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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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67
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2answers
17k views

How to measure the wavelength of a laser pointer?

I'm working on something and I need to know the wavelength of the laser pointer that I'm using. Can you suggest me a way, using some optics formulae, or anything else to calculate the wavelength?
12
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2answers
21k views

Formula for molar specific heat capacity in polytropic process

I found this formula for a polytropic process, defined by $PV^n = {\rm constant}$, in a book: $$C = \frac R{\gamma-1} + \frac R{1-n} $$ where $C$ is molar specific heat and $\gamma$ is adiabatic ...
11
votes
1answer
2k views

Understanding transverse oscillation in 1 mass, 2 spring systems

Lately I have been working through some nice problems on mass-spring systems. There are tons of different configurations - multiple masses, multiple springs, parallel/series, etc. A few possible ...
9
votes
3answers
34k views

Why would an object appear a different size when in water?

A friend of mine has a homework question and we're having some trouble figuring out what physical mechanisms come into play for this. An underwater swimmer sees a spherical air bubble that appears ...
10
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5answers
16k views

Normalizing the solution to free particle Schrödinger equation

I have the one dimensional free particle Schrödinger equation $$i\hbar \frac{\partial}{\partial t} \Psi (x,t) = -\frac{\hbar^2}{2m} \frac{\partial^2}{\partial x^2} \Psi (x,t), \tag{1}$$ with ...
4
votes
4answers
5k views

Time period of simple pendulum with varying mass

How do you find time period as a function of time for a simple pendulum that is in the form of a hollow sphere that is filled with mercury and there is a hole in the bottom through which the mercury ...
6
votes
4answers
9k views

Capacitor with different charges on each plate

I am confused as to whether/how capacitance changes when each plate has a different charge. For example, consider a coaxial cable and put $20Q$ on the outer cable, and $-Q$ on the inner. Or how about ...
5
votes
2answers
1k views

These two operators commute…but their eigenvectors aren't all the same. Why?

The Hamiltonian $$H = \left[ \begin{array}{cccc} a & 0 & 0 & -b \\ 0 & 0 & -b & 0\\ 0 & -b & 0 & 0\\ -b & 0 & 0 & -a \end{array} \right] $$ commutes ...
4
votes
4answers
1k views

Show bigger amplitude of physical pendulum means bigger period

Suppose you have a physical pendulum. It is true that as amplitude increases, the period increases. Can we demonstrate this fact without explicitly finding the period (which is pretty involved and ...
10
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5answers
4k views

Elastic collision of point particle and rod

A 1 meter long rod on the ice with mass $m_2=1$ kg is perpendicularly hit on one end by a point particle with mass $m_1=0.1$ kg. The collision is elastic and the point particle is bounced back in the ...
3
votes
1answer
10k views

Commutator $[\hat{p},F(\hat{x})]$ of Momentum $\hat{p}$ with a Position dependent function $F(\hat{x})$?

I heard from my GSI that the commutator of momentum with a position dependent quantity is always $-i\hbar$ times the derivative of the position dependent quantity. Can someone point me towards a ...
3
votes
1answer
778 views

Energy-momentum tensor transformation [closed]

I've been trying to find how the energy-momentum tensor changes if we add a total derivative to the lagrangian: $$L\to L+\mathrm d_\mu X^\mu.\tag{1}$$ From the answer key: $$T^{\mu\nu}\to T^{\mu\nu}+...
-2
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3answers
861 views

Can you lift a basket up while standing inside it? [closed]

Suppose you stand in a basket and you try to pull the handles of the basket. Will you be able to lift the basket from ground? Similarly, Baron Münchhausen allegedly pulled himself and the horse on ...
6
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3answers
1k views

Using 2D position, velocity, and mass to determine the parametric position equations for an orbiting body

I have a gravity-related question. I am programming an orbit simulator. I have everything up and running, but I would like to render the smaller body's orbital path (the larger body is fixed). To do ...
5
votes
1answer
303 views

How are the Lagrange points determined?

According to Hyper Physics, there are 5 equilibrium, or Lagrange points of the Earth-Moon system and only 2 of them are said to represent stable equilibrium points. This made me think if there is an ...
4
votes
3answers
9k views

Commutators involving functions

I am looking for the commutator: $$[e^{aq},p]$$ My approach is to Taylor expand the function: $$[\sum_n \frac{1}{n!}(aq)^n,p]$$ I know that $[q^n,p]=ni\hbar q^{n-1}$ So how do I account for $n$ ...
4
votes
1answer
53k views

Calculation of pressure from flow rate of water

Anybody kindly help me to find how to calculate pressure in bar from flow rate. I have a pipe and from that I am transferring water at a constant flow rate of 5ml/min. At this flow rate, with a 0.5 cm ...
3
votes
1answer
4k views

Elastic collision in two dimensions

Suppose a particle with mass $m_1$ and speed $v_{1i}$ undergoes an elastic collision with stationary particle of mass $m_2$. After the collision, particle of mass $m_1$ moves with speed $v_{1f}$ in a ...
3
votes
4answers
30k views

Calculating impact force for a falling object?

Good evening, I'm trying to calculate what kind of impact force a falling object would have once it hit something. This is my attempt so far: Because $x= \frac{1}{2} at^2$, $t=\sqrt{2x/a}$ $v=at$, ...
4
votes
3answers
2k views

If string is stretched just by weight, where does the gravitational potential energy goes if only half is converted to elastic potential energy?

If a spring is stretched by a weight of mass m, (so the extension is $\Delta x$) then $ k = \frac W{\Delta x} = \frac {mg}{\Delta x}$. So $ k\Delta x= mg $. When the Spring is stretched by distance $\...
1
vote
2answers
469 views

7 Billion people jumping at once

What would happen if every person in the world gathered at a minimum possible area and jumped all at once? Would that have any effect on Earth?
1
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0answers
115 views

What is the capacity of this circuit? [duplicate]

I simply can't figure out what the capacity of this circuit is. I can do the math myself, I just need a hint how to create an equivalent circuit where it is obvious what is parallel and what is in ...
11
votes
2answers
12k views

Is magnetic force non-conservative? [duplicate]

If magnetic field is conservative, then why not the magnetic force? My professor thinks it is non conservative but he couldn't explain to me why?
14
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4answers
3k views

Question about canonical transformation

I was going through my professor's notes about Canonical transformations. He states that a canonical transformation from $(q, p)$ to $(Q, P)$ is one that if which the original coordinates obey ...
12
votes
4answers
11k views

Derivation of Kepler's laws

How can analytically be derived the Kepler's laws? I found some extremely synthetic equations which from the Newton's laws (in particular $\mathbf{F} = m \mathbf{a}$) tried to obtain the Kepler's ...
12
votes
9answers
44k views

What's the core difference between the electric and magnetic forces?

I require only a simple answer. One sentence is enough... (It's for high school physics)
6
votes
6answers
4k views

What is the electric field flux through the base of a cube from a point charge infinitesimally close to a vertex?

I'm having some trouble with the following problem: A charge $q$ is placed on the body diagonal of the cube very close to one of the corners (distance $\delta$ from the corner, $\delta$ tending to ...
21
votes
7answers
8k views

Why does gravity act at the center of mass?

Sorry if this is a trivial question. Why does gravity act at the center of mass? If we have a solid $E$, shouldn't gravity act on all the points $(x,y,z)$ in $E$? Why then when we do problems we ...
13
votes
1answer
10k views

Fluid in a rotating cylinder

I have been wondering why a fluid in a rotating container has a parabola shape? Is it possible to prove this mathematically?
9
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2answers
3k views

Why are EM waves transverse?

I was reading Griffiths' Introduction to Electrodynamics, specifically the section on plane waves. I can see that if we want a transverse wave traveling in the $z$ direction that we are only going to ...
5
votes
2answers
10k views

How To Use Ladder Operators?

I'm studying for a test in quantum mechanics and I'm having a hard time understanding how to use ladder operators. There are no examples in my text book, only definitions that I can't understand how ...
8
votes
3answers
11k views

Example where angular momentum and angular velocity are not parallel

I am unable to visualize any case where angular momentum and angular velocity of an object are not parallel.
6
votes
2answers
8k views

Why does a perpendicular force not change speed?

I have been taught that a perpendicular force acting on an object will only change the direction of its velocity, not its magnitude. The explanation that was provided to me is that because there no ...
5
votes
3answers
34k views

Flux through side of a cube

I am looking at Griffiths introduction to Electrodynamics 3rd ED. Problem 2.10 asks for the flux of $E$ through the right face of the cube, when a charge $q$ is in the back left corner of the cube. ...
1
vote
1answer
982 views

Capacitor in a dielectric fluid

In the above problem, it states that the dielectric fluid is "pulled up" by an electric force. However, I don't see why this should be true. The electric field (and therefore any electric force) ...
5
votes
1answer
3k views

Effective mass in Spring-with-mass/mass system

Suppose you have a particle of mass $m$ fixed to a spring of mass $m_0$ that, in turn, is fixed to some wall. I'm trying to calculate the effective mass $m'$ that appears in the law of motion of the ...
6
votes
2answers
586 views

Simple QFT exercise

Consider a particle on the real line with: $L=\frac{1}{2}(\partial_0q)^2 + f(q)\partial_0q$ the equation of motion is that of a free particle $\partial_0^2q=0$. In fact $\delta[f(q)\partial_0q]=0$. ...
4
votes
3answers
2k views

What is the position as a function of time for a mass falling down a cycloid curve?

In the brachistochrone problem and in the tautochrone problem it is easy to see that a cycloid is the curve that satisfies both problems. If we consider $x$ the horizontal axis and $y$ the vertical ...
3
votes
2answers
3k views

Variable mass dynamics: Particle and Rigid Body

I'm encountering some issues in the understanding of some basic concepts about the dynamics of variable-mass particles and rigid bodies. For what I found, for example reading On the use and abuse of ...
1
vote
3answers
534 views

Force Transfer Between two bodies linked by a rope [closed]

When two bodies, free of movement, are linked by a physical constraint (a maximum distance between them) how do their masses and velocities influence each other? Which formula with theses parameters ...
1
vote
4answers
300 views

Rotation systems. Problem interpreting an equation

In this equation: $$ \mathbf a_i\overset{\rm def}{=}\left(\frac{d^2\mathbf r}{dt^2}\right)_i=\left(\frac{d\mathbf v}{dt}\right)_i=\left[\left(\frac{d}{dt}\right)_r+\boldsymbol\Omega\times\right]\left[...
6
votes
4answers
2k views

If you could ride an elevator through the earth [duplicate]

What if it was possible to ride an elevator straight through earth. If we take all the heat and pressure problems away, and assume it would be possible: What would happen with gravity? Would gravity ...
2
votes
3answers
831 views

Derviation of group velocity

I am working thru a derivation of the group velocity formula and I get to this stage: $$y=2A\cos(x\frac{\Delta K}{2} -t\frac{\Delta \omega}{2})\sin( \bar k x-\bar \omega t)$$ Then all the derivations ...
1
vote
2answers
1k views

Conditions for vertical circular motion

If a bob attached to a string is swinging in vertical circular motion, we say that the bob leaves the circular path when the tension in the string becomes zero, but even when tension becomes zero, ...
4
votes
1answer
392 views

standing waves on a cylindrical jet

as we know, there are some perturbations on a falling jet which are always present and according to their wave number and the radius of the jet, they can grow and decay over time. so, imagine a jet ...
4
votes
2answers
923 views

Magnifying power of concave mirrors

Does anybody here know how magnifying power is defined for a concave mirror? I see these labels "5×" or "3×" on mirrors being sold as shaving mirrors or make-up mirrors. How is this defined? I know ...
4
votes
2answers
849 views

Shell model of an odd-odd nucleus: $^6$Li

Lithium-6 isotope has an approximate magnetic momentum of $0.88\ \mu_N$ in its fundamental nuclear state. I'm trying to find its angular momentum and parity. I found in a standard table: $I=1^+$ and ...
2
votes
4answers
702 views

Projectile/orbital motion over very long distance

We know the optimum angle for greatest horizontal displacement when launching an object with projectile motion is 45 degrees. How to solve the angle when it is real long distance around the earth ...
1
vote
2answers
192 views

Variation of a term in the Lagrangian

I don't understand why $$\frac{\delta}{\delta\phi}\left(\frac12\partial^\mu\phi\partial_\mu\phi\right)~=~\partial^\mu\partial_\mu\phi.\tag{1}$$ If we use integration by parts, there should be a minus ...
0
votes
2answers
2k views

How does a rocket's exhaust gas' momentum propel a rocket?

During the launch of a rocket into space, the exhaust gases from the engine possess momentum. Outline, with the help of an equation, how this causes the rocket to be propelled upwards. Can someone ...