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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2answers
44 views

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 ...
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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 ...
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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 ...
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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/...
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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$)~~\ge \frac{1}{2}mv^2~$...
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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 ...
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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 ...
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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 ...
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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.
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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 ...
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3answers
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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: ...
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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 ...
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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.
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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 ...
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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 ...
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2answers
131 views

Circuit - solve Kirchhoff's laws with determinant?

Here is an exercise from my textbook. ]1 At first I solve it by using Kirchhoff's laws directly and using complex impendance: $$U_{in}=\frac{1}{Cs}(i_1-i_2)+i_1R_1$$ $$0=R_2i_2+\frac{1}{Cs}i_2+\frac{...
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2answers
67 views

Two ships, one year apart, travelling from earth to a distant planet. What is the time difference of arrival? [closed]

If a ship set off at a significant percentage of the speed of light, and landed on a distant planet, and then a second ship set off a year or so later, what would the time distance be at the ...
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2answers
104 views

How do you correctly apply $a=v\cdot\text dv/\text ds$? [closed]

I know that $a=v\cdot\text dv/\text ds$ can be deduced by simple algebra and calculus and is correct. But once I was analyzing the motion of a ball projected straight up in free gravity. If I apply $...
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1answer
94 views

How does conservation of momentum apply to this billiard ball problem? [closed]

A billiard ball, initially at rest, is given a sharp impulse by a cue. The cue is held horizontally a distance $h$ above the centerline as in the figure below. The ball leaves the cue with a speed $V$ ...
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7answers
436 views

What is the difference between position, displacement, and distance traveled?

Suppose the question is somewhat like this: If $v=8-4t$ and the position at time $t= 0\ \rm s$ is $2\ \rm m$, find the distance traveled, displacement, and final position at $t=3\...
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0answers
36 views

An Interesting Physics Problem of Calculus [closed]

A skydiver of mass m=100 kg is making a delayed drop with an initial speed of $~v=0~$.Find the law by which the diver's speed varies before the parachute is opened if the air drag is proportional to ...
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1answer
40 views

Satallite orbiting the earth [closed]

I need help understanding a question from my physics book. It goes like this: a communications firm wants to place a satellite in orbit so that it is always directly above the earth’s 45th ...
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1answer
31 views

Force per unit area on conducting sheet in magnetic field [closed]

Question from I.E. Irodov (3.260) I’m having trouble with the (c) part because the external magnetic field should be towards the right to give such a result,hence the force on unit area ...
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0answers
35 views

Neutron mass fraction evolution: approximation

In Mukhanov's "Physical foundations of cosmology" on page 102 the author considers an equation for the evolution of the neutron mass fraction $X_{n}\equiv n_{n}/(n_{p}+n_{n})$: $$ \tag 1 \dot{X}_{n}(t)...
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1answer
65 views

Identity for the inverse metric tensor using its determinant

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

Expected value of Momentum in a square infinite well [closed]

Say I have a particle with mass $m$, in a potential infinite well centered at $x=0$ with length $d$ which wave function at $t= 0$ is represented by: $$\Psi(x)=\begin{cases} \frac{1}{\sqrt{2}}\left[\...
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1answer
31 views

What is $v(t)$ in a sliding conducting rail in a magnetic field?

This is problem 7.7c from David J. Griffiths - Introduction to Electrodynamics. A metal bar of mass $m$ slides frictionlessly on two parallel conducting rails a distance $l$ apart. A resistor $R$ ...
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1answer
60 views

How to prove that $\vec{E}$ is an intensive property?

In my homework I had a question to sort a few variables into intensive properties and extensive properties. I wrote that $\vec{E}$ (electric field) is an extensive property, thinking of a situation ...
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1answer
50 views

How many degrees of freedom does a spring pendulum have? [closed]

I've been looking at a spring pendulum system, but I'm not sure how many degrees of freedom it has.
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2answers
39 views

What is the direction of force acting on a current carrying conductor? [closed]

Let magnetic field be from left to right side of the screen and current be flowing from top to bottom part of the screen. Then the force acting on the conductor is out of the screen (towards the ...
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1answer
66 views

If we say “an object is at rest,” can we also say “the object is moving at a constant velocity?” [closed]

If we say "an object is at rest," can we also say "the object is moving at a constant velocity?" Of course, the constant velocity would be zero, so it's mathematically sound. However, the wording ...
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2answers
130 views

Trouble understanding Sakurai's calculation of $\exp\left(\frac{iS_Z\phi}{\hbar}\right) \;S_x \; \exp\left(\frac{-iS_Z\phi}{\hbar}\right)$

I'm having some trouble with a derivation in Sakurai's Modern Quantum Mechanics (specifically Derivation 1 on §3.2, p. 159), where he computes $$ \exp\left(\frac{iS_Z\phi}{\hbar}\right) \;S_x \; \exp\...
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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?
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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 ...
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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 ...
5
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1answer
91 views

What potentials have infinitely many bound states? [closed]

Some potentials have only finitely many bound states (the finite square and delta function are two good examples) Others have infinitely many bound states (for example the infinite square well and $1/...
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1answer
36 views

Relativistic beaming/ Aberration effect derivation

I'm researching applications of relativistic beaming and I want to derive a formula for the aberration effect but I am stuck (I am off by a factor of 1/c). Here's what I have: Consider a star in its ...
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2answers
41 views

Find the work done against the force

If there is a force $\mathbf F(x)=ax\hat i$ and an object is moving from $x_2>0$ to $x_1>0$ in the opposite direction of force. Then work could be calculated as follows $$\int_{x_2}^{x_1} -F(x)\...
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1answer
50 views

Friction in opposite directions on a rotating disc [closed]

A disc with radius R rotates at constant angular velocity $ω$. At time $t=0$ a person steps onto the disc at point $A$ and moves at constant velocity $V$ (with respect to the rotating framework) to ...
0
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1answer
47 views

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. ...
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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 ...
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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 ...