# 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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### Force acting on an object traveling upwards (ignoring air resistance) [closed]

Could someone please help explain to me which formula should be used for a question like this... A ball with the mass of 166.1 g is thrown vertically upwards with an initial velocity of 18.5 m/s. It ...
3answers
94 views

### Doubt in a question in Newton's Laws of Motion [closed]

The following question is from JEE (Joint Entrance Examination) 2007. As it is clear from the solution of the problem, they have included only the horizontal component of acceleration and not the ...
1answer
27 views

### Find the third side of the triangle when two sides are given in terms of vectors [closed]

If vector $\vec A= \hat i+ 2\hat j+ 4\hat k$ and $\vec B= 5\hat j$ represent the two sides of a triangle, then the third side of the triangle can have length equal to This can be solved easily by ...
0answers
50 views

### How do we move from formula of coupling constant alpha_strong(energy) to alpha_strong(distance). Just using energy=hc/distance?

How do we move from QCD strong interaction formula of coupling constant alpha_strong(energy) to the expression as a function of distance : alpha_strong(distance). Is it just by using energy=hc/...
1answer
69 views

### Total energy of a two particle system [closed]

Question: Velocity of center of mass of two particles is $~v~$ and the sum of the masses of two particles is $~m~$. Kinetic energy of the system is: A$)~~=\frac{1}{2}mv^2~$ B$)~~\ge \frac{1}{2}mv^2~$...
0answers
64 views

### Logic for Eq.(9.68) in Griffiths' “Intro. to Elementary Particles” (2nd edition)

Treating charged pion decay $\pi^{-} \rightarrow \ell^{-} + \bar{\nu}_{\ell}$ (where $\ell$ designates a lepton of first- or second-generation) by the representation of the figure below, Griffiths ...
0answers
64 views

### Volume element if given metric tensor in spherical coordinates

Given the spatial part of the metric tensor $$g^{\mu\nu} =\begin{bmatrix} g^{rr}&0&0\\ 0&r^{2}&0\\ 0&0&r^{2}sin^2 \theta \end{bmatrix} \tag{1}$$ What would be the ...
2answers
63 views

### Acceleration of the centre of mass of a hinged rod [closed]

This is a freely falling rod of mass m and length L hinged at one end. I have to find the acceleration of its centre of mass. 1) I don’t think its acceleration can be greater than g in any case as ...
0answers
49 views

### Cosmology and Fluid Dynamics

What will be the relation between the barotropic index (w) of fluid and the velocity (v) of the fluid ??? and please mention some citation or book.
2answers
50 views

### Energy Eigenvalue for SHO Classical and Quantum

Let's assume we are given a potential for coupled harmonic oscillator: $$U = \frac{k_1(x_1^2 +x_3^2)+k_2 x^2+k_3 (x_1x_2 + x_2x_3)}{2}$$ If I solve the normal modes of the oscillator I get the ...
3answers
74 views

### Differing results from different conservation laws

I am currently studying for the GRE Physics subject test by working through published past tests. My question is about problem 44 from the test GR8677: $44.$ A uniform stick of length $L$ and ...
0answers
23 views

### Salt concentration in flowing water

A basin contains $N_s(t)$ moles of salt dissolved in $N_w(t)$ moles of water. The basin receives fresh water at a constant rate $\Omega_w^{in}$. This water is assumed to be thoroughly mixed in the ...
0answers
23 views

### Calculate viscous damping coefficient given force

With a force metre I recorded the force vs time of a spring with a disk on the end in water, experiencing viscous damping, during damped oscillatory motion. I pulled the disk to the bottom of the ...
1answer
63 views

### Why there are the hyperbolic (not harmonic) functions in Rindler coordinates

Usually the Rindler coordinate transform is written as $$T = \frac{1}{a} \sinh(at) \tag{1}$$ $$X = \frac{1}{a} \cosh(at) \tag{2}$$ where $a$ is the uniform acceleration. The transforms lead to the ...
0answers
53 views

### Problem on springs [closed]

(ans: D) I have tried the problem by finding relation between extensions of the springs which comes out to be F/3k for the upper and lower spring and 2F/3k for the middle two. And then i get stuck as ...
1answer
44 views

### Does stacking two magnets together increase the magnetic strength?

Just wondering if adding two (or more) identical magnets together increases their magnetic strength (in Tesla) as I am doing a physics write-up on the Lorentz force (Fleming's left-hand rule) as I ...
2answers
46 views

### relative acceleration of ball in a train [closed]

A boy is standing in a train with a ball in his hand. The train is having a constant acceleration equal to x m/s^2. While still in train he throws the ball with a constant velocity of 20 m/s at an ...
3answers
92 views

### What helps us carry things around? [closed]

Say I move from point A to point B. I carry an apple in my hand. What causes the apple to move from point A to B? In other words, what force is responsible for keeping the apple stuck to my hand and ...
0answers
10 views

### Algebra Word problem [migrated]

Before I posted this question I have researched it with no results that helped me. The graph below shows: • the two existing curved roads are represented by a rectangular hyperbola with the equation: ...
1answer
105 views

### Hamilton's equation of motion with other momentum

I wrote here a problem couple days ago. I figured out what was the problem there, but now it made another problem. Sorry for similiar question. I'm trying to draw phase portrait for my ODE and for my ...
1answer
179 views

### How much dark energy will fit in an average cup of coffee? [closed]

I am looking for the answer in Joules for obvious reasons.
0answers
18 views

### Why does the ion and electron currents saturate in Langmuir probes?

From the I-V characteristics of the Langmuir probes used in Plasma diagnostics, we can calculate the plasma density, temperature, etc from the ion and electron saturation currents. But why does the ...
0answers
68 views

### Maximum range of a projectile (launched from the cave) [closed]

A cannon located under a cave forms an alpha angle with the horizontal launching a series of projectiles. The cannon is at point A, at a distance L from the base of the cave (point B). If the initial ...
2answers
131 views

1answer
65 views

### Identity for the inverse metric tensor using its determinant

I would like to prove this relation: $$g^{\mu\nu} = \frac{1}{3!} \frac{1}{g} \epsilon^{\mu\rho\sigma\kappa}\epsilon^{\nu\alpha\beta\gamma} g_{\rho\alpha} g_{\sigma\beta} g_{\kappa\gamma}, \tag{1}$$ ...
3answers
56 views

1answer
53 views

### Number operator - annihilation operator commutation

Is there a rigorous way to prove that $$(N+1)^{-1/2} a = a N^{-1/2}$$ where $a$ is a bosonic annihilation operator and $N=a^\dagger a$ is the corresponding number operator?
1answer
29 views

### Potential energy of an object (with non-negligible size compared to distance from ground level)

Let's say I have a cylindrical water tank (with area $A$ and height $h$), and the bottom of the tank is $H$ meter from the ground. So what is the potential energy of the water tank? If the $h$ is ...
2answers
57 views

### Possible mistake in the solutions? [closed]

This is from Kleppner's introduction to mechanics and I've been having trouble making sense of the solution in the solution manual for quite a while and I've concluded that its wrong but I need some ...
1answer
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1answer
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### Unitary Transformation of an Interfering Beam Splitter

I was reading this research paper Quantum interference enables constant time quantum information processing and was confused by one particular expression involving the Hamiltonian of a beam splitter. ...
0answers
56 views

### Mechanics: how to find the generalized force (specific case)?

I know this may seem like a homework problem at first, but please bear with me... In this problem, we have two masses sliding without friction in a horizontal and vertical track, connected by a ...
1answer
32 views

### Deriving terminal velocity

In my book (Young and Freedman's University Physics) they derive terminal velocity where and use these steps: ...we must find the relationship between velocity and time during the interval before ...