Recent content by lua

  1. lua

    Upper bound for first excited state - variational principle

    Oh! I did't think of that at all. Thank you!
  2. lua

    Upper bound for first excited state - variational principle

    I'm solving problem number 5 from https://ocw.mit.edu/courses/8-05-quantum-physics-ii-fall-2013/resources/mit8_05f13_ps2/. (a) Here I got: $$ \beta = \frac{\hbar^{\frac{1}{3}}}{(\alpha m)^\frac{1}{6}} $$ and: $$ E = \left ( \frac{\alpha \hbar^4}{m^2} \right )^\frac{1}{3}e $$ (b) Using Scilab I...
  3. lua

    Solving Spool Acceleration Problem Using Newton's Laws

    Are we talking only about the case (c) or any case listed above? I think I understand what you are trying to say, but I don't understand why system has to start sliding. I understand that when system is rolling, if the resulting velocity of the point of contact with the ground isn't zero...
  4. lua

    Solving Spool Acceleration Problem Using Newton's Laws

    I think I understand the source of my confusion. I assumed that the condition ##F_{f} \le \mu N## was closely related with the (c) case. But it is not the case. I first considered the case of system dynamics in the middle of the movie. I found parameters of system dynamics (translational and...
  5. lua

    Solving Spool Acceleration Problem Using Newton's Laws

    I got: $$F_{max}= \frac{1}{2} \frac{sin 2 \alpha}{cos(\alpha - \phi)}mg$$
  6. lua

    Solving Spool Acceleration Problem Using Newton's Laws

    If you pull harder, I assume that either string will brake or the spool will start to move with constant speed because of zero acceleratios. But I can't prove that. When I look once more through equations, ##F_{max}=T_{max}= \frac{\mu}{cos \phi + \mu sin \phi} mg## is maximum straining force of...
  7. lua

    Solving Spool Acceleration Problem Using Newton's Laws

    First, for the case (c), I would say that the zero values of translational and rotational acceleration mean one of the following three things: 1. If the spool was accelerating (to the left or right) before meeting requirement (c), it will keep moving with constant linear and rotational speed...
  8. lua

    Solving Spool Acceleration Problem Using Newton's Laws

    I solved this problem using second Newton law for translational motion and the same law for rotational motion, and got $$a= \frac {F} {m+ \frac {I} {R^{2}}} (cosϕ−rR)$$ where m is spool mass. Now, we have three cases: (a) ##cos\phi>\frac{r}{R}##, when spool is accelerating to the right, (b)...
  9. lua

    What Are Some Must-Read Books for Physics Enthusiasts?

    Hi everyone! I'm a physics anthusiast. I fell in love with physics as soon as I got it in the middle school. Love to read books of the famous physicists (Feynman, Susskind, B. Greene, Penrose, etc.). If my English is sometimes clumsy, I hope you won't mind me - English is not my native...
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