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Homework Help: Object in a test tube

  1. Aug 3, 2005 #1
    An object is put in a test tube . The test tube is put in a centrifugal machine where it spins around. Would it be correct to say that the net force on the object is zero since it is not moving. I know the test tube has a net inward force that makes it change direction. But the object wants to fly out of the tube but is stopped by the bottom of the test tube.

    Am I totally wrong here?
     
  2. jcsd
  3. Aug 3, 2005 #2
    What?????????
     
  4. Aug 3, 2005 #3
    What I meant is that the object doesn't accelerate. But then again it changes direction. A direct answer would be appreciated.
     
  5. Aug 3, 2005 #4

    Doc Al

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    Staff: Mentor

    centripetal acceleration

    An object spinning in a circle is most definitely accelerating! It is accelerating towards the center of the circle; this is usually called centripetal acceleration. And, since it is accelerating, there must be a net force pulling the object towards the center.
     
  6. Aug 3, 2005 #5
    That's what I thought. But wasn't sure because the object isn't in an inertial frame of reference.
     
  7. Aug 3, 2005 #6
    If an object isn't in an inertial frame of reference then pretty much by definition you will observe that a force is acting on it.
     
  8. Aug 4, 2005 #7
    O.K. I think I understand this but the real problem I don't understand, here it comes.

    An incompressible fluid with density rho is in a horizontal test tube of inner cross-sectional area A. The test tube spins in a horizontal circle with angular speed w. Gravitational forces are negligeble. An object of volume V and density RHOob has its center of mass at a distance Rcmob from the axis. Show that the net horizontal force on the object is rhoVw^2Rcm, where Rcm is the distance from the axis to the center of mass of the displaced fluid. I have already derived expressions for the pressure at a distance from the surface of the water, and for the pressure difference for a volume element of thickness dr. It seems to me that the net force on the object is the mass*acceleration of the displaced fluid volume.

    I don't know how to treat this problem. I see the force as the mass*acceleration of the object + displaced water.


    Could anyone please help me.
     
  9. Aug 4, 2005 #8

    Doc Al

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    Staff: Mentor

    The net force on any object is its mass time its acceleration. This object is being centripetally accelerated, so [itex]F_{net} = m a_c[/itex].
     
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