Is gravitational energy always conserved?

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If I take a body to a height $h$ then I did the work $mgh$, but gravity does the work of $-mgh$, so the net work done would be 0. So why do we say that at that height $h$ the body will have potential energy $mgh$?










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  • If the object is dropped, it will have a final kinetic energy of mgh. This is why we say it has potential energy.
    – Kenshin
    Aug 19 at 10:31






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    This question addresses Newtonian gravity in which energy is conservative, but FWIW, in general relativity with a cosmological constant, global conservation of energy does not exist.
    – ohwilleke
    Aug 19 at 21:48














up vote
1
down vote

favorite












If I take a body to a height $h$ then I did the work $mgh$, but gravity does the work of $-mgh$, so the net work done would be 0. So why do we say that at that height $h$ the body will have potential energy $mgh$?










share|cite|improve this question























  • If the object is dropped, it will have a final kinetic energy of mgh. This is why we say it has potential energy.
    – Kenshin
    Aug 19 at 10:31






  • 1




    This question addresses Newtonian gravity in which energy is conservative, but FWIW, in general relativity with a cosmological constant, global conservation of energy does not exist.
    – ohwilleke
    Aug 19 at 21:48












up vote
1
down vote

favorite









up vote
1
down vote

favorite











If I take a body to a height $h$ then I did the work $mgh$, but gravity does the work of $-mgh$, so the net work done would be 0. So why do we say that at that height $h$ the body will have potential energy $mgh$?










share|cite|improve this question















If I take a body to a height $h$ then I did the work $mgh$, but gravity does the work of $-mgh$, so the net work done would be 0. So why do we say that at that height $h$ the body will have potential energy $mgh$?







forces newtonian-gravity work potential-energy conservative-field






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edited Aug 19 at 21:41









Peter Mortensen

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asked Aug 19 at 10:09









Santam

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152











  • If the object is dropped, it will have a final kinetic energy of mgh. This is why we say it has potential energy.
    – Kenshin
    Aug 19 at 10:31






  • 1




    This question addresses Newtonian gravity in which energy is conservative, but FWIW, in general relativity with a cosmological constant, global conservation of energy does not exist.
    – ohwilleke
    Aug 19 at 21:48
















  • If the object is dropped, it will have a final kinetic energy of mgh. This is why we say it has potential energy.
    – Kenshin
    Aug 19 at 10:31






  • 1




    This question addresses Newtonian gravity in which energy is conservative, but FWIW, in general relativity with a cosmological constant, global conservation of energy does not exist.
    – ohwilleke
    Aug 19 at 21:48















If the object is dropped, it will have a final kinetic energy of mgh. This is why we say it has potential energy.
– Kenshin
Aug 19 at 10:31




If the object is dropped, it will have a final kinetic energy of mgh. This is why we say it has potential energy.
– Kenshin
Aug 19 at 10:31




1




1




This question addresses Newtonian gravity in which energy is conservative, but FWIW, in general relativity with a cosmological constant, global conservation of energy does not exist.
– ohwilleke
Aug 19 at 21:48




This question addresses Newtonian gravity in which energy is conservative, but FWIW, in general relativity with a cosmological constant, global conservation of energy does not exist.
– ohwilleke
Aug 19 at 21:48










3 Answers
3






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6
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so net work done would be 0




Net work of all forces is 0, and that is why kinetic energy of the body does not change - it remains 0. This is an example of the general theorem



$$textwork of all forces while body moves from A to B = textkinetic energy at B - kinetic energy at A$$



It does not mean that change in potential energy is zero.



Gravitational potential energy increases when you move the body against the gravity force.






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    1
    down vote













    There is no relationship between net work and potential energy in general. Potential energy only relates to the work done by the force that is associated with that potential energy.



    So for gravity we can say for the work done by gravity and change in potential energy: $$W_grav=-mg(h_2-h_1)=-Delta U_grav$$. Assuming the object starts at $h_1$, ends at $h_2$, and $h_2>h_1$ (i.e. the object is lifted up).



    Now what about the net work done on the object (the total work done by you and gravity) when we lift the object up and then hold it in place? Well in general the force you supply can be complicated. For example, you aren't going to be applying a constant magnitude of force, and we don't exactly know how this magnitude changes over time. However, we can use the work-kinetic energy relation $$W_total=W_you+W_grav=Delta K$$
    If the object starts and ends at rest, then $Delta K=0$, so we know the work you do is $$W_you=-W_grav=mg(h_2-h_1)$$



    So we have accounted for all work and energy in the system. Gravity does negative work, which gives the object an increase in potential energy, but the net work is $0$.






    share|cite|improve this answer



























      up vote
      0
      down vote













      When you lift a body, you add some potential energy to the body-earth system.



      While doing it, you are performing positive work against the gravitational force, which is an internal force in the body-earth system.



      Since the gravitational force is internal, it cannot change the energy of the system and, therefore, its effect should not be counted, when we calculate the final energy of the system.



      This is similar to stretching a spring. When you stretch a spring, you perform
      positive work against its internal elastic forces and add some potential energy to it, but you don't consider the negative work one half of the spring performs on the other, because the internal forces cannot change the energy of the spring and, therefore, their effect should not be counted, when we calculate the final energy of the spring.






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        3 Answers
        3






        active

        oldest

        votes








        3 Answers
        3






        active

        oldest

        votes









        active

        oldest

        votes






        active

        oldest

        votes








        up vote
        6
        down vote














        so net work done would be 0




        Net work of all forces is 0, and that is why kinetic energy of the body does not change - it remains 0. This is an example of the general theorem



        $$textwork of all forces while body moves from A to B = textkinetic energy at B - kinetic energy at A$$



        It does not mean that change in potential energy is zero.



        Gravitational potential energy increases when you move the body against the gravity force.






        share|cite|improve this answer
























          up vote
          6
          down vote














          so net work done would be 0




          Net work of all forces is 0, and that is why kinetic energy of the body does not change - it remains 0. This is an example of the general theorem



          $$textwork of all forces while body moves from A to B = textkinetic energy at B - kinetic energy at A$$



          It does not mean that change in potential energy is zero.



          Gravitational potential energy increases when you move the body against the gravity force.






          share|cite|improve this answer






















            up vote
            6
            down vote










            up vote
            6
            down vote










            so net work done would be 0




            Net work of all forces is 0, and that is why kinetic energy of the body does not change - it remains 0. This is an example of the general theorem



            $$textwork of all forces while body moves from A to B = textkinetic energy at B - kinetic energy at A$$



            It does not mean that change in potential energy is zero.



            Gravitational potential energy increases when you move the body against the gravity force.






            share|cite|improve this answer













            so net work done would be 0




            Net work of all forces is 0, and that is why kinetic energy of the body does not change - it remains 0. This is an example of the general theorem



            $$textwork of all forces while body moves from A to B = textkinetic energy at B - kinetic energy at A$$



            It does not mean that change in potential energy is zero.



            Gravitational potential energy increases when you move the body against the gravity force.







            share|cite|improve this answer












            share|cite|improve this answer



            share|cite|improve this answer










            answered Aug 19 at 10:36









            Ján Lalinský

            13.2k1233




            13.2k1233




















                up vote
                1
                down vote













                There is no relationship between net work and potential energy in general. Potential energy only relates to the work done by the force that is associated with that potential energy.



                So for gravity we can say for the work done by gravity and change in potential energy: $$W_grav=-mg(h_2-h_1)=-Delta U_grav$$. Assuming the object starts at $h_1$, ends at $h_2$, and $h_2>h_1$ (i.e. the object is lifted up).



                Now what about the net work done on the object (the total work done by you and gravity) when we lift the object up and then hold it in place? Well in general the force you supply can be complicated. For example, you aren't going to be applying a constant magnitude of force, and we don't exactly know how this magnitude changes over time. However, we can use the work-kinetic energy relation $$W_total=W_you+W_grav=Delta K$$
                If the object starts and ends at rest, then $Delta K=0$, so we know the work you do is $$W_you=-W_grav=mg(h_2-h_1)$$



                So we have accounted for all work and energy in the system. Gravity does negative work, which gives the object an increase in potential energy, but the net work is $0$.






                share|cite|improve this answer
























                  up vote
                  1
                  down vote













                  There is no relationship between net work and potential energy in general. Potential energy only relates to the work done by the force that is associated with that potential energy.



                  So for gravity we can say for the work done by gravity and change in potential energy: $$W_grav=-mg(h_2-h_1)=-Delta U_grav$$. Assuming the object starts at $h_1$, ends at $h_2$, and $h_2>h_1$ (i.e. the object is lifted up).



                  Now what about the net work done on the object (the total work done by you and gravity) when we lift the object up and then hold it in place? Well in general the force you supply can be complicated. For example, you aren't going to be applying a constant magnitude of force, and we don't exactly know how this magnitude changes over time. However, we can use the work-kinetic energy relation $$W_total=W_you+W_grav=Delta K$$
                  If the object starts and ends at rest, then $Delta K=0$, so we know the work you do is $$W_you=-W_grav=mg(h_2-h_1)$$



                  So we have accounted for all work and energy in the system. Gravity does negative work, which gives the object an increase in potential energy, but the net work is $0$.






                  share|cite|improve this answer






















                    up vote
                    1
                    down vote










                    up vote
                    1
                    down vote









                    There is no relationship between net work and potential energy in general. Potential energy only relates to the work done by the force that is associated with that potential energy.



                    So for gravity we can say for the work done by gravity and change in potential energy: $$W_grav=-mg(h_2-h_1)=-Delta U_grav$$. Assuming the object starts at $h_1$, ends at $h_2$, and $h_2>h_1$ (i.e. the object is lifted up).



                    Now what about the net work done on the object (the total work done by you and gravity) when we lift the object up and then hold it in place? Well in general the force you supply can be complicated. For example, you aren't going to be applying a constant magnitude of force, and we don't exactly know how this magnitude changes over time. However, we can use the work-kinetic energy relation $$W_total=W_you+W_grav=Delta K$$
                    If the object starts and ends at rest, then $Delta K=0$, so we know the work you do is $$W_you=-W_grav=mg(h_2-h_1)$$



                    So we have accounted for all work and energy in the system. Gravity does negative work, which gives the object an increase in potential energy, but the net work is $0$.






                    share|cite|improve this answer












                    There is no relationship between net work and potential energy in general. Potential energy only relates to the work done by the force that is associated with that potential energy.



                    So for gravity we can say for the work done by gravity and change in potential energy: $$W_grav=-mg(h_2-h_1)=-Delta U_grav$$. Assuming the object starts at $h_1$, ends at $h_2$, and $h_2>h_1$ (i.e. the object is lifted up).



                    Now what about the net work done on the object (the total work done by you and gravity) when we lift the object up and then hold it in place? Well in general the force you supply can be complicated. For example, you aren't going to be applying a constant magnitude of force, and we don't exactly know how this magnitude changes over time. However, we can use the work-kinetic energy relation $$W_total=W_you+W_grav=Delta K$$
                    If the object starts and ends at rest, then $Delta K=0$, so we know the work you do is $$W_you=-W_grav=mg(h_2-h_1)$$



                    So we have accounted for all work and energy in the system. Gravity does negative work, which gives the object an increase in potential energy, but the net work is $0$.







                    share|cite|improve this answer












                    share|cite|improve this answer



                    share|cite|improve this answer










                    answered Aug 19 at 11:40









                    Aaron Stevens

                    3,085319




                    3,085319




















                        up vote
                        0
                        down vote













                        When you lift a body, you add some potential energy to the body-earth system.



                        While doing it, you are performing positive work against the gravitational force, which is an internal force in the body-earth system.



                        Since the gravitational force is internal, it cannot change the energy of the system and, therefore, its effect should not be counted, when we calculate the final energy of the system.



                        This is similar to stretching a spring. When you stretch a spring, you perform
                        positive work against its internal elastic forces and add some potential energy to it, but you don't consider the negative work one half of the spring performs on the other, because the internal forces cannot change the energy of the spring and, therefore, their effect should not be counted, when we calculate the final energy of the spring.






                        share|cite|improve this answer
























                          up vote
                          0
                          down vote













                          When you lift a body, you add some potential energy to the body-earth system.



                          While doing it, you are performing positive work against the gravitational force, which is an internal force in the body-earth system.



                          Since the gravitational force is internal, it cannot change the energy of the system and, therefore, its effect should not be counted, when we calculate the final energy of the system.



                          This is similar to stretching a spring. When you stretch a spring, you perform
                          positive work against its internal elastic forces and add some potential energy to it, but you don't consider the negative work one half of the spring performs on the other, because the internal forces cannot change the energy of the spring and, therefore, their effect should not be counted, when we calculate the final energy of the spring.






                          share|cite|improve this answer






















                            up vote
                            0
                            down vote










                            up vote
                            0
                            down vote









                            When you lift a body, you add some potential energy to the body-earth system.



                            While doing it, you are performing positive work against the gravitational force, which is an internal force in the body-earth system.



                            Since the gravitational force is internal, it cannot change the energy of the system and, therefore, its effect should not be counted, when we calculate the final energy of the system.



                            This is similar to stretching a spring. When you stretch a spring, you perform
                            positive work against its internal elastic forces and add some potential energy to it, but you don't consider the negative work one half of the spring performs on the other, because the internal forces cannot change the energy of the spring and, therefore, their effect should not be counted, when we calculate the final energy of the spring.






                            share|cite|improve this answer












                            When you lift a body, you add some potential energy to the body-earth system.



                            While doing it, you are performing positive work against the gravitational force, which is an internal force in the body-earth system.



                            Since the gravitational force is internal, it cannot change the energy of the system and, therefore, its effect should not be counted, when we calculate the final energy of the system.



                            This is similar to stretching a spring. When you stretch a spring, you perform
                            positive work against its internal elastic forces and add some potential energy to it, but you don't consider the negative work one half of the spring performs on the other, because the internal forces cannot change the energy of the spring and, therefore, their effect should not be counted, when we calculate the final energy of the spring.







                            share|cite|improve this answer












                            share|cite|improve this answer



                            share|cite|improve this answer










                            answered Aug 19 at 23:57









                            V.F.

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