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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34 views

Why is the electric field negative?

I have a doubt in an exercice of a Thomson's apparatus deflecting an electron beam. The problem is: Electrons pass undeflected through the plates of Thomson's apparatus when the electric field is ...
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21 views

Efficiency of kettle

I have the following table of results for an experiment in which water is boiled in a kettle. For the final column to calculate efficiently it says divide the internal energy change by the work ...
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2answers
66 views

Why can't I choose blocks attached with pulley B as a system?

Three blocks of masses m1, m2 and m3 are connected as shown in the figure. All the surfaces are frictionless and the string and pulleys are light. Find the acceleration of the block of mass m1. ...
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28 views

Estimate the force on your legs if you jump off a 2m high wall and land on your feet [on hold]

My final answer was 686.7N. I used F = ma, so let the mass be 70 because the average weight of a 15-year-old is near that. (the question was purposed for A-level students). 70kg x -9.81 m/s^-2 = 686....
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1answer
40 views

How to find the possible measurements of a quantum system?

A wave function of an infinite square well is given as $$ \psi(x) = \frac{1}{\sqrt{5a}}\sin\left(\frac{\pi x}{a}\right) +\frac{2}{\sqrt{5a}}\sin\left(\frac{3\pi x}{a}\right),\quad x\in[0,a] $$ How do ...
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Pseudorapidity: Derive conversion to Cartesian momenta

I am working on the ATLAS opendata as part of a lab course at my uni at the moment and stumbled upon the identity $p_{z} = p_{T}*\sinh(\eta)$ with the pseudorapidity $\eta = -\ln(\tan(\frac{\Theta}{...
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Evaluating the Heisenberg Hamiltonian for a spin chain in the z basis

The problem I need to evaluate the expectation value of energy for a spin-1/2 chain governed by the Heisenberg Hamiltonian (Wikipedia link). Specifically, $$ H = \sum\limits_{\langle i j \rangle} \...
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22 views

A block of mass M bound to a weightless bar is hit by a projectile. How many laps does the block travel? [on hold]

I have solved the following problem, but the solution is not available to me, so I'd like to know I made any mistakes. A block of mass "M", initially still, is bound to a weightless bar of length "b"....
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23 views

Method of resolution of forces numerical Question [on hold]

The resultant of two forces F1 and F2 is at right angles to F1. Determine the angle between the forces.
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1answer
34 views

Linearizing Equations (Question given below): [on hold]

This question is mainly asking to rewrite a different graph equation (maybe parabolic, curved, etc) and changing it to a normal linear equation in the form y = mx+b. The question 5 and 6 can be seen ...
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1answer
38 views

How to convert $\rm kg/m^3$ to $\rm J/m^3$ for natural gas and biogas?

I want to convert from mass density to energy density: Natural gas has a density of $0.8\: \rm kg/m^3$. Biogas has $1.15\:\rm kg/m^3$. I want to convert them into $\rm J/m^3$ so that I can ...
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1answer
53 views

Show Galilean invariance of Schrödinger eq

I'm trying to show the Galilean invariance of the (time-dependent) Schrödinger equation by transforming as follows: $$ \left\{\begin{eqnarray}\psi(\vec{r},t) &=& \psi(\vec{r}'-\vec{v}t,t),\\ \...
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32 views

Doppler effect with two moving resonators [on hold]

Sound source with frequency $\mathcal{V}_0$ is located between two moving resonators set to wavelengths of $ \lambda_1$ and $\lambda_2$, respectively. Determine speed ratio of the two resonators $\...
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28 views

Exhaustion of a gas Pressure Tank [on hold]

Gas tank of the volume $V$ is exhausted with the axial piston pump. It pumps $\Delta V$ of volume per one working cycle. After how many cycles does the pressure in the gas tank reduce by $K$ times? ...
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16 views

Evaluating the radius of a spherical cavity that will make a glass cube just sink in water [on hold]

A glass cube of side 5cm having spherical cavity within just sinks in water. If the specific gravity of glass is 2.5, what is radius of spherical cavity?
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Momentum of neutrino and beta particle [on hold]

In carbon-14 decay beta particles with end point energy 0.155MeV are emitted. A beta particle with 0.025MeV energy is emitted at 135 degree to the direction of motion of recoiling nucleus ,calculate ...
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2answers
58 views

Show $\langle \alpha| (\cos \mu)^{-a^{\dagger} a} | \alpha \rangle =e^{|\alpha|^2(\frac{1}{\cos \mu} -1)}$ for coherent states $|\alpha \rangle$

I am reading"Quantum continuous variables, A primer of Theoretical Methods" by A.Serafini, page 120. Let $ a $ be the annihilation operator for the Fock basis. I want to show $$\langle \alpha| (\...
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24 views

Calculate the time taken for a body to hit earth's surface [on hold]

Find the time taken for an iron cube of dimensions 0.1m × 0.1m × 0.1m, whose density is 7.85 g/cm³ to reach the earth's surface released from a height of 10m from earth's surface, provided gravity = 9....
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16 views

Electric field inside a homogenous distribution for slightly different Coulomb's law

I am trying to show that the electric field inside a homogeneous distribution of superficial charge is of the order of magnitude of $\delta$, with: $$V(\textbf{r})=\int d^3\textbf{r'}\frac{\rho(\...
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1answer
65 views

Kinematics problem, only energy related approach [on hold]

I read this question: From the top of a tower, a stone is thrown up and it reaches the ground in time $t_1$. A second stone is thrown down with same speed and it reaches the ground in time $t_2$. A ...
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2answers
65 views

Calculating gravitational force with multiple planets [on hold]

I have a question regarding the following problem: Given the following system of planets (see image), calculate the total gravitational force acting on $m_3$. ($m_1 = 2 \cdot 10^{20}kg;$ $m_2 = 1 \...
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49 views

Rigid body dynamics exercise

Yesterday I came across this exercise and I can't really find a way to get the correct answer. Exercise A rigid homogeneous rod that weighs $M=5\,\mathrm{Kg}$, has length $l=0.8\,\mathrm{m}$ and a ...
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1answer
63 views

Distance between two drops [on hold]

2 drops are thrown away simultaneously in $t=0$, with initial velocity of $v_i$ and in angle of $\theta_i$ in opposite directions as seen in the picture. What is the distance between them as a ...
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0answers
66 views

Simple/elementary explanation for $\mathbf{3} \otimes \mathbf{\bar{3}} = \mathbf{8} \oplus \mathbf{1}$? [duplicate]

I am preparing a talk on the Eightfold Way, and am attempting to explain the spectra of the light mesons/baryons via representation theory. It will be delivered to students who have never seen ...
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33 views

Interference questions [on hold]

non reflecting surfaces are made by coating very thin films of transparent materials . find the maximum thickness of such coating is u=5/4 and l= 5.5*10-5 cm. What does it mean by maximum thickness?
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Determining the z-component of the electric field at a point near a plate [on hold]

I'm struggling with all three parts a,b,c. Any help would be great, thanks. Regards Roy Browning
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23 views

Tension due to unequal forces on a massless spring [duplicate]

When a massless spring is pulled by 5N on both sides the tension in the spring is 5N (proved by considering COM at rest and breaking the spring into two springs of 2k each)...what if the forces ...
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1answer
37 views

Simple harmonic motion qsn [on hold]

Have been stuck with this question from classical mechanics under the simple harmonic motion the question is saying that if $$y=a\cos(\omega t)+b\sin(\omega t)$$ show it represents simple harmonic ...
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19 views

Probability of finding $N$ particle in volume $V$ [on hold]

A vessel of volume V contains 3 molecules. The probability of finding all molecules in volume V/2 is_____________?
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3answers
64 views

Finding energy Eigenvalue from two spin Hamiltonian

Let's consider a system of two spins, named spin 1 and spin 2. Let's also consider, in a Hamiltonian, spin part has been defined as $\sigma_1 \cdot \sigma_2$. For example: $$H= E_0 + \sigma_1 \...
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38 views

How to solve a general planet orbit differential equation? [on hold]

According to Newton's gravitation law, the following differential equation can be made $$\frac{d^{2}}{d t^{2}} \mathbf{x}{\left(t \right)} = - \frac{G M }{\left|{\mathbf{x}{\left(t \right)}}\right|^{...
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33 views

Rotational inertia [on hold]

Consider two bodies, A and B, of equal mass set at a short distance. Body A is spinning and body B is at rest. Then, through some kind of electromagnetic device, a strong repulsive force is ...
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1answer
28 views

Reading energy Eigenvalues from a Hamiltonian matrix for 1D harmonic oscillator

After a perturbation $V(x)$ added to the system, a matrix element $H_{nn}$ calculated in unperturbed Eigenstates for one-dimensional harmonic oscillator is given as: $$\epsilon \hbar \omega_0\begin{...
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37 views

Finding the molar ratio of gases: what the heck am I doing wrong? [on hold]

Note: This is not a homework question or something like that, and I've been trying to solve this question over 2 days, but I always find a negative answer, for some reason. In the book of Kondepudi, ...
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19 views

How to determine the direction of acceleration for block A and man? [on hold]

My confusion is how to determine the direction of acceleration of block and man. I know that in the same direction. acceleration of Man wrt rope/block will be Acceleration of Man minus Acceleration ...
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0answers
59 views

Conserved quantities of a simple Lagrangian

Suppose the following Lagrangian with 2 degrees of freedom: $$L = \frac{3}{2}\dot{q}^2_{1} \ + \frac{3}{2}\dot{q}^2_{2} \ + \dot{q}_{1}\dot{q}_{2}$$ My aim is to find all the conserved quantities of ...
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1answer
53 views

Show for $r \in \mathbb R$, $e^{(a_1 ^\dagger a_2^\dagger - a_1a_2)r}|0,0 \rangle = \frac{1}{\cosh r} \sum_{j=0}^\infty (\tanh r)^j |j,j \rangle$

Let $ a_1, a_2 $ be annihilation operators for the first and second component in the product state $|m,n \rangle$ using Fock basis. Following "Quantum continuous variables, A primer of Theoretical ...
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30 views

Determining whether I hit the bed when jumping from a cliff [on hold]

For simplicity, assume a perfectly spherical object with uniform density falling from some height to a lake. How can I determine whether I hit the bed of the lake? Maybe this has something to do with ...
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0answers
25 views

Relation between current (not at saturation) and voltage in photoelectric effect

This is the question I got for an assignment. How do I determine stopping potential from this data? I can see that the relation between $V$ and $I$ seems to be linear, so can I just use the equation ...
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0answers
31 views

The exact location of normal force and friction vectors [on hold]

I am struggling with a following question: "A cylinder of radius $r$ and height $h$ is standing on an inclined plane pitched at an angle $\theta$ to the ground. Given the coefficient of friction $\mu$ ...
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0answers
35 views

Please check my problem about SI prefixes [on hold]

2.2 A single logic gate in a prototype integrated circuit is found to be capable of switching from the “on” state to the “off” state in 12 ps. This corresponds to: (a) 1.2 ns; (b) 120 ns; (c) 1200 ns; ...
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1answer
33 views

Change of variable in 4D space-time

I was reading Sidney Coleman's article "Fate of the false vacuum: Samiclassical theory" and i stumbled upon a change of variables that i can't seem to prove. The problem is this: trying to solve the ...
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12 views

Why the sum of deformations in given figure is zero?

When a vertical block is kept between two fixed support and when the bottom support is removed, it has the possibility of facing a deformation downwards which was impeded by the upward reaction force ...
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23 views

Toilet Paper roll [on hold]

Why we don't replace R in formula (RT=(1/2)m(R2+r2)(a/R)) into (R,outer diameter +r,inner diameter)? Does the inner roll also rotate?
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1answer
42 views

Inverted pendulum, EOM

Consider the inverted pendulum shown below: where $F$ is an external force, $B$ is the CoM of the rod, $A$ is the position of the joint where the rod attaches to the car. Angles increase in the ...
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0answers
24 views

external pressure vs internal volume plot of 1. expanding and 2. contracting cylinder-piston-gas system that obeys Boyle's law [on hold]

A gas which follows Boyle's law, is enclosed inside a standard piston-cylinder system having volume V and pressure P. If an external pressure is applied to that massless piston to 1. slowly compress ...
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0answers
28 views

How to solve for stable/unstable equilibrium in this question [on hold]

A solid cube of side b is at rest on curved surface of a cylinder(horizontal axis) of radius R. Assume no slipping. We have to derive condition for stable equilibrium. My approach: Slightly we can ...
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2answers
44 views

Can someone explain these circled points…?

Why is direction of friction in the direction of motion and here it is the platform that moves....the movement is not caused by friction so how is friction doing work? In the second one there is no ...
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1answer
80 views

How can i obtain the correction to the eigenvalues as a result of adding the gravitational potential to the hydrogenlike atom?

In treating the hydrogen-like atoms, we normally neglect the gravitational potential for the system. I am able to justify the above statement by comparing the gravitational potential to the ...
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0answers
30 views

What will be the equation of the path of spider? [on hold]

A cobweb thread of negligible relaxed length is traced between points A and B on two opposite walls as shown in the figure. In this state the thread makes an angle $\theta$ with the horizontal and ...