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Questions tagged [homework-and-exercises]

Applies to questions of primarily educational value - not only questions that arise from actual homework assignments, but any question where it is preferable to guide the asker to the answer rather than giving it away outright. Please READ THE GUIDANCE IN META before asking homework-like questions.

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388 views

Getting 2 different answers when finding spring constant $k$ when gravity is involved

OK, so I've been wracking my brain for the past hour trying to figure out how to calculate k in a problem like this: A mass of 10 kg is attached to a spring hanging from the ceiling. It is released,...
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4answers
233 views

Representing dimensions in Dirac delta function results

The Dirac delta function can be defined as $$\delta(x)=\frac{1}{2\pi}\int_{-\infty}^\infty e^{itx}dt$$ From this we see that the dirac function has units of $x^{-1}$. How do we represent the units ...
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1answer
235 views

Final velocities of a two point-masses in inelastic collision [duplicate]

Two particles of same mass in a 2D frame collide with known initial (i) velocities. I would like to know the final (f) velocities of them after the collision. As in any other collision, momentum is ...
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3answers
1k views

Capacitors in parallel final potential difference

I was provided with the following problem. So I first calculated the total capacitance for (i), which was $$4.5 + 1.5 = 6.0 \mu F$$ Now part (ii) is the question i'm struggling at. I know that ...
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4answers
63 views

Why does only one of the DC circuit power equations work for me here?

I know that $$ P=IV=I^2R=\frac{V^2}{R}$$ I solved for the current using the loop rule $$I=.47$$ but to solve for the Power output of the 16V battery I could only find the power by finding the ...
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1answer
155 views

Operator Transformation and Time Evolution

UPDATE: See update at bottom of post Short Version: $\sigma^-_H$ in the Heisenberg picture. $U = e^{+i\omega (|e\rangle \langle e)_H}$. Prove that $$ \frac{d \sigma^-_H}{dt} e^{+i\omega t} = U^{\...
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1answer
532 views

Condition for Maximum Power in the circuit [duplicate]

Maximum Power is transferred to a load when load resistance is equal to internal resistance of source. I want to know How ? If I consider a source with internal resistance 'R' ,connected with ...
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2answers
1k views

Acceleration during collision with ground

For my physics class, I have to calculate an objects acceleration while it came to a stop. It was traveling at $6.26\: \mathrm{\frac{m}{s}}$ at impact, and travels a distance of $0.025\: \mathrm{m}$ ...
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1answer
85 views

Air Pressure in a Mine

In Sunday's "60 Minutes" TV program the correspondent descended into a gold mine said to be 2 miles (3 km) deep. What equation describes the air pressure relative to sea level atmospheric pressure?
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1answer
1k views

Distance and displacement of an object on a straight line [closed]

I had this homework problem, but don't actually know if what I did is right, or that I even read the problem correctly. Can someone please tell me if this is the right interpretation of the problem ...
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2answers
7k views

Work done by magnetic field on magnetic dipole

In the above slide, it reads that $W=\int\mu B sin(\theta)d\theta=\mu B cos(\theta)$. But, I thought that $\int\mu B sin(\theta)d\theta=-\mu B cos(\theta)$ by some calculus calculation. Can somebody ...
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2answers
314 views

Effective resistance of a weird looking electric circuit [closed]

A electric circuit (in the picture) is given where all the resistance are of 1 ohm. I have to find its equivalent resistance. (9,10, 11th points are conncections) My attempt: I think electron flow ...
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1answer
677 views

Equations of Fermat's principle/Snell's law in a gradient lens (sugar aquarium)

I'm trying to animate a beam of light inside a substance with gradient index of refraction as a function of y. A good example of that is a syrup inside an aquarium like here https://www.youtube.com/...
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5answers
2k views

Can a capacitor be charged without having resistance in the circuit?

I was looking for the fact when a capacitor is directly connected to battery without resistor what will happen? If possible then tell the time for charging.
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1answer
77 views

A pearl that moves in a smooth vertical hoop (Circular motion) [closed]

I couldn't understand something about the situation of a pearl that moves in a smooth vertical hoop in circular motion. When the normal force equals 0 , the pearl didn't disconnect from the smooth ...
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1answer
570 views

Two-state system problem

Given a 2-state system with (complete set) orthonormal eigenstates $u_1, u_2$ with eigenvalues $E_1, E_2$ respectively, where $E_2>E_1$, and there exists a linear operator $\hat{L}$ with ...
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1answer
2k views

Plotting Hydrogen's $2P_{x,y,z}$ Probability Densities in MATLAB [closed]

I have spent an unreasonable amount of time trying to plot $F(r,\theta,\phi)$ plane slices in MATLAB. I want to look at $x-y,y-z,x-z$ planes. Here's the function, specifically: $$F(\rho,\theta,\phi)~=...
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1answer
972 views

Effective spring constant of springs in series [closed]

When we consider the analogy of a rod as a spring while considering the combination of rods for finding the stretch we do this- Let for any rod considered as a spring $$k=\frac{AY}{L}$$ If two rods ...
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0answers
35 views

Coupled Harmonic Oscillator (Forced Vibration)

I derived two equations for a 2DOF harmonic oscillator system, declared state variable equations, and placed them into matrix form: $Ax' + Bx = C$. I have a Matlab script to determine the constants ($...
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1answer
57 views

Write a specific Lagrangian

I'm pretty new to Lagrangian mechanics, and after some thoery I'm facing the first exercises, as the following: Consider a p.particle $P$ of mass $m$ which is constrained to a semi-circle of radius ...
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1answer
299 views

EM vector potential

We can write the electromagnetic field tensor as $$\begin{bmatrix} 0 & -E_x/c & -E_y/c & -E_z/c \\ E_x/c & 0 & -B_z & B_y \\ E_y/c & B_z & 0 & ...
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2answers
4k views

Reflection formula for spherical surface from Fermat's principle (Query)

The snip shows a part of the method shown by my teacher, to describe the reflection formula for spherical surface. However I do not understand how the relation of AB and BI (which I have highlighted) ...
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1answer
10k views

Magnetic field inside finite solenoid

In my book they don't really derive the equation of the magnetic field inside of a finite solenoid. They just give me equation 1 and image and the end result, equation 2. $$dB=\frac{\mu_0Ndlr^2I}{2ly^...
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2answers
3k views

Tensor of inertia of a hollow cube

I have found the tensor of inertia of a rectangle of sides $a$ and $b$ and mass $m$, around its center, to be $$I_{11}=ma^2/12,$$ $$I_{22}=mb^2/12,$$ $$I_{33}=(ma^2 + mb^2)/12.$$ All other elements of ...
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0answers
264 views

QFT Propagator across spacelike separation

I have this general formula for the propagator. $$ D(x)=-i\iiint\dfrac{ d^3k}{\big( 2\pi \big)^32\omega_k}[e^{-i[\omega_kt-\vec k\cdot\vec x]}\Theta(t)+e^{i[\omega_kt-\vec k\cdot\vec x]}\Theta(-t)] $...
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1answer
3k views

Can I use Newton's second law to solve what seems to be a torque problem?

The Problem: An 8-m-long beam, weighing 14,700 N, is hinged to a wall and supported by a light rope that is attached 2.0 m from the free end of the beam. If the beam is supported at an angle of ...
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2answers
472 views

Propagator in momentum basis from first principles

I have a propagator for a free particle, $$ G(x,t;y,t_0) = \sqrt{\frac{-im}{2\pi \hbar(t-t_0)}} \exp\bigg(\frac{im(x-y)^2}{2\hbar(t-t_0)}\bigg). $$ one of the exercises in the quantum section of my ...
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2answers
1k views

What is wrong with this derivation of moment of inertia of a sphere?

I know the moment of inertia of a solid sphere is $\frac 2 5 MR^2$, but I keep getting $\frac 3 5 MR^2$ when deriving it: For a sphere of mass $M$ and radius $R$, $$\rho = \frac {M}{\frac 4 3\pi R^3}...
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1answer
58 views

Center of Mass/Torque

So, I have recently learned about 'Centers of Mass' and have discovered I was completely ignorant to the fact that the point where a force is applied will determine whether the force is a rotational ...
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1answer
212 views

Cycling vs. Walking [closed]

Suppose I want to go from point A to Point B on a straight level road. I have 2 options: use a cycle or go walking. Now, which one of the 2 should I prefer if I want to minimise the amount of work ...
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1answer
88 views

General formula for relativistic Energy/momentum conservation?

Say we have a particle of mass $M$, which is at rest in a laboratory. This particle then decays into a particle of mass $m$ and speed $v$ and a photon of frequency $f$. How would one describe the ...
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1answer
8k views

Tension in a massless string around a pulley [closed]

A pulley having some mass has a massless string around it, with two unequal masses at the end of the string. Sufficient friction is present between pulley and the string such that the string does not ...
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1answer
334 views

Energy of a system of conductors

Electrostatic potential and charges on conductors that are closed to each other can be put in relation with the capacitance matrix . Can the energy of the system of two (or more) conductors be ...
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2answers
1k views

Aerodynamic drag on a cannonball?

I'm trying to build a ballistics simulation where I shoot a cannonball. I want to allow for drag and am trying to work out the math to do so. I can work the drag out using $F = C_d\times S\times V^2\...
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4answers
4k views

Why doesn't the Gravitational Force causes body to fall towards orbital center moving with constant tangential speed? [duplicate]

Suppose a satellite is orbiting the Earth. The gravitational and centripetal force supposedly point towards the Earth. Therefore, the net force is towards the Earth. Since the satellite doesn't fall ...
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3answers
1k views

Proof divergence of magnetic field is 0

I work in an R&D role that involves magnetism. I am refreshing my memory of electromagnetic and this stumps me. In polar coordinates, the magnetic field of a current loop for distances $R >>...
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1answer
132 views

Cup of water and cup of water with oil on top [closed]

the teacher gave me this problem to solve. So i hope you can help me with it. Here is the problem: John poured 150ml ob boiling water in 2 cups made out of polystyrene. Cups are open on the top so ...
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2answers
30k views

What happens when non-equal voltages are put in parallel? [duplicate]

If two batteries, say 2 volts and 5 volts, are connected in parallel, are there any problems? The higher voltage will then want to flow out, but also towards the lower 2 volt battery end, right?
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1answer
108 views

How to determine basis transformation for state vectors given a Hamiltonian written in two bases?

A same system can be written in two basis: $$\psi^\dagger H_1\psi=\begin{bmatrix}c_k^\dagger&c_{k+\pi}^\dagger \end{bmatrix} \begin{bmatrix}A&iB\\-iB&-A \end{bmatrix} \begin{bmatrix}c_k\\...
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2answers
334 views

My book uses helium weight in reaction formula instead of weight alpha particle?

I'm suppose to write out reactions where atoms send out alpha radiation and decay. The book uses the 4-2 H, 4 as nucleon number and 2 as proton number, but isn't that wrong? The mass of helium is ...
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3answers
308 views

Meaning of EMF induced in a loop

Q) Consider a square loop of side 'l' made of a metallic wire moving with a velocity 'v' which is perpendicular to one of its sides. There exists a uniform magnetic field 'B' perpendicular to the loop'...
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1answer
62 views

cross over to another object that has same height with our last position, is that really possible?

I have got confused with this. Well..In that picture, lets say the height is 8m, and the car moves and going to cross over to another object that has the same height with its last position..my ...
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2answers
3k views

Find the minimum force that has to be applied to the block $m_1$ so that the other block just begins to slide

This is a problem from the book 'Problems in General Physics' by I E Irodov. Two blocks of masses $m_1$ and $m_2$ are placed on a rough horizontal surface, connected by a light spring. Find the ...
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3answers
11k views

Solve for Initial Velocity of a projectile given Angle, Gravity, and Initial and Final positions?

I've found equations http://www.physicsclassroom.com/Class/1DKin/U1L6a.cfm for solving everything (and rearranged to solve everything) to do with projectile motion EXCEPT this, even though it should ...
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2answers
506 views

Light of a specific wavelength going through a prism

I won't post the entire question here since I would just like a bit of help getting started as I am quite lost. The question is essentially saying that a light ray parallel to the x axis with a ...
0
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1answer
87 views

Falling from a 100 meter tall building into a 100 meter deep hole of balloons [closed]

I'm wondering if I were to fall from a 100 meter tall building into a 100 meter deep hole of balloons, what would happen? Would I suffer irrecoverable injuries and die a horrible death? Or would the ...
-1
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3answers
258 views

Bird on electric wire: theoretical distance between the two bird legs [closed]

Hey guys, please someone help me with this exercise :) For our exercise, assume that the bird’s body resistance (from leg to leg) is 50kΩ. Given is a high voltage power line with a current of 100A ...
-1
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1answer
72 views

Kinematics Issue w/ negative Velocity [closed]

Given: $$Y = v\sin(\theta)t-\frac 12 gt^2$$ $$D=v\cos(\theta)t$$ Thus: $$\frac{D}{v\cos(\theta)} = t$$ Substituting we get: $$Y=v\sin(\theta)\frac{D}{v\cos(\theta)}-5\left( \frac{D}{v\cos(\...
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1answer
2k views

Water equivalent of calorimeter

I am trying to solve numerical problem based on calorimetry. The water equivalent of a calorimeter is given in grams. But how is it possible as w= mc and unit of m*c is Cal/°C. where w= water ...
-1
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1answer
5k views

Throwing an object in the air [closed]

Studying formulas about velocity and acceleration I came up with a question: if I throw an object in the air with a velocity $v_0$ (suppose i throw it vertically) in how much time its final velocity $...