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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17 views

getting wrong answer when i vector sum relative velocity and velocity of observer(river in my case)

so there's this question, and I get the right answer if i don't vector sum relative velocity and river flow of the water, when if i do I get velocity of man wrt ground equal to √41/2, and I get the ...
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2answers
27 views

Calculating probability of quantum measurement [closed]

Consider the measurements of an observable $A$, with orthonormal eigenstates $$f_1=\frac{1}{\sqrt{6}}\begin{bmatrix} {-i} \\ {2} \\ {1} \end{bmatrix},\enspace ...
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A rifle is fired at a target 700 m away. How far above the center of the target must the rifle be aimed? What is the maximum height reached? [closed]

The initial speed of a bullet fired from a rifle is v = 630 ms−1 . The rifle is fired at the centre of a target D = 700 m away at the same level as the target. In order to hit the target the rifle ...
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1answer
25 views

How do I figure out how much velocity should be given to a mass orbiting at radius $h_1$ so that it will orbit at $h_2$ , using energy methods?

We can find out how much work or energy needs to be added to an orbiting mass so that it lands at a new orbit with a different orbital radius, provided we know the new and old orbital radii and the ...
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23 views

Two cylinders containing the same amout of moles of ideal gas

The system is heated from temperature $T_p$ to $T_k = \frac{3}{2}T_p$ Known: cylinders contain the same amount of moles of gas specific heat capacity $c_v$ Surface areas of cylinders $S_1>S_2$ $...
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32 views

Show matrix satisfies equation of motion for observables in the Heisenberg picture [closed]

We will study the time-evolution of a finite dimensional quantum system. To this end, let us consider a quantum mechanical system with the Hilbert space $\mathbb{C}^2$. We denote by $\left . \left | ...
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29 views

Is there a simple way to derive Kepler First law? I.e. orbit is an ellipse? [duplicate]

Somehow the first law of kepler is the simplest way to state and the hardest to prove. The calculus way is lengthy and very obscure. It's just manipulating equations and then finally you have an ...
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28 views

Hilbert space and find function for $\phi(t)$ based on Hamiltonian

We study a quantum particle conned to a one-dimensional box with walls at the positions ±1. The Hilbert-space of this system in the Schrödinger representation is again given by $L_2(-1,1)$. In this ...
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1answer
25 views

Static equilibrium of a small spring network

Three springs $AB$, $OB$ and $CB$ with equal spring constants are fixed at the nodes $A$, $O$ and $C$ respectively and attached to a common node $B$, as shown below. The springs are at rest in this ...
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15 views

Three spinless particles with two-body harmonic forces

Problem Consider a system of three spinless particles, each of mass $m$, moving on a straight line and bound to each other by two-body harmonic forces. The Hamiltonian of the system is $$ H = − \frac{\...
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1answer
83 views

Show that evolution of uncertainty is parabolic

Consider the case of a free particle with wavefunction $$\Psi(x, t=0) = \left(\frac{a}{\pi}\right)^{1/4} e^{-ax^2/2} \quad a>0$$ Prove that the uncertainty product $(\Delta x)(\Delta p)$ is ...
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40 views

Is there a way to solve this statics problem algebraically?

This problem can be solve in 2 ways either I solve it with vectors which would be relatively painful and more time consuming and the other faster way is algebraically but I faced a problem when trying ...
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1answer
42 views

How to calculate the trace of six gamma matrices multiplied to $\gamma_5$?

I read from Weinberg that, the gamma matrices have the following property: \begin{equation} \text{Tr}\{\gamma_5 \gamma_\mu \gamma_\nu \gamma_\rho \gamma_\sigma\}=4i\epsilon_{\mu \nu \rho \sigma} \end{...
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29 views

Why is the escape "energy" $e=1$ for a massive object in Schwarzschild metric?

Being $e$ the quantity found through Killing vector $(-1,0,0,0)$, $$e = (-1,0,0,0)\,\cdot\,(\dot{t},\dot{r},\dot{\theta},\dot{\phi})$$ For the Schwarzschild metric, $$e = \left(1 - \frac{2M}{R}\right)\...
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2answers
86 views

How can one generally prevent silly mistakes in very long physics calculations? [closed]

I am a student working on certain open-ended research problems in quantum systems that mostly have long calculations and deal with a large number of terms. I tend to make a lot of silly mistakes ...
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12 views

Probability of finding the electron of a hydrogen atom within a cone of a given angle

I am working on a question where I must find "the probability of an electron being located within a cone of semi-angle 20 degrees w.r.t the z-axis" for the 2s and 2p states of a Hydrogen ...
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1answer
27 views

Why are the components of elasticity tensor 21?

I know there's a duplicate but I didn't understand the whole answer which was: A 6×6 matrix has 36 different components. When you reduce it to a symmetric case it has 1+2+3+4+5+6=21, where we are ...
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1answer
63 views

How to show the equivalence between Lagrangians?

I have a Lagrangian of a form: $$\mathcal{L}=\frac{1}{2}\left (A_\mu g^{\mu\nu}\partial^2 A_\nu-A_\mu \partial^\mu \partial^\nu A_\nu\right ) $$ And I want to show that it is equivalent to the ...
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21 views

Time Dependent Generating Function

A certain physical process results in an event occurring with a rate $\omega(t)$ that is not constant. Represented by n is the number of events that have occurred since $t = 0$: The evolution equation ...
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1answer
28 views

Deriving the two-point function in CFT

I am trying to understand the textbook derivation of the two-point function in CFT as spelled out in this CFT book by Francesco. The same derivation can also be found in this thread. However, I don't ...
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1answer
31 views

I am trying to calculate the charge of the following electric circuit after an infinite amount of time [closed]

The answer is apparently Q=2/3CV. I have tried equating the UR potential with the 3UR and UC but haven't succeeded to get the answer.
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24 views

Find resistance in the D.C circuit [closed]

I'd appreciate it if someone could help me with this. According to my friend, it is achievable if you have a thorough understanding of Kirchhoff's Laws. Additionally, I am an A-level student. The ...
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13 views

Finding the acceleration of an object when forces acting on it is given [closed]

Think a man stands on a plank which he use to move up by pulling down a rope as given in the below figure. The force he exert on the plank is 300N. Mass of the man is 75kg and mass of the plank is ...
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11 views

Use polarization identity to prove a linear operator over a finite-dimensional Hilbert space is completely specified by its expectations on a sphere

This is from the book Quantum Theory from First Principles: An Informational Approach, which I thought I'd give a read as I found the authors' two papers on the same subject to be rather impenetrable. ...
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20 views

Can we apply shooting method for mixed boundary conditions for boundary value problems in ODE?

My question Solve for the steady state concentration profile $y(x)$ in the reaction-diffusion problem given by $y"(x)- y(x)=0$ with $y(0)=1$ and $y'(1)=0$. Solve this using shooting method. Now my ...
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25 views

Deriving the form of the metric on the Poincare half-plane in polar coordinates

This question relates specifically to problem 3.11 from Sean Carroll's book Spacetime and Geometry. After having proven in the text that the Poincare half-plane is a maximally symmetric space and that ...
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30 views

Calculating the mass of the sun [closed]

Calculate the mass of the sun. Given is the distance between Earth and Sun: d = 1 AU ~ 150 * 10^9 m, and the duration the Earth takes to be at the same spot again (one year). You are allowed to say ...
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57 views

Is there a physics related problem which this integral can transform into? [closed]

I know about this integral can be solved using various methods like riemann integral(summation ) , i thought there might be a physics way to approach this problem can this integral be converted to a ...
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1answer
51 views

Proving an identity in creation and annihilation operators

How do I prove this equation for any function $f$ (can this even be proven for an arbitrary function?), where $a$ and $a^{\dagger}$ are the creation and annihilation operators for the 1D harmonic ...
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1answer
40 views

How to calculate torque required to rotate a rectangular prism about its center? [closed]

I'm trying to buy a motor, but first need to find out how much torque I need. I've been struggling with this one, and any advice/help would be greatly appreciated! The motor/motor shaft (blue) will be ...
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40 views

How can I solve this? [closed]

How can I solve this equation?
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2answers
86 views

Is there a particle with charge to mass ratio such that the gravitational attraction cancels electrostatic repulsion?

Consider two masses $m$ with electric charge $q$ at a distance $r$. Magnitude of Gravitational force = $\frac{Gmm}{r^2}$ Magnitude of electrostatic force = $\frac{kqq}{r^2}$ So, If the forces are ...
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2answers
59 views

Electric flux due to a point charge through an infinite plane using Gauss divergence theorem

I'm learning the basics of vector calculus when I came across this problem: A point charge +q is located at the origin of the coordinate system. Calculate the flux of the electric field due to this ...
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1answer
56 views

What is the gravitational field in the middle of a thin rod?

I just calculated the gravitational field on the $x$-axis created by a thin rod of mass $M$ and length $L$ by applying the formula: I got this: However there are some issues that I don't get. If I ...
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18 views

Finding the melting point of a metal from enthalpy and entropy [closed]

I have been given this problem and honestly am not sure where to start. The question asks me to find the melting point of a material given some enthalpy $H$ and an entropy of its solid state as $S_s$ ...
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1answer
28 views

What does the area under a velocity displacement graph represent? [closed]

The question wants me to find acceleration through a velocity displacement graph. I found the equation to be $v(s)= 1/5s.$ I am not sure how to get the acceleration from this
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1answer
46 views

Understanding of a pendulum with (perpendicular) moving masses

I'm currently working on my thesis and am stuck on solving the last part of my work. The problematic system evolves around a rigid pendulum frame with two masses. This pendulum consists of a fixed ...
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1answer
29 views

Pressures in Bernoulli's equation

Let's say a pipe runs along the seafloor with velocity $v_1$, then exits at the surface with velocity $v_2$. I want to use Bernoulli's equation to find $v_2$, but I am confused about the pressures in ...
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0answers
26 views

Thermal physics [closed]

A combination of 0. 50 kg of water at 20.0°C, 0.600 kg of Silicon at 35.0°C and 0.300 kg of copper at 100°C is mixed in an opened container and allowed to come to thermal equilibrium. The amount of ...
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20 views

Thermal energy emitted by the Earth in a blackbody approximation [closed]

For the purpose of this exercise, we consider the Earth as a blackbody at a temperature of 300 K. a. Assuming that it is spherical with a radius equals to 6370 km, calculate the total amount energy ...
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34 views

Quantum mechanics: verifying that wavefunction satisfies eigenvalue equation [closed]

I have this homework problem: The problem is that I have no idea what do they want into the answering field? Do I have to take the second derivative of the wavefunction? I tried that, but it wasn't ...
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1answer
35 views

Energy released from destruction of an object [closed]

In the movie “Star Wars: A New Hope”, Luke Skywalker blows up the „Death Star‟. Assume that the „Death Star‟ is a perfectly spherical spaceship with uniform mass distribution. The mass of „Death Star‟ ...
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28 views

Power counting with cubic and quartic vertices (scalar quantum field theory) [closed]

I would like to find which feynman diagrams are divergent using the power counting thechnique with respect to this theory: I'm not sure that these relations are corrected: $$L=I-V1-V2+1$$ $$3V1+4V2=E+...
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1answer
30 views

Does the pressure in dynamic fluids depend on speed or cross sectional area?

I have encountered this question in my Giancoli Physics textbook, and I am pretty convinced that the answer should be A and E. But the solutions manual has neglected E as a potential answer and ...
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1answer
55 views

Centre of mass of a quarter of disc (doubt in my solution) [closed]

Can please anyone tell where am i wrong in this approach of solving this question.. The ans i am getting is (4 root2)/pi but ans is (4 root2)/3pi
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4answers
60 views

Some books write coulomb force is medium independent and some write it is medium dependent why so?

Some authors say coulomb force is medium independent others say it is medium dependent. I know value of universal gravitational constant does not depend on medium.But value of permittivity does depend ...
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4answers
67 views

Do object properties such as mass and dimension affect friction force on inclined surface?

If we have two blocks, first weighing $2 \text{ kg}$ with dimensions $10 \times 2$ and second weighting $4 \text{ kg}$ with dimensions $20 \times 2$, and place them on an inclined surface, would they ...
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1answer
41 views

General Method for Calculating Excluded Volume

In section 5.3 of Kardar's Statistical Physics of Particles, the van der Waals equation is given as: $[P+\frac{u_0 \Omega}{2}(\frac{N}{V})^2][V-\frac{N\Omega}{2}]=Nk_BT$ The van der Waals parameters ...
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1answer
25 views

How do I calculate the uncertainty of a fraction raised to a power? [closed]

What is the uncertainty of: $y=(\frac{a}{b})^{n}$ Would it be: $\Delta y = n (\frac{\Delta a}{a}+\frac{\Delta b}{b}) y $

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