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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Why is the probability of a cat catching a mouse 100%?

On a one-dimensional number axis, there is a mouse at the origin O and a cat at x=1. The cat can press 1 to the left or right to move one space at a time with a probability of 1/2, respectively. It is ...
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Anomalous calculation about stellar collision

Suppose two bodies of mass $m$, one of them is fixed and the another is free to move,they are separated by a distance $l$ initially and the system is at rest. What would be the speed of the free body ...
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Kinematics constant acceleration problem

A stone is being thrown vertically upward with a speed of 12.5m/s from the edge of a cliff 75.0m high, what’s the total distance did it travel? It is a constant acceleration kinematics problem, I ...
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Octopus Ride how much +G force in upward Jerk?

This is a version of the Octopus Ride here: https://www.youtube.com/watch?v=8flmhIAKTvQ They call it Hip Hop but really it is what you call it in other places, I felt my left Butt Cheek or Thigh cramp ...
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Kelvin–Helmholtz instabilities - how to solve these questions? [closed]

The Kelvin-Helmholtz problem occurs when horizontal wind and density change at a discontinuity with $U_1,ρ_1$ in the upper layer and $U_2,ρ_2$ in a lower layer. It can be shown that the phase speed ...
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About pressure and density [closed]

The diagram is a U tube that consisted with 3 immiscible liquids . i) Calculate the pressure exerted on point Q by the water column. ii)What is pressure exerted on P? iii)Calculate density of liquid X....
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Where did I go wrong in separating the Hamiltonian? [closed]

I am trying to show that the Hamiltonian of a two-body system can be rewritten in the form $$\frac{\textbf{P}^2}{2M}+\frac{\textbf{p}_{\text{rel}}^2}{2\mu}+V(\textbf{r}_1,\textbf{r}_2),$$ (where $\...
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Calculate total number of particles hitting a projectile [closed]

Let's assume a projectile with known size has a known trajectory in Euclidean coordinate $(t, x, y, z)$. This projectile is moving inside a radiation zone with known flux $\phi(t, x, y, z)$ (in units ...
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Are any points at rest on a globe spinning both horizontally and vertically?

Suppose there was a globe which could be spun about polar and horizontal axis. It is first spun about the polar axis, then promptly spun about the horizontal axis. Would any points be at rest?
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Charge in crossed $E$ and $B$ fields

This post describes the motion of a charge in crossed electric and magnetic fields as: $$ x = r \cos ωt + \dfrac EB t\\ y = r \sin ωt\\ $$ Can you please explain how these equations are derived. Why ...
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How to find the electric field in a inductor? [closed]

There's a problem that I didn't understand when I was at school, and it's still unclear. Suppose a simple circuit, an AC constant current source $I=I_{0}\exp(j\omega t)$ the current is, and an ...
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Moving spaceship problem in Special Theory of Relativity [closed]

Answer is (a). I am thinking like this way. According to passengers in moving spaceship, they take 1 hr to reach the Pegasus. Or we can say that as they will find themselves at rest, so the Pegasus ...
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$(a - a^t)e^{\frac{1}{2} a^ta^t} | 0 \rangle = 0$ [closed]

When talking about the limits of squeezed states, we reach the conclusion that $e^{\frac{1}{2} a^ta^t} | 0 \rangle$ must be an eigenstate for momentum since the uncertainty in momentum becomes zero. ...
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Will the mango dislodge? [closed]

A boy throws a rock having a mass of 0.2 kg with a speed of 16 m/s to dislodge a mango of mass 0.25 kg which is 10 m above the ground. Will the mango dislodge?
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Computing the maximum force a rod can bear [closed]

Suppose I had a rod of diameter $d$ composed of some material with tensile strength $T$. If I then exterted a pulling force $F$ on the ends of the bar, how do I compute the force $F$ for which the ...
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A block of mass $m$ is kept on a the incline surface of wedge of angle $\theta$. Find minimum acceleration of the wedge so that mass $m$ falls freely [closed]

enter link description here All surface are frictionless. I tried solving this question by resolving normal along x and y but i couldn't get the answer
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Electric Potential in Dielectric [closed]

I am currently preparing for an exam. One of the sample questions was: A rectangular region of space extending from z=0 to $\infty$ having a height $a$ and a width $b$ is filled with homgenoues, ...
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Prove that Majorana mass term is Lorentz invariance

I have a homework to prove that using one kind of chirality, let's say left-handed, we can construct a mass term. The argument is to show that this term $\psi^TCP_L\psi$ is satisfy the dimensionality ...
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Probability for an Energy measure of a quantum state [closed]

I'm stuck on a request in a problem about Quantum Mechanics. The problem starts by giving the ket of an harmonic oscillator $1D$: $$|z\rangle = \sum_{n = 0}^{+\infty} |n\rangle \frac{z^n}{\sqrt{n!}} \...
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What will be the change $E2-E1$ in the Energy? [closed]

A 15 kW motor can lift two quintals of water to a height of 300 meters in one minute. If the efficiency of the motor is increased by 5 percent, what will be the change(E2-E1) in the energy consumed to ...
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What will be the tension in the string in following pendulum question? [closed]

Before downvoting, please read following, you can skip following if you are not downvoting Okay, first of all , before someone downvotes, I want to tell them that this is not just a homework problem ...
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Calculating the total energy of this thrown ball [closed]

My question is as follows. Assume that a ball of $2kg$ is thrown upwards from the ground at a velocity of $100m/s$. The ball is facing a hindrance by air of $1N$. What is the total energy ($E_p+E_k$) ...
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1 vote
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Field shift in free Klein-Gordon theory

I am reading Peskin & Schroeder Ch9 and am stuck on a calculation going from equation 9.36. The problem is essentially a change of variable of a Klein-Gordon field. Beginning, we have an integral ...
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Stopping too soon [closed]

I have an object going $1000\frac ms$, $vi$, that I want to slow down to $250 \frac ms$, $vf$. I want it to slow down in $10000m$, $d$. I want to know how much deceleration is necessary, and how long ...
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1 vote
2 answers
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Understanding dot product in quantum mechanics [closed]

Let's say we have a two-state-system with state $\vert 1\rangle$ and state $\vert 2\rangle$. From my understanding one can assume the base vectors of this system to be $\vert1\rangle \mapsto (1,0)^\...
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What is the right option for this question? I think its d but some sources on internet say its c but their explanation is not convincing enough [closed]

According to me, first, the incident rays parallel to principal axis on the convex mirror will meet at focus, so v is 30 cm. for concave mirror, u is -20 cm and by using the mirror formula, the value ...
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Use the plane wave expansion to explain the fundamental limit of resolution?

As stated in the title I don't really understand how I can explain the fundamental limit of resolution using plane wave expansion. The question was asked by my professor and seems a bit vague to me. ...
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Interference of Waves question

Given : $\phi_1(x,t)=A\cdot \cos(k_1x-\omega_1t)\hat{x},\phi_2(x,t)=A\cdot \cos(k_2x-\omega_2t)\hat{x}$ with no difference phase,$k_1-k_2 \ll k_1,k_2,\omega_1-\omega_2 \ll \omega_1,\omega_2 .$ I have ...
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How did Noether use the total time derivation to get her conservation of energy? [duplicate]

I was informed by @hft that by combining the total time derivation: $$\frac{dL}{dt} = \frac{\partial L}{\partial x}\dot{x} + \frac{\partial L}{\partial \dot{x}}\ddot{x} + \frac{\partial L}{\partial t}$...
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1 vote
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Magnetic dipole moment due to folded loop [closed]

A steady current i flows in a small square loop of wire of side L in a horizontal plane. The loop is now folded about its middle such that half of it lies in a vertical plane. Let $ μ_1 $ and $ μ_2 $ ...
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3 answers
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What is the formula for momentum in a lab reference frame?

When learning momentum in introductory physics, I was taught this formula: $m_1 v_{1i}+m_2 v_{2i}=m_1 v_{1f}+m_2 v_{2f}$. However, my new calculus-based textbook states advises to use the formula $v_{...
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Where do these expressions in this "block on an inclined plane" problem come from? [closed]

I'm a returning physics student after nearly a decade being away from the subject matter. I'm doing some self-study to refresh myself on the material and am starting with reading through David Morin's ...
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Question on orthogonal functions for Fourier series [migrated]

so we say that $$\int_{-\pi}^\pi \cos(nx) \cos( mx) dx = \frac{1}{2} [\frac{sin((n+m)x)}{n+m}+ \frac{sin((n-m)x)}{n-m}]_{-\pi}^{\pi} = 0 $$ for $n\not=m$ but if $n =m$ then $$\frac{1}{2} [0+ \frac{...
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1 vote
3 answers
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Confused about tensor notations of how vector and covectors act on each other

I'm learning/playing around with tensors and somehow got this contradiction, suppose $\{v_i\}$ and $\{w_i\}$ are basis for a vector space $V$ and $\{ v^i \}$ and $\{w^i\}$ are basis for the dual space ...
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Showing that the distance between two adjacent planes in a crystal is $d=2π/|\vec{G}|$ [closed]

The first problem of the second chapter of Kittel's Introduction to Solid State Physics book asks to prove that, if $(hkl)$ is a plane of a crystal, then the distance between two adjacent parallel ...
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Evaluating a Gaussian integral [closed]

there is a integral I read in a book related to renormalization. They calculate in Schwinger-Dyson way. First I have equation (4.56) like this: $exp(-\frac{1}{2}\sum_{j=1}^{n_2}\sum_{\alpha_1,\alpha_2\...
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Integration over moments in path integral [closed]

The amplitude that a particle “propagates” from point $A$ to point $B$ is given by the path integral $$\int\mathcal{D}q(t)\int\frac{dp_j}{2\pi}\,\exp\left\{i\delta\prod_{j=0}^{N-1}\left[p_j\frac{q_{j+...
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2 votes
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Clarification on clock synchronization passage from Kleppner and Kolenkow

I have a question about the following passage from An Introduction to Mechanics by Kleppner and Kolenkow. The passage reads as follows: The Newtonian procedure would work if the speed of light were ...
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1 vote
1 answer
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Angle between the two vectors [closed]

While I'm solving for the angle between the vectors A = 10j+2k and B = -4j+0.5k,using dot product I got 161.5 degrees and using cross product I got 18.43 degrees. The correct answer was 161.5 degrees. ...
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Canonical transformation of the harmonic oscillator‘s Hamiltonian [closed]

I could deduce the Hamiltonian of the damped harmonic oscillator: $$ H=\frac{p^2}{2m}e^{-2 \gamma t}+\frac{m \omega_0^2 q^2}{2}e^{2 \gamma t} $$ Using the canonical transformation $Q=e^{\gamma t}q, P=...
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Prove that every component of angular momentum commutes with $f$

Let $f( \hat {\vec r} , \hat {\vec p} )$ be the any polynomial in variables $r^2, p^2 $ and $(\vec r \cdot \vec p)$. prove that every component of angular momentum commutes with $\hat f$: $[\hat L_k ,...
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Magnification of an object placed in water due to a concave mirror [closed]

Here is a question that appeared in my test: A concave mirror of focal length 15 cm is placed in water of refractive index $\mu = 3/2$. Water is filled upto 30 cm. An object of height 1 cm is placed ...
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1 vote
1 answer
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Problem trying to graphically represent a 2D vector given angle and intensity [closed]

I'm very new to physics so forgive me if it's a trivial question, but it's something I have trouble figuring out. I'm trying to solve an exercise, and the exercise says that we're given $|\...
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On the motion of a particle [closed]

A particle starts from the origin at $t = 0$ under a variable acceleration $\alpha$, it stops at $t = 1$ at $(0,1)$, provided that the motion takes place along the x-axis. Show that: i) The value of $\...
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Force diagram - Circular motion [closed]

If the bike is maintaining a horizontal trajectory, what are the forces on it? The solution o this shows weight and a force labelled N at the angle a to the wall. I don't understand that because if N ...
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Multiplying non-constant acceleration by a constant on every point - would the total path be multiplied by the same constant?

If the non-constant acceleration is multiplied by a constant (on every point), would the total path also be multiplied by the same constant over the same time? Both starting and ending speeds are zero ...
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Can't understand integration steps of the Wigner function equation [closed]

I'm now reading the section which introduces about Wigner function in the Optics textbook. What I want to ask is that I've got a problem for understand the converting process of these two equations. ...
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I thought that the tension will be in the perpendicular outward direction….. but it was not so as given. I am high school student help with this [closed]

A circular loop of thick rope of mass m and radius R placed on a smooth table is revolving with a speed v about a vertical axis coinciding with the symmetry axis of the rope. Find the tension in the ...
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Query Regarding circular motion [closed]

Suppose a particle is moving with tangential acceleration of constant magnitude but with centripetal acceleration magnitude variable with time (suppose proportional to $\,t^2$). Then what does the ...
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Finding the interaction energy of two spherical charge distributions [closed]

A question asks for the total electrostatic energy of a system of two uniformly charged hollow insulating balls of different radii (say $R_1$ and $R_2$) and charges (say $Q_1$ and $Q_2$), placed at ...
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