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Pseudo force

  1. Nov 13, 2011 #1
    let me first donate a(A,B) is the acceleration of A relative to B
    Observer 2 and a subject A with mass m are falling down from a building
    Observer 1 is standing on the ground to observe the motion of these two objects
    Ignore the air resistance
    In observer 1,he sees the force acting on A
    =ma(A,1)
    =m[a(A,2)+a(2,1)]
    In observer 2,he sees the force acting on A
    =ma(A,2)
    Obviously a(A,2)=0,but this doesn't make sense
    So, we introduce pseudo force f=-ma where a is the acceleration of the frame
    The problem is here,which equation should I add the pseudo force into?
    I don't know the above assumption is correct or not,please check!
     
  2. jcsd
  3. Nov 13, 2011 #2

    Doc Al

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    The pseudo force is added when viewing things from the accelerated frame.
     
  4. Nov 13, 2011 #3

    Andrew Mason

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    Why does a(A,2) = 0 or ma(A,2) not make sense? They are both falling at the same rate so their relative acceleration is 0. Both are in a state of free-fall and experiencing no inertial effects. As far as I can see, there is nothing that would require introduction of a pseudo force to explain.

    AM
     
  5. Nov 13, 2011 #4

    Doc Al

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    Leaving general relativity aside, there is a gravitational force acting on the mass yet the acceleration is zero in the falling frame. Thus a pseudo force is introduced to rationalize Newton's laws.
     
  6. Nov 13, 2011 #5

    Andrew Mason

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    But, unlike acceleration due to an electrical force, say, the accelerating observer observes no inertial effects that would require introduction of an inertial force.

    The pseudo force that is required in the case of an electrical central force is a centrifugal force. The charged body that is subject to the electrical force experiences an inertial effect that is opposite to the direction of the electrical force. So a centrifugal pseudo force is introduced to explain that effect in the accelerating body's frame. But no such effect appears with a body that is subject only to a gravitational force. The reference frame of a body in gravitational freefall/orbit is equivalent to an inertial frame. If a pseudo force is introduced you would no longer have a frame of reference that is equivalent to an inertial frame.

    AM
     
  7. Nov 13, 2011 #6

    A.T.

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    That's why gravity can modeled as a inertial force, and in General Relativity it is. But this is the classical physics forum, where gravity is an interaction force.
    Sure you would. In the classical non-inertial free falling frame, the inertial force exactly cancels the force of gravity. So that frame is equivalent to an inertial frame with no gravity acting.
     
  8. Nov 13, 2011 #7
    I wouldn't say that we introduce the pseudo force. It simply results from Newton's second law.
     
  9. Nov 13, 2011 #8

    Andrew Mason

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    If I carry a net charge (one my shoes, say) and I am being whirled around a body by a central electrical force, I experience something that is trying to rip me out of my shoes. So, in my reference frame I postulate a centrifugal force acting on me trying to send me away from my shoes. The pseudo force allows me to analyse motion in my (non-inertial) reference frame.

    But I don't have this effect with gravity as the only real force. Since I cannot sense gravity as a force there is no reason to introduce a force to counteract it. Unless one is experiencing tidal effects in free-fall, I have difficulty understanding why it would be necessary to introduce a pseudo force.

    In this respect, there is a fundamental difference between gravity and other forces even in classical physics. I don't think you need GR to explain that difference.

    AM
     
  10. Nov 13, 2011 #9

    A.T.

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    What you can sense is completely irrelevant. In classical mechanics the free falling frame (in a g-field) is an accelerated frame. In an accelerated frame there is an inertial force, per definition. Period.

    Yes, it behaves like inertial forces. But in classical physics it is still modeled as a real force.

    It is about how gravity is modeled:
    Newton : real force
    Einstein : pseudo force
     
    Last edited: Nov 13, 2011
  11. Nov 13, 2011 #10

    Andrew Mason

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    There is no inertial "force". Are you suggesting there is an inertial effect? How does it appear?

    AM
     
  12. Nov 13, 2011 #11

    A.T.

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    http://en.wikipedia.org/wiki/Fictitious_force
     
  13. Nov 13, 2011 #12

    Andrew Mason

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    Which is exactly my point. It is not a real "force". It is an inertial effect. But that is just terminology. My question is what inertial effect does a pseudo force explain if the only real force is gravity?

    AM
     
  14. Nov 14, 2011 #13

    A.T.

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    No, that wasn't your point. You said that there is no inertial force, which is wrong.
    The lack of coordinate acceleration from that single real force acting.
     
    Last edited: Nov 14, 2011
  15. Nov 14, 2011 #14

    Andrew Mason

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    No. I said there is no inertial "force". My point in saying that, and my only point, was an inertial effect not a "force". It isn't.
    What do you mean? Can you give me an example of a phenomenon observed in the free-falling frame that requires introduction of a pseudo force to explain?

    AM
     
  16. Nov 14, 2011 #15
    The rest frame of ISS is a free-falling frame. As ISS is at rest there is no net force. But as there is a gravitational force acting between ISS and Earth there must be a pseudo force keeping ISS at its position.
     
  17. Nov 14, 2011 #16

    Andrew Mason

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    ?? Why? The ISS is accelerating. No pseudo force is needed to keep the ISS in its orbit.

    In the rest frame of the earth, the motion of the ISS is completely explained by gravitational force.

    In the rest frame of the ISS, there are no phenomena appearing that require a pseudo force to explain.

    AM
     
  18. Nov 14, 2011 #17

    Doc Al

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    In the rest frame of the ISS there is no acceleration.

    Right. And that gravitational force exists in all frames. In the rest frame of the earth, there is a gravitational force and the resulting acceleration; no modifications to Newton's laws are required.

    You have a gravitational force yet no acceleration.
     
  19. Nov 14, 2011 #18

    A.T.

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    There is an inertial force, because it is a accelerated frame.
    Inertial forces are introduced to make Newton's 2nd law applicable to non-inertial frames, not to "explain phenomenons".
     
  20. Nov 14, 2011 #19

    Andrew Mason

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    So what pseudo force do you introduce?

    [Comment: Pseudo forces are introduced in order to apply Newton's laws of motion when the accelerating reference frame is treated as an inertial reference frame.

    One can apply Newton's laws in the accelerating reference frame, treating it as an inertial frame, without introducing any pseudo forces. You cannot do that if the frame is accelerating due to central mechanical or electric force. You can only do that with a non-inertial reference frame that is in gravitational free-fall.

    So my question is: why do we have to introduce a pseudo force in this case?]

    AM
     
  21. Nov 14, 2011 #20

    Andrew Mason

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    But Newton's laws of motion work perfectly in a non-inertial reference frame that is experiencing only gravitational force. You do not need a pseudo force to make them work. If you disagree, tell us what pseudo force is needed in order to make f=ma work in a reference frame that is in gravitational free-fall.

    Am
     
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