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.
23,525 questions
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Cylinder Hollowness vs Speed Down Incline Plane [closed]
We know that the speed of a hollow can is slower down an incline than the speed of a filled can of the same mass and dimensions. If the can is not completely hollow, but not completely filled (so the ...
1
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2
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814
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Lagrange multipliers - isothermal-isobaric ensemble
I know that the entropy of isothermal-isobaric ensemble is given by:
$$S = -k \sum_{i=1}^M p_i \ln p_i \quad \textrm{where $p_i$ must be normalized} \quad \sum_{i=1}^M p_i = 1 \, .$$
The average ...
0
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5
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Two objects, one thrown up at an initial velocity, one dropped, meet when they have the same velocity?
My physics instructor said that this is not intuitive but a correct assumption to make. I cant figure out why this must be. Assume the objects are released at exactly the same time. They meet at the ...
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1
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Estimate the reaction force on each leg of a 4-legged table
Assume you have a table with four legs with a weight placed somewhere inside the boundary created by the legs. The task is to determine the reaction force at each leg. Here are the problem ...
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1
answer
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How much would this shelf support? [closed]
Consider the following scenario: I am would like to mount a shelf to my wall. To support the shelf, I am using two drywall anchors, which each are rated at 50 lbs. If each anchor is placed on one end ...
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0
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103
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How to show that quantum theory conforms to laboratory behavior of pendulums
In the last assignment given to me by my professor, there is a question which asks:
In classical theory, it says that in presence of air friction, a pendulum continuously loses energy with time and ...
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2
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Relative velocity in two dimensional motion [closed]
I came across the following problem in my textbook:
"Two particles A and B are projected in air. A is thrown with a speed of 30m/s and B with a speed of 40m/s as shown in the figure. What is the ...
user106570
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9
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Deceptively simple mass-spring problem?
This question is inspired by two other, similar, so far unanswered questions (posed by different OPs).
Mass $m_2$ sits on a incline with angle $\theta$ that provides just enough friction for it not ...
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3
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718
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Obtaining $\beta = \frac{1}{k_B T}$ from first principles derivation
I'm nearly at the end of this derivation but totally stuck so I'd appreciate a nudge in the right direction
Consider a set of N identical but distinguishable particles in a system of energy E. These ...
- 2,542
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1
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Calculating maximum induced current problem [closed]
I have this problem about magnetic fields and induction.
The figure shows a wire that has been bent into a circular arc of radius $r = 27.0 cm$, centered at $O$. A straight wire $OP$ can be rotated ...
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1
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Repeated Cavitation?
Consider the following situation : Suppose i have a powerful laser beam. I somehow manage to use it to vaporise 10cc of water from inside a pool(pond) almost instantly(within 1-2 s). Note: i mean that ...
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2
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How do you find new speed of a object knowing the momentum and impulse?
I know that both momentum and impulse (change in momentum) are measured in kg m/s and the formula for momentum is mass x velocity and the formula for impulse is force x time. However I have a question ...
David
2
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3
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317
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Moment of inertia related question [closed]
Sorry for the undetailed title, but when the moment of inertia is calculated in a solid cylinder, the volume of a "sheet" of the cylinder is calculated. I've only seen the volume as $$length*thickness*...
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2
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Coordinate transformation bringing $ds^2 = y^2 dx^2 + x^2 dy^2$
In Wolfgang Rindler's book "Essential Relativity" there is an unsolved exercise about coordinate change in two dimensions (pp 140-141). The author proposes as example four infinitesimal distances, ...
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1
answer
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Doubt regarding question on Bogomolny equations
PROBLEM:
Let $\bf E$ and $\bf B$ be static, and source free electric and magnetic fields in $\mathbb R^3,$ respectively which are infinitely many times differentiable. Also assume that they satisfy ...
- 3,626
2
votes
0
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543
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Mass hung from the middle of a wire [closed]
I am doing the exercises of "Vibration and Waves", French; and I got stuck in the point 3-7. This is the exercise:
A wire of unstretched length $l_0$ is extended by a distance $10^{-3}l_0$ when a ...
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2
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2
answers
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How many arcseconds the light of a star unfolds in the vicinity of jupiter?
One of the main demonstrations made to test the theory of relativity were the images of the solar eclipse of May 26, 1919, (causing a shift in the positions observed in celestial coordinates of its ...
- 1,526
1
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0
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358
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Modelling a water-bottle rocket, version 2. (long post warning) [closed]
Task
The modelling of a Water Rocket's flight profile for a set of predefined variables.
TL;DR: I am wondering if my assumptions and mathematics are correct. If they are, this is merely an ...
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5
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When should you jump off a falling ladder?
If you stand on the top of a falling ladder you will hit the ground at a higher speed (and therefore presumedly sustain more injury) if you hold on to the ladder than if you jump off it.
This was ...
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1
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If 1 kg of mass is converted to energy and used to accelerate a second 1 kg mass, what would be the final velocity?
A bit rusty, tried using $E=mc^2$ to figure out how much kinetic energy would 1kg of mass convert to, and then work backwards to figure out what would be the final velocity of a 1kg mass having ...
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1
answer
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Form of acceleration for motion in an ellipse [closed]
I came across the following question:
The coordinates of a particle moving in a plane are given by $x(t)=a\cos(pt)$ and $y(t)=b\sin(pt)$, where $a>b$ and $a$ and $b$ are positive constants of ...
user106570
1
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2
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263
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2 dimensional relative motion
I came across the following question:
Airplanes A and B are flying with constant velocity in the same vertical plane at angles $30°$ and $60°$ as shown in the following figure. The speed of A is $...
user106570
5
votes
1
answer
913
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Working of potentiometer [closed]
So can you simply explain why current increases in lower loop as we move towards A why it increases in upper loop as we move towards X and please give explanation based upon what changes occur voltage ...
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vote
1
answer
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Derivation of the radial momentum operator
I have been studying Quantum Mechanics and when my book was going through the Hydrogen wave equation, it was talking about this equation:
$$ \frac{p_r^2}{2\mu} +\frac{L^2}{2\mu r^2}+V(r)=E$$
I ...
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1
answer
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Max velocity for a body to remain in contact with surface while exhibiting circular motion
Q. A particle of mass is attached to one end of a sting of length l while the other end is fixed to a point $h$ above the horizontal table. The particle is made to revolve in a circle on the table so ...
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0
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Is the force experienced by one jumping into a stagnant body of water and a body such as a river similar?
Is the force experienced similar or different? By how much? Suppose the height from which the person is falling is 25 m and the mass is 85 kg.
2
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1
answer
509
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Conserved currents for Lagrangian given by a trace
Let the Lagrange density $\mathcal{L}$ be given by
$\mathcal{L}=\mathrm{Tr}\left(\partial_\mu U^\dagger \partial^\mu U\right)$,
where $U=U(x)\in U(N)$. Suppose there are two matrices $A,B\in SU(N)$ ...
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Quantum mechanics, spin half particle in a magnetic field probability question.(schrodinger)
My understanding of how to solve this is a little fuzzy around certain areas.
Consider a spin-1/2 particle with a magnetic moment. At time $t = 0$, the state of the particle is$|\psi(t =0)\rangle = |+...
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1
answer
337
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Error in calculating binding energy of Beryllium 8 [closed]
I don't know where I am going wrong with regards to calculating the binding energy of $^8$Be. This is what I am doing:
I look up online and find that the mass excess of $^8$Be is $5305 \mu$u. Thus, ...
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1
answer
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Of what order of magnitude is the effect of spontaneous forward-and-backward reaction H2O <=> OH- + H3O+ on the Gibbs Free Energy of H2O (l)?
Consider a box of liquid water:
One can calculate the Gibbs free energy by considering the enthalpy and the entropy:
$$ \Delta G = \Delta H - T\Delta S $$
For liquid water, the enthalpy is the ...
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1
answer
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How to predict length of conductor?
A long round conductor of cross sectional area $S$ is made of material whose resistivity depends only on a distance $r$ from axis of the conductor $\rho=\frac{\alpha}{r^2}$, where $\alpha $ is ...
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1
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To prove that an operator commutes with any function of it
(This is a homework question.) The question is to prove that a general operator $\hat{A}$ commutes with any function $\hat{B} = f(\hat{A})$.
$$
\newcommand{\ket}[1]{\left| #1 \right\rangle}
\...
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votes
3
answers
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Standing waves: How are the waves not respecting the boundary conditions "cancelled" from the normal mode?
I'm asking this question because I did not find any explanation in textbooks.
Consider a string fixed at both ends with an impulse provided to it (like in a guitar). The impulse can be described ...
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1
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Can we build a space tower out of ICE? [duplicate]
Sounds crazy i know, but hear me out there are place's all over the universe with ice glaciers much bigger then what we can even imagine on earth.
So what if he build a Tower in the middle of ...
2
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1
answer
339
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Help with non-equilibrium Green functions with a time-dependent Hamiltonian
I'm trying to solve a problem with a time dependent Hamiltonian
$$H = H_0 + V(t)$$
where $H_0$ is a Hamiltonian with a non explicit time-dependence and $V(t)$ has an explicit time dependence.
My ...
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2
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714
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Force needed to move blocks against friction
Two blocks of masses 3kg and 5kg are connected by a spring of stiffness k. The coefficient of friction between the blocks and surface is 0.2 . Find the minimum constant horizontal force F to be ...
5
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2
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1k
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Kinetic energy of photoelectrons
I came across the following question:
A photon of energy $h\nu$ is absorbed by a free electron of a metal having work function $W<h\nu$. Then:
The electron is sure to come out
The electron is ...
user106570
2
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2
answers
1k
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Newton's third law confusions [duplicate]
According to Newton's third law of motion, if body A exerts a force on body B, then body B exerts a force on body A that is equal in size but opposite in direction, then how do things move?
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1
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How does tension in string change when object suspended from it is dipped in water?
A copper cylinder hangs from the bottom of a steel wire of negligible mass. The top of the wire is attached to the ceiling, and once struck the wire emits a sound with a fundamental frequency of 300Hz....
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3
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1
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Righting moment for object submerged in water
I am looking to determine the lateral angle at which an underwater camera system will no longer right itself. When on the ocean floor it is $-24.30~\text{kg}$ buoyant with the difference between its ...
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4
answers
277
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How does $E = -\nabla V$ work for a dipole? [closed]
For a dipole, the potential is zero at any point on the perpendicular axis, but the electric field isn't zero along that axis. Now, how do I get $E$ from $V=0$ (at that point/axis) from the relation:
...
0
votes
1
answer
181
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Electromagnetic loop [closed]
A circular Loop of radius R is bent along a diameter and given a shape as shown in the figure one of the semicircles (KNM) lies in the x-z plane and the other one (KLM)in the y-z plane with their ...
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1
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0
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282
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Forces (Using Lagrange multipliers) of a fixed bicycle wheel
I'm having doubts about my Lagrangian when I release my constraints:
I'm using Euler angles and using a system which is referenced to the wheel. It's quite straightforward to get the Lagrange ...
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1
vote
3
answers
941
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Doubt in Lorentz Transformation [closed]
I've tried to do the following exercise:
Show that $\sum_{\mu} D^{\mu\mu}$ and $\sum_{\mu}D_{\mu\mu}$ are not invariant under Lorentz transformations but $\sum_{\mu} D^{\mu}_{\mu}$ are.
I've had ...
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5
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1
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How to find the null geodesics?
The metric below was considered in [Spacetime perspective of Schwarzschild lensing]
$ds^{2}=2f du^{2}-\frac{2}{l^{2}} du dl-\frac{1}{2l^{2}}(d\theta^{2}+\sin^{2}\theta\, d\phi^{2})$
The authors gave ...
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2
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How fast will a jacuzzi cool down over time? [closed]
If I have a Jacuzzi full of water with $37^{\circ}\text{C}$that is currently not heated within a room full of air with $20^{\circ}\text{C}$, how long will it take for the water (and room) to reach ...
- 103
1
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2
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149
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Difficulty figuring out how to calculate the angular frequency
I've been tasked with finding the angular frequency for a oscillating mass on a supposed friction-less surface. I've been told that the mass is pulled to the left and 0.25 seconds later reaches the ...
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4
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2
answers
717
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How to put this metric in matrix form? [closed]
Given the metric
$$ds^{2}=dt^{2}-2 dr dt-r^{2}(d\theta^{2}+\sin^{2}\theta \,d\phi^{2})$$
How to put this metric in matrix form?
I ask this because the metric is obviously not diagonal so what will ...
- 789
0
votes
2
answers
3k
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Mass in accelerated wedge [closed]
I got this exercise from Kleppner's Introduction to Mechanics:
A 45° wedge is pushed along a table with constant acceleration A. A block of mass m slides without friction on the wedge. Find its ...
- 11
2
votes
2
answers
2k
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What is the physical meaning of the zeroth component of the Minkowski force 4-vector?
In David Griffiths' Intro to Electrodynamics, section on ED and relativity, he poses a simple problem regarding the zeroth component of the Minkowski force 4-vector for a charge $q$ moving with ...
