Homework and exercise Definition and 38 Threads

Hi all, I am working through Sean Carroll's Textbook, particularly Chapter 5 regarding the Schwarzschild Solution. In this chapter, Energy and Angular Momentum are defined as follows: $$ \begin{align} E &= (1-\frac{2GM}{r})\frac{dt}{d\lambda} \Rightarrow \frac{dt}{d\lambda} = (1-...

This is a problem from the textbook Supergravity ( by Daniel Z. Freedman and Antoine Van Proeyen ). I am trying to learn general relativity from this book. I am attempting to do the later part of the Exercise 7.14 ( on page 148 ). Basically it asks us to explicitly show that the Levi-Civita...

I am an electrical engineer and I like to educate high school physics

This is from Modern Cosmology, Scott Dodelson, Chapter 6. For the part "Show that its energy density dilutes as ##a^{−3}##", following is my attempt: In the equation ##\frac{\partial \rho}{\partial t} = -3H(P+\rho)##, put ##P = \frac{1}{2} \dot{\phi}^2-V(\phi)## and ##\rho=\frac{1}{2}...

This is the exercise: [FONT=georgia]Please help me ( question 4 and 5). Here is my effort: First, I represented the forces on both objects. Then, i found F⁰ = 5N (question 1) After that, (question 2) + (question 3) I hope it's even correct.

My attempt: The electric field in the interior of a conductor is ##0##. By symmetry, the electric field is directed radially outward. Take the Gaussian surface as the thin cylindrical shell of radius ##\rm 3\ cm## and length ##L##. ##\displaystyle\oint\limits\vec{E}\cdot d\vec{A} =...

I am trying to solve the following problem from Ballentine: (a) For finite-dimensional matrices ##A## and ##B##, show that ##Tr[A, B] = 0.## (b) Paradox. From this result it would seem to follow, by taking the trace of the commutator ##[Q, P] = i\hbar##, that one must have ##\hbar =...

I am trying to solve Problem 2.4 in Ballentine: I note in my attempt below to what (2.6) and (2.7) refer. My attempt thus far is as follows: A ##2 \times 2## state operator can be represented in a particular orthonormal ##\beta = \{\phi_i\}## as below, where we have enforced trace...

As a part of our physics high-school self-study, we are making a stroboscope. We have a small 5-V DC motor that powers the strobe disk. It works as expected, but, clearly, the motor makes the disk spin at a constant speed. Is there an easy, but effective and reliable way to control its speed...

I noticed that ##V(\phi)## has nonzero minima, therefore I found the stationary points as ##{{\partial{V}}\over{\partial\phi}}=0##, and found the solutions: $$\phi^0_{1,2}=-{{m}\over{\sqrt{\lambda}}}\quad \phi^0_3={{2m}\over{\sqrt{\lambda}}}$$ of these, only ##\phi^0_3## is a stable minimum...

On ***page 38*** of Becker Becker Schwarz, we're given ***equation 2.69*** which is the Hamiltonian for a string given as $$H=\frac{T}{2}\int_{0}^{\pi}(\dot{X}^{2}+X^{'2})$$ Considering the open string we have...

The hint says the following: "Since the cords are inextensible, every particle of a cord must be in circular motion about the point where it is affixed to the ceiling. Therefore, the velocities of the points where the cords are leaving the disc are perpendicular to the string" Due to the fact...

Fig.1 Fig 2 (the net of the cone) Point C is the turning point. ##\phi##= 90°. I wonder why the angle ACP is 90°. Is this a coincidence, or the "wire of minimum length" has anything to do with this? (Though, I thought the minimum length of the path can be acquired if ABP is a right angle)

In order to be able to solve the problem, I think I must find the equation of ##h## with respect to ##\dot h##. Assuming that ##F## is the action-reaction force between the stone and the end of chain, then the Newton's equation For the stone:$$-F-mg=m \ddot h$$ $$-\int (F+mg)dh = \frac 1 2...

Ok. So, I already worked on this problem, and get ##m_c## = 2m/3, which is correct according to the book. However, I also want to know the value of the tension (T) between rod A and B. Note: Before we start working on my modified question, I want to point out that the force exerted by the...

I'm currently confused in determining whether an image formed by the 1st mirror (the left one) is a real or virtual object for the 2nd mirror. Here is the solution manual: This is what I have in my mind: Since the object is located between the focus and radius point of the first mirror, the...

Vertical components: dy = 0m ay = 9.8m/s^2 [down] t = 1.34s V1y = required V2y = 0 i first tried to find V1y dy =vi t + 1/2 a t^2 and got V1y = -6.566 then i solved for time of flight dy =vi t + 1/2 a t^2 0 = -6.566t + 4/9t^2 and for 1.34 seconds does this mean the time of flight is the...

$$L = \frac {mv^2}{2} - mgy$$ It is clear that ##\dot{x}=\dot{\theta}L## and ##y=-Lcos \theta##. After substituting these two equations to Lagrange equation, we will get the answer by simply using this equation: $$\frac {d} {dt} \frac {∂L}{∂\dot{\theta}} - \frac {∂L}{∂\theta }= 0$$ But, What if...

Consider a rocket with mass ##m## in space is going to move forward. In order to do so, it needs to eject mass backwards. Let the mass that is ejected has velocity ##u## relative to the rocket. What is the equation for the final velocity? It is said that after ##dt## second, the rocket will...

In the solution manual, it says that: the resultant of friction force is ##<= kmg##, hence $$m\sqrt{\omega_t^2 + (\frac {v^2} {R})^2} <= kmg$$ and from this equation, we will get $$v^2 <= R \sqrt{(kg)^2 -\omega_t^2}$$ which will make ##v_{max}^2= R \sqrt{(kg)^2 -\omega_t^2}## Finally, they...

In the solution for question ##(a)##, it is written that the equation of translational motion for the center of mass is ##N-mg=ma_y## Why ##N## is also included inside of the equation? In my opinion, the rail does not exerting force (N) to slow down the mass' acceleration. Instead, the purpose...

Hi everyone is able to help solve this question for my assignment in university? I've draw a free body diagram for each component of the question but now i am stuck. [Mentor Note -- Poster has been reminded to show their work when starting a new schoolwork thread]

I tried to solve it by integrating force from 0 to L dF=dm.g where dm=λdx And then I multiplied it with velocity to get power because velocity is constant ∫(vdF)=v ∫(dF) But the book used integration to find work done and divided it by time for power My answer was λlgv(Option B) Giving...

My solution is However can someone explain in detail why will be equal to the weight? and why does it have to be multiplied by 6?

My solution is now I am asked for the same result but in this form but I don't know where to start.

https://www.physicsforums.com/threa...f-a-translating-and-rotating-pancake.1005990/ So,I think I posted this in the wrong place. So, I will move it to here. Here, in post #6, it is stated that ##\int R dm = M R##. As far as I know, R change from time to time and it is not constant. Hence, isn't...

This is the picture of the problem. My solution is: I'm not sure if the limit is 0 to 2 or 0 to 4...

Consider that the particle is moving in circular with tangential velocity v, and (0,0)is its origin. I wonder why dr/dt is equal to tangential velocity instead of radial velocity (since dr/dt means how much change in radial distance in a really short duration of time)

Summary:: A nitric acid solution enters at a constant rate of 6 liters / minute into a large tank that originally contained 200 liters of a 0.5% nitric acid solution. The solution inside the tank is kept well stirred and leaves the tank at a rate of 8 liters / minute. If the solution entering...

I tried to solve it and I got the following, is it correct?

I tried to solve it and I got the following is it correct? and 2 My solution... is a negative distance?

This is the image of the problem: I tried to solve it and I got the following is it correct? derive and equal to 0 because it is between an angle of 0 and 180° is this statement correct?

I am currently reading David Morin book and found this statement : ##\,\,\,\,\,\,\,\,## "It is important to remember that you are free to choose your origin from the legal possibilities of fixed points or the CM" Is it really alright to choose the center of a...

delta q=rho deltaV rho=dq/dV dq=rho4pir^2dr Then integrate dq from 0 to a because A is to be uniform in shell. Ans: A= 5.3*10^-11 C/m^2 How do we approach these problems? Looking at the answer A seems to be surface charge density. What is A? What is the direction of uniform field E. I don’t...

This is the image of the problem I tried to solve it and I got the following is it correct?

This is the solution from my textbook, and I have some questions about the method The mass of hanging chain : $$m_h =\frac m 5$$ the center of mass of the hanging chain : $$h_1 = - \frac{1} {2} \cdot \frac L 5 = - \frac L {10}$$ (the minus sign here means that it is under the table surface)...

I have read that an electron requires certain minimum energy of threshold frequency to move an orbit However the energy needed decreases with increase in shell number The transition energy is reduced with each orbit For example The energy to shift an electron from 1st to 2nd orbit is much...