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  1. S

    Demorgan's Theorem

    Your post is difficult to understand. DeMorgans shows how the negation distributes over the conjunction and disjunction. For example ~(A & B) <--> (~A V ~B) This makes sense. The left hand side says "It is not the case that both A and B are true." The right hand side says, "Either A is...
  2. S

    Question regarding W-E theorems

    Right, as long as the planet isn't also rotating. You can consider it rotating about an axis through the Sun. Then you have K=\frac{1}{2}mv^2=\frac{1}{2}mR^2\left(\frac{v^2}{R^2}\right)=\frac{1}{2}I\omega^2 But if in addition the planet spins, it has an additional kinetic energy due to its...
  3. S

    Question regarding W-E theorems

    Ok, so in conclusion, W_{net,real}=\frac{1}{2}\left(I\omega_f^2+mV_f^2\right)-\frac{1}{2}\left(I\omega_0^2+mV_0^2\right) And W_{net,real}=W_{trans}+W_{rot} where W_{trans}=\int_{\vec{x}_0}^{\vec{x}_f}\vec{F}(x)\cdot d\vec{x}and the limits of integration are the final and initial...
  4. S

    Question regarding W-E theorems

    Ok, so I'm still kinda confused. What is the cylinder was only able to rotate. Then W=\int_{0}^{L/R}FRd\theta=FL=\DeltaKE In this case, the change in KE is only due to rotational motion. What if the cylinder could only move translationally. Then if the force acts over a distance L...
  5. S

    Question regarding W-E theorems

    So two questions: How would I find delta s? What is the real (general) work-energy theorem?
  6. S

    Question regarding W-E theorems

    I figured it as such: The rope has length L and the disc radius R. So the angle over which the torque acts will be (L/(2piR))(2pi)=L/R. So taking &omega;0=0, \omega_f=\sqrt{\frac{2}{I}\int_{0}^{L/R}FRd\theta}=\sqrt{\frac{2FL}{I}} I did this by imagining the disc as a pulley. I then wanted...
  7. S

    Help with a Dice problem (need an expert although the problem seems simple)

    I was a bit confused at first as to why you asked the same question twice and got different results. I think I figured it out. You meant The question "what is the probability of exactly three sixes?" is, as Doug said, 1 out of 216: \frac{1}{6} \cdot \frac{1}{6} \cdot \frac{1}{6} \approx...
  8. S

    Question regarding W-E theorems

    I apologize severely. Mass and radius are given.
  9. S

    Great criminal?

    Yes, I like your answer, but it uses the present tense "kills". That would make Cain seem out of the question.
  10. S

    Circular Motion - Help

    Are you aware that the force for gravitation is \vec{F}=-\frac{Gm_1m_2}{r^2}\hat{r} You have two masses m and 4m and some unknown mass m_2, so the magnitude of the gravitational attraction between m and m_2 is F_1=\frac{Gmm_2}{r_1^2} where r_1 is the distance between m_2 and m. The...
  11. S

    Circular Motion - Help

    "a third object would experience no gravitation force." what they mean is, no net gravitation force imagine a particle C lying on the line connecting A and B - what is the force that C feels from A? what is the force that C feels from B? What is the net force?
  12. S

    Rolling motion and torque

    Fr=I(a_1-a_2)/r F=ma_2 (ma_2)r^2=I(a_1-a_2) a_2(m+I)r^2=Ia_1 a_2=Ia_1/(m+I) I believe this to be the correct solution, and this is in the rest frame of the ground. I'm not quite sure what to put in for I, though.
  13. S

    Question regarding W-E theorems

    Can you give specific example and work it both ways? That is, first considering the quantities are representing fractions of the total work and then the quantities representing the whole work. I can see what you're saying, but I don't see how to apply it to a problem. I asked this...
  14. S

    Question regarding W-E theorems

    Are these quantites: W=\int_{\theta_0}^{\theta_f}{\tau}{d}\theta=\frac{1}{2}I(\omega_f^2-\omega_0^2) W=\int_{r_0}^{r_f}Fdr=\frac{1}{2}m(v_f^2-v_0^2) the same or different? Is "v" in the second equation the speed of the center of mass? IOW, does the bottom integral give the change in...
  15. S

    Absurdly easy tension problem

    I know. I've found at least four in the last two chapters, and I've verified these with my professor, so it's not just stupid Stephen being less smart than the author. The book is PHYSICS by Ohanian 2ed.
  16. S

    Absurdly easy tension problem

    BOOK's WRONG AHAHAHAHA!
  17. S

    Dual pulley

    You must consider torques about the axis through the center. The net external torque is m_1R - m_2r=I_{net}\alpha so \alpha=\frac{m_1R - m_2r}{I_{net}} where I_{net}=\frac{1}{2}MR^2+\frac{1}{2}mr^2+m_1R^2+m_2r^2 you know r=1/2R, so you should be able to find the relation between m and M...
  18. S

    Absurdly easy tension problem

    The book and I aren't getting along tonight. Maybe you can help. A rope of length L has a tension T. Someone pushes on the rope with a force F at its midpoint and deflects the rope by a distance d. What is T is terms of L,d and F. This is so simple I won't even explain my work...
  19. S

    Boom problem help!

    I don't understand your description of the problem. If you can make it more clear I can help.
  20. S

    Wave on a string

    A 24m nylon rope has a tension of 1.3x104N. The total mass of the rope is 2.7kg. If a wave pulse starts on one end, how long does it take to reach the other end. I get 0.07s v=\sqrt{\frac{T}{\mu}} t=d/v=d\sqrt{\frac{\mu}{T}} \mu=\frac{m}{l}=\frac{2.7kg}{24m}...
  21. S

    Rolling motion and torque

    But if it spins about an axis, it must spin about any parallel axis. That's what's throwing me off. The angular acceleration should be the same about any parallel axis. If I use the CM as a axis, then I get F=ma, FR=Ia/R, eliminating F, I get maR=Ia/R, but then a drops out!
  22. S

    How should you stack the blocks to achieve the maximum protrusion?

    Ok, I am still interested in knowing how you so easily knew what the projections must be without any apparent calculation. I got these same results, but I had to calculate the CM one at a time and then add the results together to find the projections.
  23. S

    Rolling motion and torque

    A bowling ball sits on a level floor of a subway car. If the car has a horizontal acceleartion a, what is the acceleration of the ball wrt the ground? Ball rolls w/o slipping. The forces that act on the ball are its weight, a normal force, and static friction. The weight and normal offset...
  24. S

    How should you stack the blocks to achieve the maximum protrusion?

    How did you determine the necessary projections?
  25. S

    Pool Ball Problem

    This question makes no sense. A ball doesn't travel with force. I agree with Jason's answer. The 8 should go off at a 45 degree angle to the initial velocity of either ball with speed v*sqrt2 where v is the initial speed of the 6 ball.
  26. S

    How should you stack the blocks to achieve the maximum protrusion?

    So how would I determine the torque extered by the normal force?
  27. S

    How should you stack the blocks to achieve the maximum protrusion?

    Five identical wood blocks of sides L and thickness H are shifted in one direction to form a leaning tower of the maximum protrusion. How should you stack the blocks to achieve the maximum protrusion? What is the maximum protrusion? What if you had an infinite number of blocks? For any...
  28. S

    Collisions problem (How should I approach it)

    by cons of p, m_1v_{1i}=m_1v_{1f}-m_2v_{2f} where v_2f is reckoned as negative By the energy conditions, m_1v_{1i}^2=\frac {1}{2}(m_1v_{1f}^2+m_2v_{2f}^2) which gives two equations with two unknowns.
  29. S

    Doppler Shift

    Yes that helps a lot. Do you use - on the botton when they are moving apart and + on the top when they are moving apart? Also, can you clearly define f and f'? f is the frequency as observed by the source? f' is the frequency as observed by the detector? Also, these speed v_d and v_s are...
  30. S

    Doppler Shift

    My book derives two formulas for Doppler shift. One for when the source moves and one for when the observer moves. What about when both are moving? I tried deriving it myself... but I couldn't :( If you want, you could just give me a hint on how to derive it.
  31. S

    Forced oscillations

    I still don't see how a driving force without damping won't cause the amplitude to keep increasing. Are you not continually doing positive work on the system and thus adding energy to the system?
  32. S

    Forced oscillations

    No, I'm just given that a driving force is acting on the system. In my book it talks about driving forces in the context of couteracting the effects of damping. In class (where the above equation came from), we talked about driving forces without damping. But without damping the amplitude...
  33. S

    Area between curve and axes

    I do believe this integral is equivalent to the one I posted. But how does your integral follow from the problem?
  34. S

    Forced oscillations

    It is very hard for me to understand something if I cannot derive it. I'm going to have to dig through my calc book to do this one. I think in any event my professor is more concerned with the qualitative features of a driving force. This is very confusing. Is F always acting to pull the...
  35. S

    Find the height of the rectangle

    If I understand #2 correctly Consider only x positive. A=bh=(2x)(y)=(2x)(6-x2)=12x-2x3 dA/dx=12-6x2=0 12=6x2 x=sqrt2 This is the only solution (if x were negative, you'd get the same area) so it's probably a max. Check just to be sure. d2A/dx2=-12x<0 yup a max (by the way x=-sqrt2...
  36. S

    Solving h(x)=-h(-x)

    f(x)=x^2 does not satisfy the hypothesis f(x)=-f(-x) f(x)=x^2 is EVEN f(x)=-f(-x) means f is ODD
  37. S

    Area between curve and axes

    You have to perform the integral \int_{0}^{1}\sqrt{1-x}dx Try the substitution u=1-x
  38. S

    Solving h(x)=-h(-x)

    There's only one possible answer. 0 \int_{-a}^{a} h(x) \,dx =\int_{-a}^{0} h(x)dx + \int_{0}^{a}h(x)dx=\int_{-a}^{0}-h(-x)dx+\int_{0}^{a}h(x)dx Suppose H(x)+C=\int h(x) \,dx \int_{-a}^{0}-h(-x)dx+\int_{0}^{a}h(x)dx=\int_{0}^{-a}h(-x)dx+\int_{0}^{a}h(x)dx Using u=-x, du=-dx...
  39. S

    One more Universal Gravitation

    I'll take you through it. How is angular speed of the star related to the linear speed of an object on the equator of the star?
  40. S

    Forced oscillations

    If you solve the Diff Eq with either an inital displacement or velocity, in addtion to the driving function, then you shold see some terms representing non driven oscillations. Ok, That's relieving. So it does reduce. How would you write the equation of motion with an initial...
  41. S

    Forced oscillations

    For forced oscillations we have \frac {d^2x} {dt^2} = -\omega_N^2x+\frac {F_0} {m} cos\omega_Ft The solution is x(t)=\frac {F_0} {m(\omega_N^2-\omega_F^2)}cos\omega_Ft This doesn't seem to reduce to oscillations where F0=0. Shouldn't it?
  42. S

    One more Universal Gravitation

    What is the escape velocity at the surface of such a star?
  43. S

    One last problem

    What does the integral represent if the integrand is positive!? AREA! What's the area of a half circle?
  44. S

    Is this possible?

    let y=F(x) f(x)=dy/dx=0 [inte](dy/dx)dx=[inte]0dx y=C=F(x) If F(0)=3, then C=3.
  45. S

    Solving h(x)=-h(-x)

    Draw a picture! It should be clear. What does h(x)=-h(-x) mean? What does a definite integral represent if h(x) is positive? Think of h(x)=x3 for instance. This should make the answer clear.
  46. S

    Billiards problem

    So its acceleration relative to the table is zero. And since the initial velocity of that point was zero, at all successive instants, the point in contact with the surface should be at rest relative to the table. And thus no slipping because slipping would imply movement relative to the table...
  47. S

    Pulley problem

    This is genius. I'm putting it on my wall.
  48. S

    Billiards problem

    Hi, I'm trying to understand what's going on here. When you write F=Ma, a is the acceleration of the center of mass. When you write F=I &alpha;=I a/R, a is the linear acceleration of a point at a distance R from the axis of rotation (as if the ball were not moving at all). So these are not...
  49. S

    Pulley problem

    This advice isn't entirely correct. I didn't take into account the pulley's mass. Try solving these for a. m1a=m1g-T1 m2a=T2 (T2-T1)R=Ia/R=(1/2)MRa DocAl's approach might work also, but I would avoid that direction simply because I don't feel comfortable using it.
  50. S

    Kinetic energy changes in collisions

    I've come to love this site. You will too. http://scienceworld.wolfram.com/physics/CoefficientofRestitution.html
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