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Physical position eigenfunction normalisation

We know that the Dirac function $$\delta(a)=\lim_{a \rightarrow 0} \delta_{a}(x)$$ can be written as an infinitesimally narrow Gaussian: $$ \delta_{a}(x) := \frac{1}{\sqrt{2\pi a^2}}e^{-x^2/2a^2}$$ ...
5
votes
2answers
130 views

Thermal equilibrium in general relativity

The Newtonian condition for thermal equilibrium for a static system is $T = \mathrm{const}$. In this homework I'm asked to show that it's curved space generalization is $T(-g_{00})^{\frac{1}{2}} = ...
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1answer
180 views

Calculating the change in entropy in a melting process

I have a homework question that I'm completely stumped on and need help solving it. I have a $50\, \mathrm{g}$ ice cube at $-15\, \mathrm{C}$ that is in a container of $200\, \mathrm{g}$ of water at ...
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1answer
815 views

The electric field of a conductive sphere containing a charge - grounded vs not grounded

Let's suppose we have a sphere but unlike theoretical ones it'll have some thickness say $\Delta r$ and inner radius $R$. What I was wondering about is how will it behave if we place some charge $q$ ...
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1answer
505 views

Minimal Kinetic energy for particle in a box

This is driving me crazy! The question goes as follows: A proton is enclosed in a zone of length 2pm along the x-axis. The minimal kinetic energy of the proton lies closest to: 5000eV 0.5eV 50eV ...
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1answer
447 views

Occupied lattice sites, determining number of microstates and energy

A solid consisting of $N$ molecules on a lattice of $N$ sites is isolated from its environment, and has energy $E$. Each molecule is fixed in position and independent of all others. It can be in any ...
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1answer
105 views

How to calculate the amout of time for oil to get out from a pneumatic cylinder?

I have a system. You can assume it is just a 1" diameter steel pneumatic cylinder (1 foot long). Assume we ignore the bore size issue at this point. One chamber is filled up by oil (6" of volume), ...
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1answer
205 views

Why can't this speed be measured?

Superman and Supergirl were playing catch. When Superman is moving with a speed of 0.800c relative to Supergirl, he threw a ball to Supergirl with a speed of 0.600c relative to him. a. ...
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1answer
32 views

Is there any significance to the negative sign on this speed?

A girl is riding a bicycle along a straight road at constant speed, and passes a friend standing at a bus stop (event #$1$). At a time of $60$ s later the friend catches a bus (event #$2$) If the ...
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1answer
8 views

Thermal resistance of thermal interface materials?

Thermal conductivity are often used for surfaces between the computer chip and the heat sink to increase heat transfer and they want high thermal conductivity to decrease the thermal resistance. By ...
0
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1answer
24 views

Change of field intensity/flux density and energy

The answer for this question in the solutions manual is (D). I tried to solve it using $$ W_e = \frac12\int_\nu ED d\nu $$ Which gives me (C). Any idea where I have gone wrong?
0
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1answer
68 views

Relative motion setting course of closest approach

Let $r_{P/Q}$ be the position vector of $\overrightarrow P$ relative to vector $\overrightarrow Q$ and $v_{P/Q}$ the velocity vector of $\overrightarrow P$ relative to $\overrightarrow Q$. Suppose ...
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1answer
32 views

Latent heat of vaporization

The molecular weight of water is 18.015 gram. The number of moles of water in one liter (1000 gram) will be: $3.34\times 10^{25}$ molecules (in 1kg). We know that latent heat of vaporization of water ...
0
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1answer
21 views

Finding power with Drag Force equation

The mass of the car is 1500 kg. The shape of the body is such that its aerodynamic drag coefficient is $C_D=0.330$ and the frontal area is $2.50 m^2$. Assuming that the drag force is proportional to ...
0
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1answer
27 views

Quantifying the current drawn by a motor at half speed

I have a h/w question regarding the current in the armature of a motor when it is operating at half it's normal speed. The question is; A motor is designed to operate at 118V and draws a current ...
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1answer
32 views

Ground state degeneration

I wonder how can i know degeneration of ground state of certain elements? I'm doing Boltzmann distribution problems, and I'm not sure what to do. I have to calculate ratio of ions in 3p excited state, ...
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1answer
43 views

Finding friction forces of stacked boxes on a table

Consider the following system. The given friction coefficients are for static. Let $g=10$ (meter per square second). If the $F(t)=10t$, for example, determine the friction forces $f_{AB}(t)$ ...
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1answer
24 views

Minimize initial velocity of projectile to arbitrary point

I'm supposed to shoot a projectile from the origin to a point $(x_0 , y_0)$ with minimal initial velocity $v_0$. (no air resistance; regular gravity) The flight time should be $T=\frac{x_0}{v_x}$. ...
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1answer
39 views

Hydrogen ionization energy

Proton and electron have a distance equal to the Bohr radius apart in the hydrogen atom. Knowing this, what's the ionization energy of the atom? So we know $U = -kq^2/a_B$, but this is potential ...
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1answer
56 views

Lagrangian for a moving spring device

How can I write the proper Lagrangian for such as system as the one shown in picture? Am confused about what is the suitable way to designate the coordinate.
0
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1answer
60 views

Magnetic Shielding?

Can magnetic fields be "blocked"? For example, in the game, TitanFall, a robot stop bullets with ( presumably ) a magnetic shield. I wish to calculate the magnetic force required to stop a bullet ...
0
votes
1answer
102 views

Calculating the electric potential in cylindrical coordinates from constant E-field

I am having so much trouble with this problem. I feel like I shouldn't be, but I am. A uniform electric field, $\vec{E} = E_0\hat{x}$. What is the potential, expressed using cylindrical ...
0
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1answer
52 views

Relative Velocities and Conservation of Kinetic Energy

An object of mass m moves with velocity $v$ towards a stationary object of same mass. Impact is an elastic collision. $v_1$ is the velocity after impact of the mass originally moving $v_2$ is the ...
0
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1answer
27 views

Can I apply symmetry to this boundary value problem (BVP)?

Let's say I have a hollow cylindrical shell with inner radius $a$ and outer radius $b$ and length $L$. The temperature at at z=L is $T_{2}$ and the temperature at z=0 is $T_{1}$. There is also an ...
0
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1answer
144 views

Electric field from current without Maxwell's law of induction

A long, straight wire carries a current that decreases linearly with time. What is the direction of the induced electric field outside the wire? I would interpret this as follows: A current induces ...
0
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1answer
72 views

Infinite motion on a 3D curve

Suppose we had a curve defined by $$\underline{r}(s) = \alpha \cos(s) \underline{i} + \gamma s \underline{j} + \alpha \sin (s) \underline{k}$$ with $\alpha^2 + \gamma ^2 = 1$ and suppose we had a ...
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1answer
108 views

Ladder Operator killing state

So in my last question, @joshphysics showed me how to prove $K_\pm$ were ladder operators. Now I need to show that there is a lowest state, i.e $$\langle m_0|K_+=K_-|m_0\rangle=0$$ I am not ...
0
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1answer
78 views

Contradiction regarding friction of a rolling cylinder in an inclined plane

I came upon this while wondering whether the friction of a rolling cylinder on an inclined plane depends on the value of friction coefficient. now, $$f\leqq\upsilon N$$ Again after calculating I ...
0
votes
1answer
77 views

photon polarization, uncertainty in Energy

A beam of red light is sent along the $z$ axis through a polaroid filter that passes only $x$ polarized light. The beam is initially polarized at $30$°, and the total energy is $10$ Joules. Estimate ...
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1answer
70 views

Rigid body problem in 2d

I have some questions about this exercise: In an horizontal plane, a $OA$ bar with mass $m$ and length $a$ moves, with another bar $AB$ (same mass, double length) attached in the point A. In the ...
0
votes
1answer
54 views

Rigid body problem

I have some doubts about the next excercise: A bar of length $2a$ and mass $m$ moves freely with both of its extremes on a ring of radius $\sqrt2a$. The ring can rotate freely in a certain ...
0
votes
1answer
150 views

How does temperature affect magnets?

How does an increase/decrease in temperature affect: Strength of the magnet Polarity Other changes? I have made some research and I have found that increasing the temperature turns ferromagnetic ...
0
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1answer
127 views

Satellites and gravitation

A satellite with mass $m$ orbits a planet of mass $M$ in a circular path with radius $r$ and velocity $v$. Due to some internal technical failure, the satellite breaks into two, similar parts with ...
0
votes
1answer
52 views

Calculting the magnetic field from rectangular conductor?

I want to apply the Biot-Savart law to calculate the magnetic field at a point created by current flowing through a square/rectangular conductor. More specifically, a trace on a printed circuit board. ...
0
votes
1answer
124 views

Block Sliding Down a Plane (Perpendicular Velocity)

I'm having trouble understand the concepts for this problem. Here's the problem: A block is placed on a plane inclined at angle $\theta$. The coefficient of friction between the block and the ...
0
votes
1answer
121 views

Doubt in question related to optics---magnification?

Ok here is the question given in my text-book Find the distance of the object from a concave mirror of focal length 10 cm so that image size is 4 times the size of the object. The solution in my ...
0
votes
1answer
216 views

Coordinate system

Quoting from 'Nuclear Physics - Theory and Experiment' by RR Roy, BP Nigam 2005 edition Link to text How did the author arrive at equations (23a, 23b,23c)? Chapter 8 Nuclear model II, 8.7 ...
0
votes
1answer
180 views

Magnetic field, alternated current and EMF

If I apply an alternated current to a solenoid and insert into it a smaller solenoid, I could measure the induced EMF (electromotive force) and study how it changes in relation to the frequency of ...
0
votes
1answer
238 views

1D Kinematics - Relative Motion involving non-inertial frames of reference

I recently came across a question involving non-inertial frames of reference. I didn't quite understand the way it had been solved due to some conceptual confusion regarding certain deductions made to ...
0
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1answer
904 views

Calculating the coefficient of thermal expansion in liquid

I am trying to write a matlab function that calculates the coefficient of thermal expansion of water from a given temperature. From what I understand the thermal expansion coefficient is calculated as ...
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votes
1answer
92 views

Magnetic field inside and outside cylinder with varying current density

I am reading through Introduction to Electrodynamics by David J. Griffiths and came across the following problem: A steady current $I$ flows down a long cylindrical wire of radius $a$. Find the ...
-1
votes
1answer
826 views

Finding the point of collision between two objects when acceleration is constant

$\newcommand{\accunit}{\mathrm{m}/\mathrm{s}^2}$ A coin is dropped 60.0m above the top of an elevator car. The coin is dropped just as the car begins to move upwards. The elevator first ...
-1
votes
1answer
653 views

Potential due to a spherical surface charge

The potential at the surface of an insulating sphere (radius R) is given by $$V(R,\theta) = k \cos(3\theta)$$ where $k$ is a constant. Use separation of variables to find the potential inside the ...
-1
votes
1answer
145 views

electrical forces of two charges repelling each other

If I place two positive charges of different magnitudes on the x-axis (one at the origin, one at the some position x), as the two charges repel each other are the forces that they impart on each other ...
-1
votes
1answer
358 views

Find generating function $F_1$ for canonical trasformation

I'd like to know the steps to follow to find the generating function $F_1(q,Q)$ given a canonical transformation. For example, considering the transformation $$q=Q^{1/2}e^{-P}$$ $$p=Q^{1/2}e^P$$ ...
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votes
1answer
127 views

Implications of rotational invariance

The state $$|\psi\rangle ={1\over \sqrt 2}(|+\rangle|-\rangle-|-\rangle|+\rangle)$$ of system made up of 2 spin-$1\over 2$ particles is invariant under the operator $$\exp{i\theta S_y}.$$ What ...
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votes
1answer
66 views

Elastic Spring And Energy Issue

I`m trying to write an expression ( Work & Energy ) of spring that is not loose and it has a box on it with a weight of 1Kg. how its should be? this is what I tried to do: $$\frac{kx^2}{2}-mg$$ ...
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votes
1answer
349 views

Shear Flow corresponding to Eccentric Shear Force of a Closed-section Beam (Structural Analysis - Mechanics)

Been stumped with this question for way too long... its a beam with a thin-walled rectangular cross-section, and a shear force is acting at a distance from the shear center. I know my decomposition of ...
-2
votes
1answer
56 views

what is a difference in the width of the spinning bar?

The bar with length l, density r, diametr d, Young's modulus E, Poisson's ratio mu, is spinning around the cross-section, what is the change in the width of this bar?
-3
votes
1answer
135 views

2 particles collision - deriving the equation for an energy which can become mass of new particles!

Q1: Lets say a particle with mass $m_1$ and kinetic energy $W_k$ colides with a particle of mass $m_2$ at rest. Can anyone explain why do both particless ($m_1$ and $m_2$) plus an aditionall mass $m$ ...