter of a frictionless pipe as it is shown of Figure 1. Prove that ...
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1answer
22 views

Taking g to be negative - where did I go wrong?

Here's a problem I was doing. A ball bearing, $A$ of mass $450g$ is thrown vertically down with a speed of $4{ms}^{-1}$ from a height of $2m$. It bounces back and just reaches it's original height. ...
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3answers
64 views

Define velocity in terms of distance from the body's initial position with Lambert W function.

TL;DR: $$x=2t+\dfrac{\mathrm{e}^{-40t}}{20}$$ solve for t. I have a function for velocity relative to time: $$v(t)=\dfrac{gm\left(1-\mathrm{e}^{-\frac{kt}{m}}\right)}{k}$$ g,m and k are all ...
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1answer
20 views

Physics force system find acceleration

Given this setup, how far does the book slide? This is a fairly basic kinematics problem once you have acceleration, which you can get with application of Newton's 1st and 2nd laws. Which is what I ...
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1answer
25 views

Squaring the impulse operator

$$\hat p_r^2 = \hat p_r \hat p_r = (-i \hbar)^2\frac1 r \frac d {dr} r\frac1 r \frac d {dr} r=-\hbar^2\frac {d^2} {dr^2}r$$ This probably means: $$\hat p_r =-i\hbar \frac1 r \frac d {dr} r$$ I'm ...
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55 views

Body temperature of electron gun

The temperature of the body of an electron gun at the moment $t=0$ of termination of firing is described by a function $\Omega (z, \Theta) $, where z and $ \Theta $ -coordinates of the cylindrical ...
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2answers
27 views

How can the magnitude of resultant force of $(0,3)$ and $(3,1)$ be doubled by changing $(0,3)$ but keeping $(3,1)$ unchanged.

How can the magnitude of resultant force of $(0,3)$ and $(3,1)$ be doubled by changing $(0,3)$ but keeping $(3,1)$ unchanged. since magnitude of resultant force (3,4) is $\sqrt{25}$. Double of ...
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0answers
15 views

Matching the general legendrian equation to the physics form used in the hamiltonian

The theta(colatitude)-dependent portion of the Hamiltonian in physics provided by Atkins' Physical Chemistry 9th edition (p. 311): $$\frac{\sin\theta}{\Theta}\frac{d}{d\theta}\sin\theta\frac{d}{d\...
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1answer
24 views

Verlet Integration to Approximate Planetary Orbit: The First Time Step

I'm currently working on a simulation of a planet orbiting binary stars, which I want to use Verlet integration to approximate. The formula is as follows: $\mathbf{p}(t_2) = 2\mathbf{p}(t_1) - \...