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gravitational potential energy

Whiteshoes

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10+ Year Member
Jan 16, 2010
207
4
  1. Pre-Medical
    Formula given in passage: Potential Energy = -(GMm/r)

    If the distance between two masses is tripled, then the magnitude of the gravitational potential energy is:

    Ans: decreased by a factor of 3

    What about the Negative sign?? in TBR's explanation they said if you triple the radius then you get less negative but doesn't that mean you increased your potential energy by factor of 3??

    for example if at first it was -3 but because you triple the distance and now it is -1 that should mean you increased by a factor of 3. Am i wrong in my reasoning?
     

    FutureDoc2

    Full Member
    Dec 27, 2010
    149
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    1. Other Health Professions Student
      Formula given in passage: Potential Energy = -(GMm/r)

      If the distance between two masses is tripled, then the magnitude of the gravitational potential energy is:

      Ans: decreased by a factor of 3

      What about the Negative sign?? in TBR's explanation they said if you triple the radius then you get less negative but doesn't that mean you increased your potential energy by factor of 3??

      for example if at first it was -3 but because you triple the distance and now it is -1 that should mean you increased by a factor of 3. Am i wrong in my reasoning?


      Try to think of this problem more conceptually to see if this helps. After manipulating the equation above, we see that GPE is inversely proportional to the radius. So now incorporating what was given in the problem, if the radius (or distance) between the masses is increased (by a factor of 3), then the total force or Gravitational Potential Energy experienced by these same masses will therefore decrease. Do you see why this is so?

      When dealing with a problem that basically asks for comparing 2 variables it is safe to ignore all the rest of the variables and just look at the ones in question. So for this problem, GPE= -GMm/r, you will only look at GPE = 1/r and compare the starting and ending numbers. If this does not make sense try looking at it like this: ΔGPE = [-(GMm)/(R + h)] - [-(GMm)/(R)]. After doing this, you will be able to see that GPE actually does decrease and by what magnitude. I hope this helps!
       

      Whiteshoes

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      10+ Year Member
      Jan 16, 2010
      207
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      1. Pre-Medical
        Try to think of this problem more conceptually to see if this helps. After manipulating the equation above, we see that GPE is inversely proportional to the radius. So now incorporating what was given in the problem, if the radius (or distance) between the masses is increased (by a factor of 3), then the total force or Gravitational Potential Energy experienced by these same masses will therefore decrease. Do you see why this is so?

        When dealing with a problem that basically asks for comparing 2 variables it is safe to ignore all the rest of the variables and just look at the ones in question. So for this problem, GPE= -GMm/r, you will only look at GPE = 1/r and compare the starting and ending numbers. If this does not make sense try looking at it like this: ΔGPE = [-(GMm)/(R + h)] - [-(GMm)/(R)]. After doing this, you will be able to see that GPE actually does decrease and by what magnitude. I hope this helps!

        Wow this is the first time I heard of ignoring the negative when comparing variables but what you said makes total sense. I tried googleing this but didn't find it anywhere. If you could please link me to any website that goes over this type of relationship so i can review it. Thanks
         

        FutureDoc2

        Full Member
        Dec 27, 2010
        149
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        1. Other Health Professions Student
          Wow this is the first time I heard of ignoring the negative when comparing variables but what you said makes total sense. I tried googleing this but didn't find it anywhere. If you could please link me to any website that goes over this type of relationship so i can review it. Thanks

          Okay I can see how you would make that conclusion by my first post! Please do not ignore the negative sign, I actually was not paying attention and ignored it myself (even though it was included lol). However, after looking at this, as R increases, the value is increasing..

          Eventually the distance is so great there is no attractive force. Meaning as R continues to increase, eventually that R will reach infinity. Anything divided by infinity is 0. Maybe this is why there is a decrease? So GPE would increase then decrease to 0, due to R reaching infinity. (no longer a gravitational pull)

          Maybe someone else can chime in and add their 2 cents?!
           
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          FutureDoc2

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          Dec 27, 2010
          149
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          1. Other Health Professions Student
            Wow this is the first time I heard of ignoring the negative when comparing variables but what you said makes total sense. I tried googleing this but didn't find it anywhere. If you could please link me to any website that goes over this type of relationship so i can review it. Thanks

            Or the negative just means that as the radius increases, the GPE decreases due to the transferring of energy to KE?


            Sorry for all the post, Im trying to work this all out in my head right now.lol


            EDIT: This would only make sense if the radius was approaching the earth and not going away...
             

            hiaips

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            May 30, 2012
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              Formula given in passage: Potential Energy = -(GMm/r)

              If the distance between two masses is tripled, then the magnitude of the gravitational potential energy is:

              Ans: decreased by a factor of 3

              What about the Negative sign?? in TBR's explanation they said if you triple the radius then you get less negative but doesn't that mean you increased your potential energy by factor of 3??

              for example if at first it was -3 but because you triple the distance and now it is -1 that should mean you increased by a factor of 3. Am i wrong in my reasoning?

              In general, the gravitational PE *does* increase as the distance between two objects increases, for the reasons that you state. However, this question asks you to compare the magnitudes of the energies. When dealing with scalar quantities (such as energy), "magnitude" refers to the absolute value of that quantity.
               

              Whiteshoes

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              10+ Year Member
              Jan 16, 2010
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              1. Pre-Medical
                In general, the gravitational PE *does* increase as the distance between two objects increases, for the reasons that you state. However, this question asks you to compare the magnitudes of the energies. When dealing with scalar quantities (such as energy), "magnitude" refers to the absolute value of that quantity.

                crap.. cant believe i over looked "magnitude" Thanks
                 

                FutureDoc2

                Full Member
                Dec 27, 2010
                149
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                1. Other Health Professions Student
                  In general, the gravitational PE *does* increase as the distance between two objects increases, for the reasons that you state. However, this question asks you to compare the magnitudes of the energies. When dealing with scalar quantities (such as energy), "magnitude" refers to the absolute value of that quantity.

                  Wow! I can't believe I by passed that! lol Well, I am glad we finally got this answered, but seems we all need to be careful and pay attention to wording. It'll get you every time, geesh. smh lol
                   

                  hiaips

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                  May 30, 2012
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                    Wow! I can't believe I by passed that! lol Well, I am glad we finally got this answered, but seems we all need to be careful and pay attention to wording. It'll get you every time, geesh. smh lol

                    Yeah, glossing over details like that has definitely burned me a number of times, too...definitely can make the MCAT physical sciences section tricky.
                     

                    Hildace

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                    Feb 11, 2012
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                      In general, the gravitational PE *does* increase as the distance between two objects increases, for the reasons that you state. However, this question asks you to compare the magnitudes of the energies. When dealing with scalar quantities (such as energy), "magnitude" refers to the absolute value of that quantity.

                      This is correct. However, the TBR book does incorrectly state "Choices A and B definitely cannot be correct, because the potential energy decreases as the distance increases". The TBR explanation for why choices A and B are incorrect is completely wrong. Potential energy increases as the distance increases. Choices A and B are wrong because the TBR question is referring to the magnitude of the gravitational potential energy; this absolute value would ignore the negative sign. Honestly I think they should not have used "magnitude" in the question, but that is up to the author.
                       
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