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Homework Help: Block and sphere

  1. Oct 23, 2009 #1
    1. The problem statement, all variables and given/known data
    A 5kg block starts at the top of a fixed frictionless sphere of radius 10m. The ball is given a slight nudge, enough to get it going by the force of gravity (this happens on Earth) but of negligible magnitude. What is the angle, relative to the vertical line from the bottom to the top of the sphere, at which the block leaves the surface of the sphere?

    2. Relevant equations
    (I don't know)

    3. The attempt at a solution
    I don't even know where to begin with this. Perhaps consider normal force at angle theta, and integrate or something like that?
  2. jcsd
  3. Oct 23, 2009 #2


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    Homework Helper

    Perhaps you should consider the block at a general angle θ and then see what should happen for the block to stay on the sphere.
  4. Oct 23, 2009 #3

    Doc Al

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    Staff: Mentor

    Yes, consider all the forces acting on the block and apply Newton's 2nd law. (No need for integration.) Make use of the fact that it's a sphere. Come up with some criterion for when the block loses contact.
  5. Oct 23, 2009 #4
    The problem is, I don't know what the criterion is (is my brain working today?)

    It has something to do with the block's velocity and theta, but I don't know what.
  6. Oct 23, 2009 #5
    I really don't know how to do this =(
  7. Oct 23, 2009 #6
    Hint: Consider the motion of the block; how would you describe it?
    By 'ball', do you mean the sphere or ... the block?
  8. Oct 23, 2009 #7
    block (sry)
  9. Oct 23, 2009 #8
    Well, the motion of the block is at first on the surface of the sphere, then off at a tangent, i guess. I don't know what the significance of this is though...
  10. Oct 23, 2009 #9
    Ok, we are not interested in the part after it slides off the sphere, so the part we are interested in considering is the motion along the surface of the sphere. The path along surface of the sphere is curved...circular in shape when considered two-dimensionally. Does that ring a bell?
  11. Oct 23, 2009 #10
    Yes it's circular in shape. So you mean I should consider the component of the forces acting on the block perpendicular to the tangent?
  12. Oct 23, 2009 #11
    The problem is that the pseudo-"centripetal" force is entirely canceled out by the normal force. Am I right? So it has something to do with a circle/centripetal pseudoforce but I'm not getting it.
  13. Oct 23, 2009 #12
    Is it just that at some angle theta, the velocity is no longer in balance with the pseudocentripetal force and the ball therefore leaves the surface?
  14. Oct 23, 2009 #13
    "Pseudocentripetal force"? It's a real net force, not a pseudo-force. And no, the normal force does not cancel out with the normal component of gravitational force, otherwise there is no net radial force and no centripetal force. The idea is close; what happens when the block is just about to leave the surface of the sphere?
  15. Oct 23, 2009 #14
    The centripetal net force is not large enough to keep the block in "orbit"?
  16. Oct 23, 2009 #15
    Yup! (radial force would be more accurate though =)) And the net radial force on the block at the point of sliding off the sphere is given by...? Centripetal force required to keep block in circular motion given by...?
  17. Oct 23, 2009 #16
    The centripetal acceleration has to be v^2/r and thus force must be v^2/20...
  18. Oct 23, 2009 #17
    Wait: there is no centripetal force.

    For angle of theta with respect to vertical, there's only a force of [tex]mg\sin\theta[/tex], which is parallel to the inclined plane (or the sphere's tangent).
    Therefore, the block should fly off the sphere at 0 degrees. What am I getting wrong here..
  19. Oct 23, 2009 #18
    Bump, I really need help on this one.
  20. Oct 23, 2009 #19

    Doc Al

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    Staff: Mentor

    Sure there is.
    What happened to the radial component of gravity?

    Answer these questions. In general, what forces act on the block? (Hint: I'm thinking of two forces acting.) At the moment the block is about to lose contact, what can you say about one of those forces?
  21. Oct 23, 2009 #20
    There are two forces acting on a block on an inclined plane (the plane tangent to the sphere at the tangent point of the block to the sphere): gravity and normal. The net force is down the inclined plane, the magnitude of this is mg sin(theta) where theta is the inclination of the plane.

    Somewhere I'm getting this wrong.
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