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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.

2
votes
3answers
85 views

Does gravity get stronger when you climb a mountain?

As stated in the question title, what happens to the strength of the gravitational field (or equivalently, your weight) as you climb a hill or mountain? Would a weighing scale show that you were ...
0
votes
0answers
17 views

How to solve the integral below? [migrated]

$\int_{b}^{\infty} \frac{\sqrt{x^2 - b^2}}{e^{cx} - 1} \; dx$ The constants b and c are real and greater than zero.
-1
votes
0answers
29 views

Current Flowing in Two Near Inductors

While I was studying the topics of Inductance, I have come across a question about two inductors with both the self inductance. Their induced emfs are given. We are asked to find the inductor with the ...
0
votes
0answers
22 views

Covariant divergence in GR [duplicate]

In Carroll's Spacetime and Geometry (§3.2) I found $$\nabla_\mu V^\mu =\partial_\mu V^\mu + \Gamma^\mu_{\mu\sigma}V^\sigma =\frac{1}{\sqrt{\left|g\right|}}\partial_\mu \left(\sqrt{\left|g\right|}V^\mu\...
1
vote
0answers
29 views

Two ways to calculate imaginary part of vacuum polarization in pseudoscalar Yukawa theory

I consider vacuum polarization in pseudoscalr Yukawaw theory with interaction $ig\bar{\psi}\gamma^5\phi\psi$. The expression for diagram is $$i\Pi(k^2)=-g^2\int\frac{d^4p}{(2\pi)^4}\frac{\mathrm{Tr}[i\...
3
votes
1answer
32 views

Different approch on Order of magnitude confusion [closed]

My problem: How many orders of magnitude larger is the sun $(1.99$ x $10^{30} kg)$ than the moon $(7.32$ x $10^{22} kg)$. Justification 1: So according to my teacher, we can do this question by ...
0
votes
1answer
63 views

How to integrate pressure over a sphere?

if I had a function for pressure $P(y)$ dependent on $y$ (vertical position) and I had a sphere in a stationary position, how would I integrate the pressure differential over the surface of the sphere ...
0
votes
1answer
46 views

Van der Waals constant $b$ (real gas) chemical form. only

http://www2.ucdsb.on.ca/tiss/stretton/database/van_der_waals_constants.html I don't understand how to calculate exact constant - b, given only the chemical formula and nothing else. Q: T || F --- ...
1
vote
1answer
33 views

Predicting spectral lines

In the spectrum of some hydrogen-like ions the three lines are known, which belong to the same series and have the wavelengths 992, 1085, 1215 angstroms. What other lines can be predicted? I don't ...
0
votes
0answers
55 views

Does the mass affect the speed if friction is 0

A block $m_1$ strikes another stationary block $m_3$ inelastically . Another block $m_2$ is kept on $m_3$.Neglect the friction Between all contacting surfaces. Since $m_2$ is kept on $m_3$ and all the ...
1
vote
1answer
63 views

Weight Distribution of a Heap of Logs

Suppose that you have a heap of logs. Each log is the same length $l$, the same mass $r$ , and the same radius $r$. For simplification, their rotational inertia is $I=\frac{1}{2}mr^2$, their ...
0
votes
0answers
22 views

Charging two spheres by induction n times

There is a conducting sphere $S_1$ of radius 'r' mounted on an insulating handle. The sphere is given a charge Q. Another uncharged conducting sphere $S_2$ of radius R mounted on an insulating handle ...
0
votes
0answers
17 views

Application of Kepler's law [duplicate]

Suppose two equal and opposite charges are released from a relative separation of $d$ in free space. How long would it take before they collide? I believe we can use Kepler's law of T² being ...
0
votes
0answers
36 views

Derivation of classical Fokker-Planck equation

For Fokker-Planck equation in Ornstein-Uhlenbeck process, we have $$\frac{\partial p(x,t)}{\partial t}=\gamma\frac{\partial xp(x,t)}{\partial x}+D\frac{\partial^2p(x,t)}{\partial x^2}$$ However I ...
1
vote
1answer
57 views

Collision of rotating sticks

Q: Two identical uniform sticks are rotating about their stationary centers with equal angular speeds. The vertical stick is slowly raised until its top end collides with the center of the horizontal ...
1
vote
1answer
38 views

Two different values for two different methods of calculating spring constant [closed]

I'm given the question: "An oscillator consists of a block of mass .5 kg connected to a spring. When set into oscillation with amplitude .35 m, the oscillator repeats its motion every .5 seconds. Find ...
0
votes
1answer
94 views

Exponential of the Pauli matrices [closed]

My job is to prove: $$\exp(i\theta \vec{v} \cdot \vec{ \sigma })=\cos(\theta)I+i\sin(\theta)\vec{v} \cdot \vec{ \sigma }$$ where $\theta \in \mathbb{R}$ and $\vec{v} \cdot \vec{ \sigma }=\Sigma^3_{i=...
2
votes
2answers
122 views

Spin of 3 particles

I am trying to decompose the isospins of a three particle state using Clebsch-Gordan coefficients such as: $|1,1\rangle \otimes |1/2,-1/2\rangle \otimes |1,0\rangle$ Decomposing the first two ...
1
vote
0answers
43 views

Determining Electric Potential due to a line of nonuniform charge density [closed]

A rod of length $L$ lies along the x axis with its left end at the origin. It has a non uniform charge density $\lambda = \alpha x$ where $\alpha$ is a positive constant. Calculate the electric ...
3
votes
3answers
61 views

Torque due to friction on a series of disks

Recently I was looking at two situations involving friction and torque. The first situation seemed pretty straightforward at first. A disk of mass $m$ and radius $r$, with a coefficient of static ...
0
votes
3answers
50 views

Velocity and theta sign [closed]

I'm doing the following problem: A castle on a cliff has a cannon 300m above sea level. The cannon can shoot a 10kg iron ball with a velocity of 400 m/s . If the cannon is raised to an angle ...
0
votes
3answers
53 views

Brightness of lamp

Brightness of lamp (power) depends on two factors: Current which flows through the lamp. voltage (p.d) across the lamp. In the figure: When the variable resistance increases, what happens to the ...
1
vote
1answer
51 views

Voltage between two points in circuit

Calculate the voltage between terminals a and b. I am confused about a problem. I've tried to solve this using the second Kirchoff's rule, but my solution is equal to 0. What am doing wrong? E=5V R1=...
0
votes
0answers
36 views

Total charge in electron cloud in a hydrogen atom

Essentially, the problem I'm trying to solve is The potential at a distance $r$ from the nucleus that is generated by an electron in a hydrogen atom is given by: $$V(r) = \frac{q}{4\pi\...
1
vote
1answer
50 views

Calculate the length of the string if it is vibrating at the 4th harmonic [closed]

The statement is as follows: The function that describes a standing wave on a fixed string at both ends is given by $y(x, t) = 2A \sin (kx) \cos (\omega t)$, where $A = 1.5\ \mathrm{cm}$, $k = 0.3\ ...
1
vote
1answer
33 views

Problem on measurement of spin of an electron

I came across a problem which reads: "An electron is initially found to have z-component of spin=+h/4π. Then a measurement of component of its spin along x-direction is carried out but the result is ...
0
votes
1answer
79 views

Bloch sphere representation of an eigenvector

I'm trying to work through a problem that wants me to determine the Bloch sphere representation of the eigenvectors of $\sigma_{z}$. I'm working in bra-ket notation so these would be $\ v_{+} = |0\...
-1
votes
0answers
19 views

Image produced by unknown lens

Is it possible for an unknown lens to produce a real and magnified image on the side opposite the object? [Background] In a question I was given an unknown lens with a focal length of 20cm. The ...
1
vote
2answers
99 views

Show Solution to Hamilton's Equations are Given by Circular Paths

I am asked to compute Hamilton's equations and check that the solutions to said equations are circular paths, centered at the origin, with angular velocity $\xi \in R^3$. The Hamiltonian is given by $...
1
vote
1answer
30 views

Pion decaying energy

The question is: A pion decays into a muon and a neutrino (which is almost massless, so we’ll take it to have a mass of zero). If the pion is initially at rest, find the energy of the outgoing ...
0
votes
1answer
31 views

Derivation of acceleration and tension of pulley system [closed]

On this website I am considering the question that goes along with figure 30. I am going to assume downwards is negative and rightwards is positive (not to confuse upwards as the website says). The ...
0
votes
1answer
33 views

Is the force from an engine constant as a vehicle reaches top speed?

I've come across a textbook question and I've got myself confused by it although it seems like it should be simple. The van accelerates with a (supposedly) constant resistance force up to its top ...
-1
votes
0answers
22 views

Deriving gravitational acceleration $GM/r^2$ from the Schwarzschild metric [duplicate]

Reposting this at a more active time to hopefully get an answer. I am supposed to derive the newtonian equation for gravitational acceleration ($-GM/r^2$) from the Schwarzschild metric $$ds=-(1-\frac{...
0
votes
1answer
49 views

Deriving gravitational acceleration from the Schwarzschild metric

I am supposed to derive the newtonian equation for gravitational acceleration ($-GM/r^2$) from the Schwarzschild metric $$ds=-(1-\frac{r_s}{r})c^2dt+(1+\frac{r_s}{r})^{-1}dr+0$$ where $$r_s=\frac{2GM}{...
-1
votes
1answer
31 views

How can you solve for acceleration and time that a vehicle takes to stop given only the speed, distance, and crumple length? [closed]

Here is the problem: A car initially has a speed of 115km/h. Find its acceleration and the time taken to stop given that: (a) it brakes to a stop in 64.0 m; (b) it crashes head-on into a barrier and ...
0
votes
2answers
29 views

What happens to a system of capacitors when a dielectric is inserted into one of them?

sorry for my English. While doing some homework I've stumbled upon this "circuit": the system is connected to the same potential difference through a generator that is connected to points A and B. ...
0
votes
0answers
48 views

How to find density of a wire when we know information of it in polar form

We know that the wire has the "path" in the shape of the polar graph $$r = \theta, \quad 0 \leq \theta \leq \pi/2 $$ and we know at point $(\theta,\theta)$ the density of the wire is $2\theta$. I ...
0
votes
1answer
53 views

Does entropy increase with heat flow?

In an exam, I had a scenario where 2 bodies with different temperatures were put together and over time their temperatures mixed and eventually became uniform. My intuition tells me that as a result, ...
-2
votes
0answers
48 views

Well , shouldn't we know the direction of current and magnetic field also to get the answer? [duplicate]

A conducting circular loop of radius r carries a constant current I . It is placed in a uniform magnetic field B perpendicular to the plane of the loop.Find the magnetic force acting on the loop.
1
vote
0answers
54 views

Time Dilation and Particle Decay

I am teaching myself astronomy and I'm working on a basic problem regarding time dilation around black holes. The question is basically this: if a neutron were ejected from a nucleus at a distance of ...
-1
votes
2answers
41 views

A question on Work and energy in which a body is taken up a hill by a tangential force

The height of the hill is h and length of it's base is l.A force F which is always tangential is pulling the body up the hill. The friction coefficient between hill and body is $\mu$.The body is being ...
0
votes
1answer
55 views

Differential tetrahedron, area of slanted face?

The above diagram shows a cuboid containing a tetrahedron OABC. When the cuboid represents a differential volume element all sides are small in size. With the length of line $OA$ denoted by $|OA|$ ...
1
vote
0answers
38 views

Can I solve this electric forces question by integrating velocity with respect to displacement?

In my physics tutorial for electricity, there was one question in particular that struck me as interesting. It is as follows: One particle has a mass of $3.00\times10^{-3}$ kg and a charge of $+8....
-3
votes
1answer
38 views

Calculate the voltage between terminals a and b [closed]

Calculate the voltage between terminals a and b before and after connecting the external resistance R, then calculate absolute and relative difference of these voltages.
0
votes
1answer
42 views

Proving identity $\DeclareMathOperator{\Tr}{Tr} \Tr\left[\gamma^{\mu}\gamma^{\nu}\right] = 4 \eta^{\mu\nu}$

In the lecture notes accompanying a course I'm following, it is stated that $$\DeclareMathOperator{\Tr}{Tr} \Tr\left[\gamma^{\mu}\gamma^{\nu}\right] = 4 \eta^{\mu\nu} $$ Yet when I try to prove this,...
0
votes
1answer
49 views

Mathematical segmentation of an accelerating body and the resultant torques

My question is inspired by problems of the following kind: To solve such problems, what one essentially does is mathematically 'segment' the rod/body at a distance x from the pivot, and then write ...
0
votes
0answers
45 views

Matrix elements of stress-energy tensor $\langle q | T^{\mu\nu} |q\rangle$ in QFT?

In many QFTs we can define a stress tensor $T^{\mu\nu}$. What is the matrix element of $T^{\mu\nu}$ in momentum eigenstates? For instance, consider $$\langle q | T^{\mu\nu} |q\rangle$$ in QCD, ...
0
votes
0answers
96 views

Elongation of rod in two cases

Case 1: Suppose there is a rod hung vertically from the ceiling. It experiences gravitational force W (its weight).It's Young's Modulus is $Y$. Now I know that the end connected to the ceiling ...
1
vote
1answer
62 views

Two black holes colliding (classical mechanics)

I had this question come up in my exam where two identical black holes are in orbit around each other. There is a loss of energy via gravitational waves : $$\frac{d E}{d t} = kr^4\omega^6$$ where $k$ ...
0
votes
0answers
32 views

Volume within equi-energetic surface of a classical harmonic oscillator in microcanonical ensemble

$$ V(E) = \int_{H\leq E} d\mu = \int_\Gamma d\mu\, \Theta\bigl(E-H(q,p)\bigr) . $$ To compute the volume within the equinergetic surface in the microcanonical ensamble, we use the formula above, ...