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1answer
85 views

Pauli matrices identities

There are some definitions and properties for Pauli matrices and their combinations: $$ \varepsilon^{\alpha \beta } = \varepsilon^{\dot {\alpha} \dot {\beta} } = \begin{pmatrix} 0 & 1 \\ -1 & ...
2
votes
1answer
261 views

Derivation of hyperbolic motion in Special Relativity

My question pertains to the equation of hyperbolic motion in special relativity: $$x^{2} - c^{2}t^{2} = c^{4}/\alpha^{2}.$$ As far as I am aware, this equation is the key to calculating coordinate ...
1
vote
1answer
512 views

Finding a differential equation to for the amount of chemicals in a body of water

I am taking a differential equations course, and most of the problems relate to physical phenomenon. The calculus is not giving me trouble, but the way of approaching the problems is hanging me up. ...
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3answers
261 views

Collision of two balls [duplicate]

Two balls, with masses $m_1$ and $m_2$ are falling from the heigh $h$. All the collisions are perfectly elastic. Do not consider the size of the balls. $m_1 < m_2$ and lighter ball is on the top. ...
1
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3answers
576 views

Frequency of small oscillation of particle under gravity constrained to move in curve $y=ax^4$

How to find the frequency of small oscillation of a particle under gravity that moves along curve $y = a x^4$ where $y$ is vertical height and $(a>0)$ is constant? I tried comparing $V(x) = \frac ...
4
votes
2answers
198 views

Total time taken for an accelerating frame in special relativity [duplicate]

How does one derive the equation for the total time traveled in a constantly accelerating frame? I found some help at this question: Special Relativity and Constant Acceleration But the information ...
1
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0answers
63 views

Deriving the curve of a cantilever

Essentially, there is a beam of length L and negligible mass sticking out of a wall with a mass Mg hanging at the end of it. We are given an equation for elastic energy (which I don't think needs to ...
2
votes
1answer
519 views

Special Relativity and Constant Acceleration

My question pertains to the concept of a constantly accelerating rocket as it approaches the speed of light. The scenario is as follows: A rocket is constantly accelerating at 1g to reach Andromeda. ...
2
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0answers
56 views

Point charge in a five-dielectric medium [closed]

What is the electrostatic potential due to a point charge in a five-dielectric medium with planar interfaces? Specifically, consider a system with planar interfaces, and the dielectric constants: $$ ...
1
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0answers
68 views

How did Jackson get the exact solution to potential in polar coordinates

On page 45 of Jackson's Classical Electrodynamics (3ed), He solved a polar potential problem with known source distribution. $$ \frac{1}{\rho}\frac{\partial}{\partial \rho}\left( \rho\frac{\partial ...
1
vote
2answers
546 views

Electric field. Linear charge density [closed]

I was wondering if anyone could help me out in this exercise I've been struggling to solve. A straight, nonconducting plastic wire $ 8.50 cm $ long carries a charge density of 175 $ nC/m$ ...
0
votes
2answers
424 views

Equilibrium of Force Systems including Torque

please help me to solve this problem.. this is only the #3 on my homework and the only thing i didn't know here is how to calculate the tension T. please teach me how to solve the tension here ...
1
vote
1answer
122 views

If the velocity of particle $A$ exceeds that of $B$, is the acceleration of $A$ greater than $B$?

Two particles $A, B$ are travelling along parallel straight paths. At some point, the velocity of $A$ exceeds that of $B$. Does this necessarily mean that the acceleration of $A$ is greater than the ...
-1
votes
1answer
320 views

Equation of progressive wave [closed]

A progressive wave traveling in positive x-direction given by $y=a\cos(kx-\omega t)$ meets a denser surface at $x=0,t=0$. The reflected wave is then given by: I know that since the wave changes its ...
-1
votes
1answer
86 views

Lunar and solar tides [closed]

I just read the following statement in a book: If the diameter of the earth increased by 20%, both lunar and solar tides would be weakened with lunar tides weakening more than solar tides. What ...
3
votes
0answers
58 views

Setting Lagrangian [closed]

Can you help me to set Lagrangian? I found that $$\vec r_A=b\sin\theta\vec i+b\cos\theta\vec j$$ $$\dot{\vec r_A}=b\dot\theta\cos\theta\vec i-b\dot\theta\sin\theta\vec j$$ For point $G$ I've got ...
5
votes
1answer
280 views

Do mutual eigenkets imply commutation of two operators?

I have been working on this question. I have solved it, and I would like to check whether my line of reasoning is right or wrong Question: Prove that if there exists a mutual complete set of ...
2
votes
2answers
232 views

accelerated charged particles and interaction with magnetic field

In high school we are taught that magnetic field perpendicular to velocity of an charged particle experience perpendicular force that causes it to move in circular path by relation ...
-1
votes
1answer
232 views

Speed of a falling pencil [closed]

If you balance a pencil of length $d$ on its tip, and let it fall, how do you compute the final velocity of its other end just before it touches the ground? (Assume the pencil is a uniform one ...
-2
votes
1answer
54 views

Where does a sparkly (CO$_2$) water bottle have more presure [closed]

Where does a sparkly (CO$_2$) water bottle have more pressure? At a higher altitude (7000 feet) or under sea level (-8 feet)?
5
votes
1answer
231 views

Double slit paradox

This is a relativity-paradox which I can't resolve: The distance between interference lines in the double-slit experiment is: $$\ w = z \lambda/d$$ Where: w: Distance between fringes z: Distance ...
2
votes
1answer
769 views

How to find the total current supplied to the circuit?

Recently, I came across a question based on finding electric current of a circuit. Here's the image... I know, by using the formula $I=V/R$, we can easily calculate the current as $V$ is given and ...
0
votes
2answers
271 views

What are the forces used in this weightlifting example? [closed]

You have a person doing a bench press. Their hands are equidistant apart and they are centered on the bar - each hand about 1.5 feet from center of the bar. The bar weighs 45 pounds. In example 1 ...
0
votes
1answer
208 views

Centripetal acceleration for particle that moves in a circle at non-constant speed

How is $a_{R}=v_T^{2}/r$ derived for changing tangential speed? ($a_R$-centripetal component $r$-distance from axis $v_T$- tangential speed)
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0answers
250 views

Scalar field lagrangian in curved spacetime

I am studying inflation theory for a scalar field $\phi$ in curved spacetime. I want to obtain Euler-Lagrange equations for the action: $$ I\left[\phi\right] = \int ...
3
votes
1answer
652 views

Equations of motion for a spherical pendulum in a non-inertial reference frame

Take a spherical pendulum with bob mass $m$, rod length $\ell$ and physical coordinates $\theta$, $\phi$ (spherical angles) and $h$ (the hinge height with respect to the coordinate origin). The rod is ...
3
votes
2answers
1k views

Using the image charges method to find the electric field

The following is a question from a tutorial in my Physics 2 course about conductors and the Method of image charges. We are given two infinite perpendicular and grounded plains. The first ...
0
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0answers
79 views

Angular momentum contained in E&M fields

I am trying to do this question as a prep for my quals and find my solution too simplistic. I fear I am missing something important. "Iron atoms (atomic mass 56) contain two free electron spins that ...
2
votes
0answers
95 views

How to understand the transmission coefficient from the following question?

I want to understand the transmission coefficient and construct a time-independent Schrodinger equation where $$ V(x)=\left\{ \begin{array}{c c} \delta(x), & |x| < 1 \\ + \infty, & ...
1
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0answers
47 views

path planning with invasive measurements

My background is not science, and I hope the question I am about to ask doesn't look like a homework kind of a thing! Anyway, I will try my best to make the point clear. imagine there is a lake, and ...
0
votes
1answer
542 views

Electric field outside a hollow cylindrical conducting shell [closed]

Imagine that a point charge $+Q$ is located at radius $R$ and height $z=0$ inside of an infinitely long conducting cylinder shell of inner radius $a>R$ and outer radius $b$. From what we know of ...
0
votes
2answers
114 views

Can you justify force calculations using more than one of Newton's laws?

If an object is at rest on a flat surface I remember my school teacher would say, "By Newton's 1st law the normal reaction, R, is mg (mass x g)". Ok, sure this is fine because the object is at ...
2
votes
2answers
69 views

Stability of equilibrium points

For a spinning top, the linearised equation in the angle $\theta$ when the top is spinning about its axis of symmetry, which is vertical, is of the form ...
1
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1answer
64 views

A question of BRST symmetry of bosonic string theory

This question relates to this post I tried to verify Eq. (4.2.7) in Polchinski's string theory book vol I p. 127 but I miserably miss a sign $$ \delta_B (b_A F^A) = i \epsilon (S_2 + S_3) ...
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3answers
735 views

Work, Energy & Power - Body slides down a hemisphere

A small body of mass $m$ slides down from the top of a hemisphere of radius $r$. There is no friction between the surface of the block and the hemisphere. The height at which the body loses contact ...
5
votes
1answer
201 views

Walking along a moving train, we make 18 steps. Opposite: 11. How long is the train?

A man walks in the same direction as a slowly moving train ($v_{man} > v_{train}$). He counts the train to be 18 steps long. Then he turns around and counts the train to be 11 steps long. ...
2
votes
1answer
112 views

Does a 27 hp engine output the same amount of energy as lifting a 1 ton stone block almost 3 meters per second?

I’m trying to get a sense of how much energy a 27 horsepower engine outputs. 27 hp $=$ 20 133 watts (joules/second). Potential energy can be calculated as $E = mgh$ where $g = ~9.8\ m/s^2$ on earth. ...
2
votes
3answers
275 views

Problem on apparent height of postage stamp underneath paperweight

A postage stamp is placed on a surface and a glass cube of refractive index $1.5$ is placed over it. When observed through the cube, the stamp appears at a height of $1.5cm$ from the bottom of the ...
0
votes
1answer
71 views

Find the distance from the initial location [closed]

Sing Huat drives a car with initial speed 30 km/h and acceleration 2 km/h2 toward Tee, whose displacement is 200 m away from him. At the same time, Tee drives another car toward Sing Huat with ...
1
vote
1answer
250 views

Variable Tension in the string [closed]

A body of mass $m$ is hanging with a string having linear mass density $\lambda$. What is the tension at point $A$ as shown in the figure. I am aware of the scenarios in which string is ...
0
votes
3answers
783 views

Calculating acceleration function for given time, distance, initial velocity [closed]

An object has an initial velocity of v and should stop in d meters, in t seconds where v*t >= d. I can predict that this acceleration won't be constant but it is a function of time and this problem ...
0
votes
1answer
123 views

Circular motion [closed]

A small block slides down from the top of a hemisphere of radius $r$. It is assumed that there is no friction between the block and the hemisphere. At what height $h$ will be the block lose contact ...
1
vote
1answer
129 views

Relative acceleration with pullys

I have tried this question every way I can think but in the equation for particle $L$ $g$ cancels every time. Could someone show me how to do it correctly or tell me what I am doing wrong. Thanks, ...
0
votes
1answer
165 views

Free body diagram of rod in sphere

I was finding the free body diagram part of dynamics quite easy until I found this question , Here's how it goes : A rod AB is placed inside a spherical shell, whose inside surface is rough. Draw ...
-1
votes
2answers
53 views

Does a 27 hp engine output the same amount of energy as lifting a 1 ton stoneblock almost 3 meters per second? [duplicate]

I'm trying to get a sense of how much energy a $27$ horsepower engine outputs. $$27 \mathrm{hp} = 20133\mathrm{W}$$ Potential energy can be calculated as $$E = mgh$$ where $g ...
-1
votes
1answer
101 views

Some complex-number manipulation when calculating coefficients

I am going through Sakurai's quantum mechanics, and at one point the solution to a problem says: $(\sin(\beta)\cos(\alpha)-i\sin(\beta)\sin(\alpha))b+\cos(\beta)a=a$ ...
0
votes
1answer
104 views

Derivation of Pressure/Kinetic Therory problem involving hole in box

A box of volume $V_0$ has a small hole of area $A_0$. The box initially has one mole of an ideal gas at $t = 0$, which is at an initial temperature $T (t = 0)$. Find the rate of energy flow through ...
0
votes
1answer
368 views

Rigid bar suspended by two ropes, tension of first rope after second rope is cut?

This is from a practice exam, I've been sitting here thinking about it for over an hour and can't convince myself of an answer, or write down any relevant exact equations. A bar of uniform density ...
0
votes
1answer
306 views

Equation for the equipotential lines? [closed]

What is the equation for the equipotential lines in $x$-$y$ plane for a dipole oriented along the $x$ axis?
1
vote
1answer
164 views

Beads sliding on a hoop

Two particles, $P_1$ and $P_2$, of equal masses $m$ are linked by a spring of stiffness $k$ and natural length $a$. They are sliding freely without friction along a horizontal fixed hoop of radius ...