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A wonky gravitational potential and its critical points

I have tough problem I am not sure how to solve: For this question, we are confined to a plane. Consider a gravitational field that is proportional to $\frac{1}{r^3}$ instead of $\frac{1}{r^2}$, and ...
4
votes
1answer
1k views

Hooke's Law question

I have the following question to answer: a force of160 N stretches a spring 0.050m from its equilibrium position. A. what is the spring constant of the spring? The equation for Hooke's Law in my ...
4
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1answer
106 views

Continuity domain for momentum operator

I know this is essentially a mathematic question, but I received no answer on math SE. Moreover it has a direct application in physics, so I thought to ask this here too. The momentum operator in one ...
4
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3answers
169 views

Calculating the solar power hitting Earth

I'm trying to calculate the amount of power from the sun hitting the earth, but I am getting a number which is off by a factor of ~4. I calculate the "area" of the earth, as seen from the sun, and ...
4
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1answer
113 views

Integrating Radial Vector Fields

Given a integral $$\int_vd^3{r} \;\vec{r}\;\rho(r)$$ and How do you convert it to spherical coordinate system, noting that $\rho(r)$ is indeed as it is without vector, i.e. it is spherically symmetric ...
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2answers
952 views

Electrostatic Pressure Concept

There was a Question bothering me. I tried solving it But couldn't So I finally went up to my teacher asked him for help . He told me that there was a formula for Electrostatic pressure ...
4
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1answer
380 views

QED BRST Symmetry

This is a homework problem that I am confused about because I thought I knew how to solve the problem, but I'm not getting the result I should. I'll simply write the problem verbatim: "Consider QED ...
4
votes
1answer
407 views

Plotting a SHO in matlab [closed]

I have no prior experience of using matlab. My teacher want me to solve this question. I have been trying for a couple of hours now with no luck, please help! The mass of 100 g hanging in a spring ...
4
votes
1answer
437 views

Electric Potential

A nonuniform linear charge distribution given by λ = bx, where b is a constant, is located along an x axis from x = 0 to x = L. What is the electric potential at a point on the y axis? Set potential ...
4
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3answers
106 views

Using 2D position, velocity, and mass to determine the parametric position equations for an orbiting body

I have a gravity-related question. I am programming an orbit simulator. I have everything up and running, but I would like to render the smaller body's orbital path (the larger body is fixed). To do ...
4
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1answer
187 views

Constraints of massive relativistic point particle in hamiltonian mechanics

I try to understand constructing of Hamiltonian mechanics with constraints. I decided to start with the simple case: free relativistic particle. I've constructed hamiltonian with constraint: ...
4
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2answers
162 views

Weight registered of a falling chain

Let's say I have a metallic chain. Suppose I hold one of its tip of in my hand let the chain hang freely downward such that the other tip touches a weighing scale. At this point, with me holding the ...
4
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2answers
239 views

Calculating an expression for the trace of generators of two Lie algebra

Suppose we have $$[Q^a,Q^b]=if^c_{ab}Q^c$$ where Q's are generators of a Lie algebra associated a SU(N) group. So Q's are traceless. Also we have $$[P^a,P^b]=0$$ where P's are generators of a Lie ...
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2answers
145 views

Vector potential

I have difficulty understanding the following vector calculus example. Text can be found here. It is the 5th Q&A -- starting with equation (31.1035).It concerns finding the vector potential of a ...
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votes
1answer
671 views

Frictional force on a rope wrapped around a drum

So there's a rope wrapped around a circular drum, subtending an angle $\theta$. A large force, $T_A$, pulls in in one direction, and a much smaller force $T_B$ pulls in in another direction. The ...
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votes
3answers
312 views

How can a vertical force cause motion at an angle?

I just started learning physics 3 days ago and am having trouble understanding what I am doing wrong. Can someone please explain my error(s)? Thanks! We have a 1kg object on a plane at a 30 degree ...
4
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2answers
285 views

What was the muzzle velocity of a home made gun launch strait in the air if air time was 8.2sec?

I built a potato gun and wanted to calculate the muzzle velocity. I remember from physics that I could run the numbers by calculating time from launch until landing. After pointing strait into the air ...
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6answers
4k views

Velocity vs Time Bounce

Could someone please explain the trajectory of the ball that is bouncing in this picture... The vertical component of the velocity of a bouncing ball is shown in the graph below. The positive Y ...
4
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2answers
232 views

Calculating the period of a quasi-circular orbit

In solving an exercise I had to find the equation of the quasi-circular orbits of an object with the potential $V(r)=-\alpha r^{-1-\eta}$ and I expressed it as: $$r(\phi)=\frac{r_c}{1+\epsilon ...
4
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2answers
110 views

Balmer lines and their positions

I have two stars, both of which have Balmer lines at the same wavelength positions. The depths of the Balmer lines on each star are different, and the stars are different as well. Why does this ...
4
votes
4answers
730 views

What identifies an action-reaction pair of forces?

This is a question on a worksheet that I'm giving to a student: A man of weight $W$ steps into the lift. The lift then moves downwards with a constant speed. If $R$ represents the force acting on ...
4
votes
2answers
540 views

Deriving Birkhoff's Theorem

I am trying to derive Birkhoff's theorem in GR as an exercise: a spherically symmetric gravitational field is static in the vacuum area. I managed to prove that $g_{00}$ is independent of t in the ...
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4answers
972 views

Example in the book: A simple accelerometer

A simple accelerometer You tape one end of a piece of string to the ceiling light of your car and hang a key with mass m to the other end (Figure 5.7). A protractor taped to the light allows you ...
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3answers
247 views

What does it mean if a = g in this situation?

I basically solved this problem, but I am unsure what the final equation actually means. Write an expression for solving the mass of block C if mass B moves to the right with an acceleration ...
4
votes
1answer
419 views

Compound lenses and virtual images

Ok so I have this problem where I have a system of two lenses. All I know is that the distance between the object and the first lens is 30cm, the distance between the object and the final image is ...
4
votes
4answers
289 views

Blocks stacked on an incline connected by rope around pulley

Two objects A and B, of masses 5 kg and 20 kg respectively, are connected by a massless string passing over a frictionless pulley at the top of an inclined plane, as shown in the figure. The ...
4
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2answers
168 views

Angular momentum in a rod rotating around one end?

Sorry if I can't get straight to the point, I have to give a lot of details before I actually state the question. The formula for angular momentum is $L=I \omega$. If we look up $I$ for a thin rod ...
4
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1answer
188 views

What are the generators of spherical symmetry?

The title says it all. I think this should be a pretty simple question but I just couldn't find the answer. Ok -- I'll give a bit more context to my question. I'm encountering this in the context of ...
4
votes
1answer
255 views

Plastic bottle floating and sinking

I was doing this experiment: i take a plastic cup, put in a container of water, it floats – then when I put a coin in the water, it sinks and rests at the bottom. So to make the cup sink, i fill it ...
4
votes
1answer
111 views

Identifying the position of the moon

I encountered the following question in a previous year paper of a graduation-based test. On a certain night the moon in its waning phase was a half-moon. At midnight the moon will be (choose one ...
4
votes
2answers
151 views

Is there a general form for heat capacity?

Can you derive a general form (not keeping either volume or pressure constant) for heat capacity from the first law of thermodynamics? Do you have to make any assumptions to do so? It sounds trival, ...
4
votes
2answers
353 views

Equivalent RC circuit to a RRC circuit?

I'm in doubt about a situation that I've seen sometimes: imagine we have a resistor in parallel with a resistor and a capacitor in series. Since I don't know how to generate figures of circuits to ...
4
votes
1answer
233 views

Firing machine question

Suppose we have a firing machine on a frictionless surface at point $x=0$. It fires a bullet of mass $m$ every $T$ seconds. Each bullet has the same constant velocity $v_0$. There's a body of mass ...
4
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1answer
151 views

Quantum Mechanics - Hidden Variables

In Steven Weinberg's Lecture on Quantum Mechanics (p. 342), he writes: The correlation between the spins of the two particles can be expressed as the average value of the product of the ...
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2answers
697 views

Constant magnetic field applied to a quantum harmonic oscillator

I have a spinless particle of mass $m$ and charge $q$ which is an isotropic harmonic oscillator of frequency $\omega_0$, then I apply a constant magnetic field in the $z$ direction. We can show the ...
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3answers
3k views

“Find the net force the southern hemisphere of a uniformly charged sphere exerts on the northern hemisphere”

This is Griffiths, Introduction to Electrodynamics, 2.43, if you have the book. The problem states Find the net force that the southern hemisphere of a uniformly charged sphere exerts on the ...
4
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3answers
501 views

Ice cream cone and loop-de-loop

Was siting in class thinking about this problem, did some rough sketches of a solution but never really managed to solve it. Assume a boy starts at the top of a circle with radius R as described ...
4
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1answer
8k views

How do I solve for the phase constant given the amplitude and the angular frequency?

A piston (with mass M) in a car engine is in vertical simple harmonic motion with amplitude A. The engine is running at a period T. Suppose a small piece of metal with mass m were to break ...
4
votes
1answer
58 views

Calculating the electrostatic energy per unit length of a cylindrical shell surrounded by a coaxial cable

Suppose an infinitely long cylindrical shell of radius $a$ carries a surface charge density $\sigma_0$ and is surrounded by a coaxial cable of inner radius $b$ and outer radius $c$ with uniform charge ...
4
votes
1answer
71 views

Orthogonality of summed wave functions

Problem. I know that the two wave functions $\Psi_1$ and $\Psi_2$ are all normalized and orthogonal. I now want to prove that this implies that $\Psi_3=\Psi_1+\Psi_2$ is orthogonal to ...
4
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1answer
58 views

Is this oscillator driven?

A mass $m$ is attached to a vertical massless spring or a spring constant $k$. Originally, the spring was relaxed because the mass was held by a clip. Suddenly the clip was released. THe mass ...
4
votes
1answer
68 views

How to get a function for the voltage across a capacitor connected to an AC voltage source? [closed]

I am looking for the way of obtaining a solution for $V_{c}$ ,as a function of $t$ depending of $\omega$, of the following differential equation related to an electrical circuit involving a low-pass ...
4
votes
2answers
95 views

How can I find the amplitude?

Prove that the motion of a mass $m$ on a linear spring with constant $k$, has the form $$y (t) = A \sin(wt+f),$$ where $t$ is the time and $A, w, f$ are constants. We know that for $t = 0, y(0)=y_{0}$ ...
4
votes
1answer
99 views

Sign of $dr$ in Schwarzschild geodesics

There is an equation that relates energy $E$, angular momentum $L$ and other constants and variables to find $\left(\frac{dr}{d\tau}\right)^2$ in a plane. ...
4
votes
1answer
145 views

Virial theorem and variational method: an exercise (re-edited)

I have a hydrogen atom, knowing that its Hamiltonian has been modified turning the standard potential $$ V_{0}(r) = -\frac{Z}{r} $$ into $$ V(r) = -\frac{g}{r^{\frac{3}{2}}} $$ with $g$ a positive ...
4
votes
1answer
145 views

Conserved topological charge for d=3 Yang-Mills. G=U(2)

Consider a pure Yang-Mills lagrangian density $$\mathcal{L}=-\frac{1}{4}F^{\mu\nu}_aF^a_{\mu\nu}$$ with gauge group $U(2)$. Take the generators for $U(2)$ to be $t_0$, $t_i \ i=1,...,3$ with ...
4
votes
1answer
65 views

Problem Of Pumping Rubber [closed]

One can work out by either lifting weights or using a tension band, which is like a big rubber band. If we model the rubber band as a big spring with spring constant $400 N/M$ how far in meters must I ...
4
votes
2answers
201 views

Total time taken for an accelerating frame in special relativity [duplicate]

How does one derive the equation for the total time traveled in a constantly accelerating frame? I found some help at this question: Special Relativity and Constant Acceleration But the information ...
4
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1answer
168 views

Integrable equations of motion

Suppose that a force acting on a particle is factorable into one of the following forms: ...
4
votes
1answer
94 views

Photon Escape Angle From Black Hole

Consider a photon source emitting photons near the surface of a Schwarzschild black hole. What angle, as a function of the source's radius from the event horizon, must the photons be emitted at such ...