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Newton's 3rd Law is confusing me

  1. May 27, 2014 #1
    Question: A glass half filled with water is kept on a horizontal table in a train. Will the free surface of water remain horizontal as the train starts? If not, which way would it tilt?

    Attempt: I know this is similar to the 'passenger in a bus' situation discussed in texts. I've identified the following forces:
    1) 'mg': the force acting on TRAIN/GLASS due to the WATER
    2) 'ma': the force acting on WATER due to the TRAIN/GLASS (in the direction of train's motion)
    3) '-ma': the force acting on TRAIN/GLASS due to the WATER (applying Newton's 3rd Law)

    Problem: Given that the above force definitions are correct, I cannot appreciate how the force that should push the water backward, i.e. '-ma', isn't actually acting on it!?

  2. jcsd
  3. May 27, 2014 #2
    You are OK. The problem would be if you actually could appreciate that.
  4. May 27, 2014 #3
    Would appreciate a response to my query.

  5. May 27, 2014 #4


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    Which reference frame are you using?
  6. May 27, 2014 #5
    Ah I see now. You think that there should be force pushing water backwards, but it's not there? Well, if the train is accelerating forwards, why should there be a force on water backwards. The glass pushes the water forwards. Your analysis is good. The force -ma doesn't act on water as you sad in No 3.
  7. May 27, 2014 #6


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    Suppose you're in the train, looking at a glass of water sitting on a table at the train station. When the train starts, what direction does the water appear to start moving? Is there a force causing it to move in that direction?
  8. May 27, 2014 #7
    I think,
    The water will experience a force backwards (and that force is noting but a psuedo force -ma ).
    And the level of water will be more in the rear side of the glass.An equillibrium will be establised between the water's restoring force and the pseudo force.

    Attached Files:

  9. May 28, 2014 #8
    Analyze it from a non-acclerating frame of reference. A fundamental physical property of a fluid is that it's free surface cannot sustain a static response to a tangential force. But here, it's important to realize that the fluid is not static. It's moving. So the net force on the free surface must be in the direction of acceleration. If it we're completely flat, there would be no force on the free surface ( because it is infinitesimally thin ). The only way the force can point in the correct direction, so that the fluid is accelerating but not flowing, is if the surface assumes the configuration you see. This doesn't happen immediately. The fluid in fact, flows until it is static (w.r.t accelerating frame). We're analyzing the final static situation only.
  10. May 28, 2014 #9
    Appreciate the pointer, A.T.

    To answer your question, I am taking a lead from the 3 forces I identified: mg, ma, & -ma, which were considered from the point of view of a passenger on the train; and this would, therefore, be my reference frame. Although, I suppose, maybe wrongly, that a reference frame of a by-stander on the train-station platform would yield just as well.

    Look forward to your response.

    Best Regards,
  11. May 28, 2014 #10


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    In that accelerating frame you have an inertial force -ma acting on everything, including the water. Note that this inertial force is not subject to Newtons 3rd Law (contrary to what you write in point 3). Also note that this force is similar to gravity, so the two can be combined into a new "effective gravity" vector, which is perpendicular to the water surface in equilibrium. Once the water is in equilibrium in the accelerated frame, the total force of the glass on the water is equal but opposite to that "effective gravity", but not due to Newtons 3rd but rather 2nd.

    As long you consider only forces acting on the water (the only ones relevant to what the water does) Newtons 3rd doesn't come into play.
    Last edited: May 28, 2014
  12. May 31, 2014 #11
    Appreciate all attempts & suggestions.

    I have arrived at the following conclusion: the simple genius is to realise that the water is accelerating in the direction opposite to the motion of the train and is, thereby, exerting the force '-ma' I numbered as (3) in my original post.

    Higher-order concepts of reference frame (post #4) and static response (post #8) don't assist if the above is not appreciated.

    In the end, arriving at the 'effective gravity vector' (post #10) is important.

  13. May 31, 2014 #12

    Doc Al

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    In what reference frame do you think the water is accelerating opposite to the direction of the train?
  14. May 31, 2014 #13
    If your reference frame is inertial, then the fluid accelerates with the train (Once it's free surface has achieved the stated configuration of course. We cannot analyze the hydrodynamical situation here ... That would be messy. I'm simply talking about the final hydrostatic configuration ) This is obvious.
    Second, the fluid doesn't exert a force '-ma' on anything. It cannot possibly exert a force on the container because the container continues to accelerate forward with an acceleration 'a'.
    All of what you mentioned are only important if you solve the problem from a non-inertial frame. I don't like pseudo forces, so i tend to stick to inertial frames.
    Last edited: May 31, 2014
  15. May 31, 2014 #14


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    Of course it does. The fluid exerts a horizontal force -mfluid * a on the container, once the fluid accelerates at a.

    So what? There are other forces acting on the container. The total force from fluid and train on the container is mcontainer * a, so the container also accelerates at a.
  16. May 31, 2014 #15


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    No idea what you man here. It's definently not true, once the water has a stable (tilted) surface again. Then the water accelerates with the train, in exactely the same way as the train does.

    The water does exert this force on the container. But since that force doesn't act on the water, it is not relevant to what the water does.
  17. May 31, 2014 #16
    I'm sorry. You're right. There is a net force on the container from the fluid. You'd think you have this stuff down to a tee after 2 years of advanced high school physics. *sigh* ... keep slipping up.
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