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2
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2answers
69 views

Stability of equilibrium points

For a spinning top, the linearised equation in the angle $\theta$ when the top is spinning about its axis of symmetry, which is vertical, is of the form ...
1
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1answer
64 views

A question of BRST symmetry of bosonic string theory

This question relates to this post I tried to verify Eq. (4.2.7) in Polchinski's string theory book vol I p. 127 but I miserably miss a sign $$ \delta_B (b_A F^A) = i \epsilon (S_2 + S_3) ...
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votes
3answers
738 views

Work, Energy & Power - Body slides down a hemisphere

A small body of mass $m$ slides down from the top of a hemisphere of radius $r$. There is no friction between the surface of the block and the hemisphere. The height at which the body loses contact ...
5
votes
1answer
201 views

Walking along a moving train, we make 18 steps. Opposite: 11. How long is the train?

A man walks in the same direction as a slowly moving train ($v_{man} > v_{train}$). He counts the train to be 18 steps long. Then he turns around and counts the train to be 11 steps long. ...
2
votes
1answer
112 views

Does a 27 hp engine output the same amount of energy as lifting a 1 ton stone block almost 3 meters per second?

I’m trying to get a sense of how much energy a 27 horsepower engine outputs. 27 hp $=$ 20 133 watts (joules/second). Potential energy can be calculated as $E = mgh$ where $g = ~9.8\ m/s^2$ on earth. ...
2
votes
3answers
275 views

Problem on apparent height of postage stamp underneath paperweight

A postage stamp is placed on a surface and a glass cube of refractive index $1.5$ is placed over it. When observed through the cube, the stamp appears at a height of $1.5cm$ from the bottom of the ...
0
votes
1answer
71 views

Find the distance from the initial location [closed]

Sing Huat drives a car with initial speed 30 km/h and acceleration 2 km/h2 toward Tee, whose displacement is 200 m away from him. At the same time, Tee drives another car toward Sing Huat with ...
1
vote
1answer
250 views

Variable Tension in the string [closed]

A body of mass $m$ is hanging with a string having linear mass density $\lambda$. What is the tension at point $A$ as shown in the figure. I am aware of the scenarios in which string is ...
0
votes
3answers
787 views

Calculating acceleration function for given time, distance, initial velocity [closed]

An object has an initial velocity of v and should stop in d meters, in t seconds where v*t >= d. I can predict that this acceleration won't be constant but it is a function of time and this problem ...
0
votes
1answer
123 views

Circular motion [closed]

A small block slides down from the top of a hemisphere of radius $r$. It is assumed that there is no friction between the block and the hemisphere. At what height $h$ will be the block lose contact ...
1
vote
1answer
129 views

Relative acceleration with pullys

I have tried this question every way I can think but in the equation for particle $L$ $g$ cancels every time. Could someone show me how to do it correctly or tell me what I am doing wrong. Thanks, ...
0
votes
1answer
166 views

Free body diagram of rod in sphere

I was finding the free body diagram part of dynamics quite easy until I found this question , Here's how it goes : A rod AB is placed inside a spherical shell, whose inside surface is rough. Draw ...
-1
votes
2answers
53 views

Does a 27 hp engine output the same amount of energy as lifting a 1 ton stoneblock almost 3 meters per second? [duplicate]

I'm trying to get a sense of how much energy a $27$ horsepower engine outputs. $$27 \mathrm{hp} = 20133\mathrm{W}$$ Potential energy can be calculated as $$E = mgh$$ where $g ...
-1
votes
1answer
101 views

Some complex-number manipulation when calculating coefficients

I am going through Sakurai's quantum mechanics, and at one point the solution to a problem says: $(\sin(\beta)\cos(\alpha)-i\sin(\beta)\sin(\alpha))b+\cos(\beta)a=a$ ...
0
votes
1answer
104 views

Derivation of Pressure/Kinetic Therory problem involving hole in box

A box of volume $V_0$ has a small hole of area $A_0$. The box initially has one mole of an ideal gas at $t = 0$, which is at an initial temperature $T (t = 0)$. Find the rate of energy flow through ...
0
votes
1answer
368 views

Rigid bar suspended by two ropes, tension of first rope after second rope is cut?

This is from a practice exam, I've been sitting here thinking about it for over an hour and can't convince myself of an answer, or write down any relevant exact equations. A bar of uniform density ...
0
votes
1answer
307 views

Equation for the equipotential lines? [closed]

What is the equation for the equipotential lines in $x$-$y$ plane for a dipole oriented along the $x$ axis?
1
vote
1answer
164 views

Beads sliding on a hoop

Two particles, $P_1$ and $P_2$, of equal masses $m$ are linked by a spring of stiffness $k$ and natural length $a$. They are sliding freely without friction along a horizontal fixed hoop of radius ...
0
votes
1answer
250 views

General Solution of Mechanics Problem

I had a homework problem that Given velocity, $v^2(t)=\frac{K}{x(t)}$, where $x(t)$ is distance, find $v$ as a function of $t$. Of course if we assume a positive root, it is easy but what if ...
1
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0answers
875 views

Equations of motion for a pendulum and spring system

The question is available here: I've modeled the building as a rod on a torsional spring (with a pendulum hanging from the top). $\phi$ is the angle from the centre for the pendulum and $\theta$ ...
0
votes
0answers
26 views

How to calculate independent componets of tensor for crystal symmetry?

I have a question as title says. For a formula $j_i = \beta_{ijl} e_j e_l^*$, where $i$, $j$, $k$ are coordinate and $\beta_{ijk}$ is the tensor, if I know the tensor should be satisfied for crystal ...
2
votes
1answer
170 views

Distinction between Larmor frequency and Rabi frequency

Wikipedia said "In the context of a nuclear magnetic resonance experiment, the Rabi frequency is the nutation frequency of a sample's net nuclear magnetization vector about a radiofrequency field. ...
3
votes
1answer
134 views

Equations of motion of displacement field

We have an action: $$S[\boldsymbol{u}] = \frac{1}{2} \int dt \int d^3x \left\{ \mu (\frac{\partial u_{i}}{\partial t})^{2} - \nu (u_{ii})^{2} - \rho(u_{ij})^{2}\right\} $$ Where $u_{ij} = ...
1
vote
1answer
188 views

X-ray and neutron powder diffraction: peak broadening due to crystal size

When analysing powder diffraction patterns, the broadening of peaks can be used to estimate crystal sizes. Smaller crystal size gives larger broadening according to the Scherrer equation: $$ \beta = ...
3
votes
2answers
148 views

Rocket propelled by a giant monochromatic laser

I am preparing for my quals and stumbled across the following problem, and although it only requires undergraduate-level physics, I feel I can't piece everything together. "A rocket of mass $m_0$ is ...
2
votes
2answers
884 views

Angular Velocity expressed via Euler Angles

On the top of the fourth page from here, the author trivially derives the components of angular velocity, expressed via Euler angles of the system. I fail to understand how the components of angular ...
0
votes
1answer
84 views

3D billiard with no gravity nor air drag

If I have a projectile shot in a vacuum-box that has no gravity or wind resistance inside it (lets say the box is 1000 units tall and 1000 units wide), with the only rule being that the projectile ...
0
votes
1answer
153 views

Projectile maximum height [closed]

How can I determine the needed initial velocity to make a 2d wind resistance free projectile (in computer simulation) reach maximum height at a certain x distance away, with launch position and target ...
0
votes
0answers
292 views

Is it possible to solve a 2D relative motion question using components of relative velocity?

This is a question based on concepts of two dimensional motion . Here's how the question is: A plank A is floating in air, gravity has no effect on it (See its coordinates in the figure attached). ...
2
votes
1answer
162 views

Is there a way to increase photon energy by decreasing its wavelength?

Can I decrease a photon's wavelength by a medium or a vacuum? Are there other ways of decreasing the wavelength?
0
votes
2answers
173 views

What type of electromagnetic radiation strikes the Earth's surface the most?

If you can could you lists the types of light from the greatest amount to the least amount (Ex: Visible, Infrared, Violet).
1
vote
2answers
255 views

Electric potential due to circular disk

Relevant diagram is available here. The circular disk of radius $a$ lies in the $xy$ plane and carries surface charge density of $\sigma (s, \phi) = s^{2}cos\phi $, where $(s,\phi)$ are in ...
1
vote
1answer
424 views

Magnifying factors of multiple lenses (closely packed)

Well the following question I really struggle to find an answer A thin lens creates an image of an object with magnification -3. A second identical lens is positioned very close to the first ...
2
votes
1answer
68 views

How to obtain the constant $a^g$ in Eq.(2.7.19) in Polchinski's string theory book

Excuse me, I have calculated $a^g$ a lot of times, using the relation between $:\;:$ and ${}^{{}_\circ}_{{}^\circ} \; {}^{{}_\circ}_{{}^\circ}$. But I can't get the same result with the book. It is ...
1
vote
1answer
2k views

How to find the direction of the magnetic field for an infinite conducting wire?

We've got two long straight wires carrying current of 5A and placed along x and y axis respectively current flows in direction of positive axes we have to find magnetic field at a) (1 m,1 m) b) (-1 ...
0
votes
1answer
749 views

Work done on a moving particle in electric field

This is one of the "fast answer" exercises I've been given to train (should be answerable in around 6-7 minutes). I can only think of a very long-round way to solve this. The question is as following: ...
3
votes
1answer
809 views

Equivalent resistance in ladder circuit

I have stumbled upon a given question I really have a hard time to solve. Basically I need to find an equivalent resistance in some form of "ladder" configuration. Where the chain is an infinite ...
2
votes
2answers
2k views

Calculating the field of an infinite flat sheet of charge using the superposition principle

I am trying to calculate the field of an infinite flat sheet of charge (a plain with uniform charge density $\sigma$) using the superposition principle. I know that the field of an infinite line ...
2
votes
1answer
341 views

How to derive the metric for a 2-sphere

I have a question in Polchinski's string theory vol I p 167. It is said For example, $$ds^2= \frac{ 4 r^2 dz d \bar{z} }{(1+ z \bar{z})^2} = \frac{ 4 r^2 du d\bar{u}}{ (1+ z \bar{z})^2} ...
1
vote
0answers
56 views

Transformation of $t=0$ line in moving frame of reference

How does $t=0$ transform into $t - vx/c^2 = 0$ if a frame of reference is moving as given in here? It seems that the relativistic transformation is given by $$ \begin{bmatrix} x' \\ ct' ...
2
votes
1answer
99 views

Average Velocity [closed]

A car travels 100 miles in 2 hours, it then completes the return leg of the journey. How fast must it travel on the return leg to average 100mph over the total journey. My thoughts on this are that ...
1
vote
0answers
465 views

Torque of a winch with pulleys [closed]

I'm working on a project that involves using a remote-controlled electric winch to raise and lower my bicycle using a pulley system. The problem is that I don't know how much torque will be required ...
0
votes
0answers
33 views

Quantum tunelling problem - got a weird imaginary ratio in the end

1. The problem statement, all variables and given/known data Beam of electrons with energy $10eV$ hits the potential step ($8eV$ high and $0.5nm$ wide). How much of the current is transmitted? ...
0
votes
1answer
111 views

Obtaining velocity or acceleration vector of a point on a rigid body?

If I have a cube that is moving at a velocity of $v$ and spinning at an angular velocity of $\omega$, how can I determine the instantaneous velocity vector of one of the vertices of the cube? What if ...
1
vote
1answer
140 views

Torque on a Box

I think I'm missing something with torques. I seem to have gotten myself confused. I have a box that's centered at ( 0 , 0 , 0 ) with length ( $x$ dimension ) = 1 , width ( $y$ dimension ) = 0.25, ...
0
votes
1answer
99 views

Moving electron - finding the wavefunction

On our modern physics class my professor did a problem: Write down a wavefunction of an electron which is moving from left to right and has an energy $100\text{ eV}$. At first i said: "Oh i know ...
0
votes
1answer
118 views

Kinematics problem

I'm on earth and we have two spaceships $A,B$. They can instantaneously accelerate to certain velocities $v_A,v_B$. We want to travel to another planet which is $\Delta x$ lightseconds away, and we ...
2
votes
2answers
560 views

Wavefunction as a combination of two stationary states - how to find those states?

Lets say we have a particle in a infinite square well which has a wavefunction like this ($A$ is some constant and $d$ is the width of the well): \begin{align} A\left[ \sin \left(\frac{2 \pi ...
0
votes
2answers
984 views

Finite potential well problem - calculating the ground state

1. The problem statement, all variables and given/known data Electron of is in a 1-D potential well of depth $20eV$ width $d=0.2 nm$ in his ground state $N=1$. What is the energy of the ground ...
1
vote
2answers
593 views

Projectile Motion Question involving a ball and a ramp inclined at an angle

The question is to finde the initial horizontal velocity of the ball at end of the ramp, where it is released. I know how to do this using gravitational potential energy and kinetic energy ...