Can potential energy be the sum of the work done by all forces?











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I often see that the total energy of a system is the sum of potential energy+ kinetic energy. Is it always like that? Could I say that the total energy of a system is the sum of the work of all force + kinetic energy? I'm always confuse on which force gives a potential or not... But maybe at the end, it's just the sum of work of each force?










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  • Body has energy of movement, that is kinetic energy. Potential energy is defined as a work of certain (so-called conservative) forces to a body. So total energy in mechanics is simply the potential energy plus kinetic energy.
    – Pygmalion
    6 hours ago










  • @Pygmalion : why don't w consider the work of the non conservative force in the total energy ?
    – user623855
    6 hours ago










  • Because it turns into other non-mechanical forms of energy (internal energy, heat...)
    – Pygmalion
    6 hours ago






  • 1




    @Pygmalion Please post answers as answers and not as comments
    – Aaron Stevens
    6 hours ago















up vote
3
down vote

favorite
1












I often see that the total energy of a system is the sum of potential energy+ kinetic energy. Is it always like that? Could I say that the total energy of a system is the sum of the work of all force + kinetic energy? I'm always confuse on which force gives a potential or not... But maybe at the end, it's just the sum of work of each force?










share|cite|improve this question









New contributor




user623855 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.




















  • Body has energy of movement, that is kinetic energy. Potential energy is defined as a work of certain (so-called conservative) forces to a body. So total energy in mechanics is simply the potential energy plus kinetic energy.
    – Pygmalion
    6 hours ago










  • @Pygmalion : why don't w consider the work of the non conservative force in the total energy ?
    – user623855
    6 hours ago










  • Because it turns into other non-mechanical forms of energy (internal energy, heat...)
    – Pygmalion
    6 hours ago






  • 1




    @Pygmalion Please post answers as answers and not as comments
    – Aaron Stevens
    6 hours ago













up vote
3
down vote

favorite
1









up vote
3
down vote

favorite
1






1





I often see that the total energy of a system is the sum of potential energy+ kinetic energy. Is it always like that? Could I say that the total energy of a system is the sum of the work of all force + kinetic energy? I'm always confuse on which force gives a potential or not... But maybe at the end, it's just the sum of work of each force?










share|cite|improve this question









New contributor




user623855 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











I often see that the total energy of a system is the sum of potential energy+ kinetic energy. Is it always like that? Could I say that the total energy of a system is the sum of the work of all force + kinetic energy? I'm always confuse on which force gives a potential or not... But maybe at the end, it's just the sum of work of each force?







newtonian-mechanics forces energy work potential-energy






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edited 59 mins ago









Bill N

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asked 6 hours ago









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  • Body has energy of movement, that is kinetic energy. Potential energy is defined as a work of certain (so-called conservative) forces to a body. So total energy in mechanics is simply the potential energy plus kinetic energy.
    – Pygmalion
    6 hours ago










  • @Pygmalion : why don't w consider the work of the non conservative force in the total energy ?
    – user623855
    6 hours ago










  • Because it turns into other non-mechanical forms of energy (internal energy, heat...)
    – Pygmalion
    6 hours ago






  • 1




    @Pygmalion Please post answers as answers and not as comments
    – Aaron Stevens
    6 hours ago


















  • Body has energy of movement, that is kinetic energy. Potential energy is defined as a work of certain (so-called conservative) forces to a body. So total energy in mechanics is simply the potential energy plus kinetic energy.
    – Pygmalion
    6 hours ago










  • @Pygmalion : why don't w consider the work of the non conservative force in the total energy ?
    – user623855
    6 hours ago










  • Because it turns into other non-mechanical forms of energy (internal energy, heat...)
    – Pygmalion
    6 hours ago






  • 1




    @Pygmalion Please post answers as answers and not as comments
    – Aaron Stevens
    6 hours ago
















Body has energy of movement, that is kinetic energy. Potential energy is defined as a work of certain (so-called conservative) forces to a body. So total energy in mechanics is simply the potential energy plus kinetic energy.
– Pygmalion
6 hours ago




Body has energy of movement, that is kinetic energy. Potential energy is defined as a work of certain (so-called conservative) forces to a body. So total energy in mechanics is simply the potential energy plus kinetic energy.
– Pygmalion
6 hours ago












@Pygmalion : why don't w consider the work of the non conservative force in the total energy ?
– user623855
6 hours ago




@Pygmalion : why don't w consider the work of the non conservative force in the total energy ?
– user623855
6 hours ago












Because it turns into other non-mechanical forms of energy (internal energy, heat...)
– Pygmalion
6 hours ago




Because it turns into other non-mechanical forms of energy (internal energy, heat...)
– Pygmalion
6 hours ago




1




1




@Pygmalion Please post answers as answers and not as comments
– Aaron Stevens
6 hours ago




@Pygmalion Please post answers as answers and not as comments
– Aaron Stevens
6 hours ago










4 Answers
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4
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Could I say that the total energy of a system is the sum of the work of all force + kinetic energy ?




You can not do this because the work done by a force is not a state function. What this means is that we cannot define a unique "work done by all forces" of a system based on the state of the system. You would have to know how the forces acted on the system in the past, and even then you would have to define a starting time and initial energy of the system to using this method. In other words, the total energy would depend on when we decide to start adding up all of the work that has been done on the system.



The reason we define the total energy as $E=K+U$ is because of how we define these energies and forces to make life easier. I will consider a single particle, but this can be generalized to more complicated systems. We know that the net work on a particle (over some time) determines its change in kinetic energy:



$$W_{net}=Delta K$$



But we can also express the net work as work done by a sum of work done by conservative and non-conservative forces:



$$W_{net}=W_c+W_{nc}$$



But by definition of conservative forces and their associated potential energies, we know that



$$W_c=-Delta U$$



Therefore, if we define our total energy as $E=K+U$, then we see that



$$Delta E=Delta K+Delta U=W_{nc}$$



So we find that only non-conservative forces can change what we have defined as total energy. Furthermore, if there are no non-conservative forces acting on the particle, we see that total energy is conserved.



Going back to my first point, we see that our definition $E=K+U$ only depends on the state of the system (typically just the position and velocities of particles). It doesn't depend on the history of the system. Notice how work only determines changes in energy, never actual energy values.




I'm always confuse on which force gives a potential or not




Conservative forces have a potential energy associated with them. Conservative forces are forces that have zero curl, or in other words are forces where the work done by that force does not depend on the path through space the system takes. When this is the case, we can write out a potential energy such that
$$mathbf F=-nabla U$$
Or in one dimension
$$F=-frac{text d U}{text d x}$$






share|cite|improve this answer























  • Being relative to starting time is not much worse than simply relative to chosen zero point of energy. And potential energy (and thus total energy) does have this freedom.
    – Ruslan
    3 hours ago


















up vote
2
down vote













For a given system the total energy is described as the energy contained in the movement of the components of the system and a potential enery given by the conservative forces that affect the system. Other forces normally make the system either lose or gain energy so those are not accounted for in the system directly (refer to "heat" in thermodynamics) and if you consider relativistic effects you should also account for rest-mass energy with Einstein's equation.






share|cite|improve this answer




























    up vote
    1
    down vote













    This question touches on a deep subject with many facets. The other answers already posted represent some of those facets.



    I'll briefly mention one more: Noether's theorem. This theorem says that in a model that respects the action principle and that is symmetric under time-shifts, there is automatically a conserved quantity. We call it "energy." In Newtonian mechanics, this energy ends up being a sum of kinetic terms and potential terms. Other models might not have such a natural separation into "kinetic" and "potential" parts, even though they still have a conserved total energy defined via Noether's theorem.



    In electrodynamics, the force due to a magnetic field on a moving charged particle is proportional to the particle's speed but perpendicular to its velocity. This force is not the gradient of any potential energy in the more-familiar Newtonian sense, but electrodynamics still has a conserved total energy defined via Noether's theorem. Whether or not we try to separate this into "kinetic" and "potential" terms is a matter of taste and convenience. The total energy is what matters in this context, because the total energy is what's conserved.



    This definition based on Noether's theorem is just one of several related-but-different meanings of the word "energy" in physics. It's a deep subject, and the fact that the word is overloaded can make navigating the subject even more challenging.






    share|cite|improve this answer




























      up vote
      0
      down vote













      It is in fact the work done by all the forces plus some constants. These constants are just formalisms which are of no use in dynamical problems. In fact you don't even need the potential formalisms as long as you make sure to include the work done by those forces separately. In that case the work done on the system would correspond just to the change in kinetic energy of the system. The potential concept is there so that you don't need to integrate the force with x again and again, you can just use a formula. As long as you don't want to lose the sense of causality, I recommend not to use the potential; you can still get the same results by using only kinetic energy but including work by all forces.






      share|cite|improve this answer





















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        4 Answers
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        4 Answers
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        up vote
        4
        down vote














        Could I say that the total energy of a system is the sum of the work of all force + kinetic energy ?




        You can not do this because the work done by a force is not a state function. What this means is that we cannot define a unique "work done by all forces" of a system based on the state of the system. You would have to know how the forces acted on the system in the past, and even then you would have to define a starting time and initial energy of the system to using this method. In other words, the total energy would depend on when we decide to start adding up all of the work that has been done on the system.



        The reason we define the total energy as $E=K+U$ is because of how we define these energies and forces to make life easier. I will consider a single particle, but this can be generalized to more complicated systems. We know that the net work on a particle (over some time) determines its change in kinetic energy:



        $$W_{net}=Delta K$$



        But we can also express the net work as work done by a sum of work done by conservative and non-conservative forces:



        $$W_{net}=W_c+W_{nc}$$



        But by definition of conservative forces and their associated potential energies, we know that



        $$W_c=-Delta U$$



        Therefore, if we define our total energy as $E=K+U$, then we see that



        $$Delta E=Delta K+Delta U=W_{nc}$$



        So we find that only non-conservative forces can change what we have defined as total energy. Furthermore, if there are no non-conservative forces acting on the particle, we see that total energy is conserved.



        Going back to my first point, we see that our definition $E=K+U$ only depends on the state of the system (typically just the position and velocities of particles). It doesn't depend on the history of the system. Notice how work only determines changes in energy, never actual energy values.




        I'm always confuse on which force gives a potential or not




        Conservative forces have a potential energy associated with them. Conservative forces are forces that have zero curl, or in other words are forces where the work done by that force does not depend on the path through space the system takes. When this is the case, we can write out a potential energy such that
        $$mathbf F=-nabla U$$
        Or in one dimension
        $$F=-frac{text d U}{text d x}$$






        share|cite|improve this answer























        • Being relative to starting time is not much worse than simply relative to chosen zero point of energy. And potential energy (and thus total energy) does have this freedom.
          – Ruslan
          3 hours ago















        up vote
        4
        down vote














        Could I say that the total energy of a system is the sum of the work of all force + kinetic energy ?




        You can not do this because the work done by a force is not a state function. What this means is that we cannot define a unique "work done by all forces" of a system based on the state of the system. You would have to know how the forces acted on the system in the past, and even then you would have to define a starting time and initial energy of the system to using this method. In other words, the total energy would depend on when we decide to start adding up all of the work that has been done on the system.



        The reason we define the total energy as $E=K+U$ is because of how we define these energies and forces to make life easier. I will consider a single particle, but this can be generalized to more complicated systems. We know that the net work on a particle (over some time) determines its change in kinetic energy:



        $$W_{net}=Delta K$$



        But we can also express the net work as work done by a sum of work done by conservative and non-conservative forces:



        $$W_{net}=W_c+W_{nc}$$



        But by definition of conservative forces and their associated potential energies, we know that



        $$W_c=-Delta U$$



        Therefore, if we define our total energy as $E=K+U$, then we see that



        $$Delta E=Delta K+Delta U=W_{nc}$$



        So we find that only non-conservative forces can change what we have defined as total energy. Furthermore, if there are no non-conservative forces acting on the particle, we see that total energy is conserved.



        Going back to my first point, we see that our definition $E=K+U$ only depends on the state of the system (typically just the position and velocities of particles). It doesn't depend on the history of the system. Notice how work only determines changes in energy, never actual energy values.




        I'm always confuse on which force gives a potential or not




        Conservative forces have a potential energy associated with them. Conservative forces are forces that have zero curl, or in other words are forces where the work done by that force does not depend on the path through space the system takes. When this is the case, we can write out a potential energy such that
        $$mathbf F=-nabla U$$
        Or in one dimension
        $$F=-frac{text d U}{text d x}$$






        share|cite|improve this answer























        • Being relative to starting time is not much worse than simply relative to chosen zero point of energy. And potential energy (and thus total energy) does have this freedom.
          – Ruslan
          3 hours ago













        up vote
        4
        down vote










        up vote
        4
        down vote










        Could I say that the total energy of a system is the sum of the work of all force + kinetic energy ?




        You can not do this because the work done by a force is not a state function. What this means is that we cannot define a unique "work done by all forces" of a system based on the state of the system. You would have to know how the forces acted on the system in the past, and even then you would have to define a starting time and initial energy of the system to using this method. In other words, the total energy would depend on when we decide to start adding up all of the work that has been done on the system.



        The reason we define the total energy as $E=K+U$ is because of how we define these energies and forces to make life easier. I will consider a single particle, but this can be generalized to more complicated systems. We know that the net work on a particle (over some time) determines its change in kinetic energy:



        $$W_{net}=Delta K$$



        But we can also express the net work as work done by a sum of work done by conservative and non-conservative forces:



        $$W_{net}=W_c+W_{nc}$$



        But by definition of conservative forces and their associated potential energies, we know that



        $$W_c=-Delta U$$



        Therefore, if we define our total energy as $E=K+U$, then we see that



        $$Delta E=Delta K+Delta U=W_{nc}$$



        So we find that only non-conservative forces can change what we have defined as total energy. Furthermore, if there are no non-conservative forces acting on the particle, we see that total energy is conserved.



        Going back to my first point, we see that our definition $E=K+U$ only depends on the state of the system (typically just the position and velocities of particles). It doesn't depend on the history of the system. Notice how work only determines changes in energy, never actual energy values.




        I'm always confuse on which force gives a potential or not




        Conservative forces have a potential energy associated with them. Conservative forces are forces that have zero curl, or in other words are forces where the work done by that force does not depend on the path through space the system takes. When this is the case, we can write out a potential energy such that
        $$mathbf F=-nabla U$$
        Or in one dimension
        $$F=-frac{text d U}{text d x}$$






        share|cite|improve this answer















        Could I say that the total energy of a system is the sum of the work of all force + kinetic energy ?




        You can not do this because the work done by a force is not a state function. What this means is that we cannot define a unique "work done by all forces" of a system based on the state of the system. You would have to know how the forces acted on the system in the past, and even then you would have to define a starting time and initial energy of the system to using this method. In other words, the total energy would depend on when we decide to start adding up all of the work that has been done on the system.



        The reason we define the total energy as $E=K+U$ is because of how we define these energies and forces to make life easier. I will consider a single particle, but this can be generalized to more complicated systems. We know that the net work on a particle (over some time) determines its change in kinetic energy:



        $$W_{net}=Delta K$$



        But we can also express the net work as work done by a sum of work done by conservative and non-conservative forces:



        $$W_{net}=W_c+W_{nc}$$



        But by definition of conservative forces and their associated potential energies, we know that



        $$W_c=-Delta U$$



        Therefore, if we define our total energy as $E=K+U$, then we see that



        $$Delta E=Delta K+Delta U=W_{nc}$$



        So we find that only non-conservative forces can change what we have defined as total energy. Furthermore, if there are no non-conservative forces acting on the particle, we see that total energy is conserved.



        Going back to my first point, we see that our definition $E=K+U$ only depends on the state of the system (typically just the position and velocities of particles). It doesn't depend on the history of the system. Notice how work only determines changes in energy, never actual energy values.




        I'm always confuse on which force gives a potential or not




        Conservative forces have a potential energy associated with them. Conservative forces are forces that have zero curl, or in other words are forces where the work done by that force does not depend on the path through space the system takes. When this is the case, we can write out a potential energy such that
        $$mathbf F=-nabla U$$
        Or in one dimension
        $$F=-frac{text d U}{text d x}$$







        share|cite|improve this answer














        share|cite|improve this answer



        share|cite|improve this answer








        edited 5 hours ago

























        answered 5 hours ago









        Aaron Stevens

        8,03531235




        8,03531235












        • Being relative to starting time is not much worse than simply relative to chosen zero point of energy. And potential energy (and thus total energy) does have this freedom.
          – Ruslan
          3 hours ago


















        • Being relative to starting time is not much worse than simply relative to chosen zero point of energy. And potential energy (and thus total energy) does have this freedom.
          – Ruslan
          3 hours ago
















        Being relative to starting time is not much worse than simply relative to chosen zero point of energy. And potential energy (and thus total energy) does have this freedom.
        – Ruslan
        3 hours ago




        Being relative to starting time is not much worse than simply relative to chosen zero point of energy. And potential energy (and thus total energy) does have this freedom.
        – Ruslan
        3 hours ago










        up vote
        2
        down vote













        For a given system the total energy is described as the energy contained in the movement of the components of the system and a potential enery given by the conservative forces that affect the system. Other forces normally make the system either lose or gain energy so those are not accounted for in the system directly (refer to "heat" in thermodynamics) and if you consider relativistic effects you should also account for rest-mass energy with Einstein's equation.






        share|cite|improve this answer

























          up vote
          2
          down vote













          For a given system the total energy is described as the energy contained in the movement of the components of the system and a potential enery given by the conservative forces that affect the system. Other forces normally make the system either lose or gain energy so those are not accounted for in the system directly (refer to "heat" in thermodynamics) and if you consider relativistic effects you should also account for rest-mass energy with Einstein's equation.






          share|cite|improve this answer























            up vote
            2
            down vote










            up vote
            2
            down vote









            For a given system the total energy is described as the energy contained in the movement of the components of the system and a potential enery given by the conservative forces that affect the system. Other forces normally make the system either lose or gain energy so those are not accounted for in the system directly (refer to "heat" in thermodynamics) and if you consider relativistic effects you should also account for rest-mass energy with Einstein's equation.






            share|cite|improve this answer












            For a given system the total energy is described as the energy contained in the movement of the components of the system and a potential enery given by the conservative forces that affect the system. Other forces normally make the system either lose or gain energy so those are not accounted for in the system directly (refer to "heat" in thermodynamics) and if you consider relativistic effects you should also account for rest-mass energy with Einstein's equation.







            share|cite|improve this answer












            share|cite|improve this answer



            share|cite|improve this answer










            answered 6 hours ago









            Kirtpole

            1268




            1268






















                up vote
                1
                down vote













                This question touches on a deep subject with many facets. The other answers already posted represent some of those facets.



                I'll briefly mention one more: Noether's theorem. This theorem says that in a model that respects the action principle and that is symmetric under time-shifts, there is automatically a conserved quantity. We call it "energy." In Newtonian mechanics, this energy ends up being a sum of kinetic terms and potential terms. Other models might not have such a natural separation into "kinetic" and "potential" parts, even though they still have a conserved total energy defined via Noether's theorem.



                In electrodynamics, the force due to a magnetic field on a moving charged particle is proportional to the particle's speed but perpendicular to its velocity. This force is not the gradient of any potential energy in the more-familiar Newtonian sense, but electrodynamics still has a conserved total energy defined via Noether's theorem. Whether or not we try to separate this into "kinetic" and "potential" terms is a matter of taste and convenience. The total energy is what matters in this context, because the total energy is what's conserved.



                This definition based on Noether's theorem is just one of several related-but-different meanings of the word "energy" in physics. It's a deep subject, and the fact that the word is overloaded can make navigating the subject even more challenging.






                share|cite|improve this answer

























                  up vote
                  1
                  down vote













                  This question touches on a deep subject with many facets. The other answers already posted represent some of those facets.



                  I'll briefly mention one more: Noether's theorem. This theorem says that in a model that respects the action principle and that is symmetric under time-shifts, there is automatically a conserved quantity. We call it "energy." In Newtonian mechanics, this energy ends up being a sum of kinetic terms and potential terms. Other models might not have such a natural separation into "kinetic" and "potential" parts, even though they still have a conserved total energy defined via Noether's theorem.



                  In electrodynamics, the force due to a magnetic field on a moving charged particle is proportional to the particle's speed but perpendicular to its velocity. This force is not the gradient of any potential energy in the more-familiar Newtonian sense, but electrodynamics still has a conserved total energy defined via Noether's theorem. Whether or not we try to separate this into "kinetic" and "potential" terms is a matter of taste and convenience. The total energy is what matters in this context, because the total energy is what's conserved.



                  This definition based on Noether's theorem is just one of several related-but-different meanings of the word "energy" in physics. It's a deep subject, and the fact that the word is overloaded can make navigating the subject even more challenging.






                  share|cite|improve this answer























                    up vote
                    1
                    down vote










                    up vote
                    1
                    down vote









                    This question touches on a deep subject with many facets. The other answers already posted represent some of those facets.



                    I'll briefly mention one more: Noether's theorem. This theorem says that in a model that respects the action principle and that is symmetric under time-shifts, there is automatically a conserved quantity. We call it "energy." In Newtonian mechanics, this energy ends up being a sum of kinetic terms and potential terms. Other models might not have such a natural separation into "kinetic" and "potential" parts, even though they still have a conserved total energy defined via Noether's theorem.



                    In electrodynamics, the force due to a magnetic field on a moving charged particle is proportional to the particle's speed but perpendicular to its velocity. This force is not the gradient of any potential energy in the more-familiar Newtonian sense, but electrodynamics still has a conserved total energy defined via Noether's theorem. Whether or not we try to separate this into "kinetic" and "potential" terms is a matter of taste and convenience. The total energy is what matters in this context, because the total energy is what's conserved.



                    This definition based on Noether's theorem is just one of several related-but-different meanings of the word "energy" in physics. It's a deep subject, and the fact that the word is overloaded can make navigating the subject even more challenging.






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                    This question touches on a deep subject with many facets. The other answers already posted represent some of those facets.



                    I'll briefly mention one more: Noether's theorem. This theorem says that in a model that respects the action principle and that is symmetric under time-shifts, there is automatically a conserved quantity. We call it "energy." In Newtonian mechanics, this energy ends up being a sum of kinetic terms and potential terms. Other models might not have such a natural separation into "kinetic" and "potential" parts, even though they still have a conserved total energy defined via Noether's theorem.



                    In electrodynamics, the force due to a magnetic field on a moving charged particle is proportional to the particle's speed but perpendicular to its velocity. This force is not the gradient of any potential energy in the more-familiar Newtonian sense, but electrodynamics still has a conserved total energy defined via Noether's theorem. Whether or not we try to separate this into "kinetic" and "potential" terms is a matter of taste and convenience. The total energy is what matters in this context, because the total energy is what's conserved.



                    This definition based on Noether's theorem is just one of several related-but-different meanings of the word "energy" in physics. It's a deep subject, and the fact that the word is overloaded can make navigating the subject even more challenging.







                    share|cite|improve this answer












                    share|cite|improve this answer



                    share|cite|improve this answer










                    answered 5 hours ago









                    Dan Yand

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                        It is in fact the work done by all the forces plus some constants. These constants are just formalisms which are of no use in dynamical problems. In fact you don't even need the potential formalisms as long as you make sure to include the work done by those forces separately. In that case the work done on the system would correspond just to the change in kinetic energy of the system. The potential concept is there so that you don't need to integrate the force with x again and again, you can just use a formula. As long as you don't want to lose the sense of causality, I recommend not to use the potential; you can still get the same results by using only kinetic energy but including work by all forces.






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                          It is in fact the work done by all the forces plus some constants. These constants are just formalisms which are of no use in dynamical problems. In fact you don't even need the potential formalisms as long as you make sure to include the work done by those forces separately. In that case the work done on the system would correspond just to the change in kinetic energy of the system. The potential concept is there so that you don't need to integrate the force with x again and again, you can just use a formula. As long as you don't want to lose the sense of causality, I recommend not to use the potential; you can still get the same results by using only kinetic energy but including work by all forces.






                          share|cite|improve this answer























                            up vote
                            0
                            down vote










                            up vote
                            0
                            down vote









                            It is in fact the work done by all the forces plus some constants. These constants are just formalisms which are of no use in dynamical problems. In fact you don't even need the potential formalisms as long as you make sure to include the work done by those forces separately. In that case the work done on the system would correspond just to the change in kinetic energy of the system. The potential concept is there so that you don't need to integrate the force with x again and again, you can just use a formula. As long as you don't want to lose the sense of causality, I recommend not to use the potential; you can still get the same results by using only kinetic energy but including work by all forces.






                            share|cite|improve this answer












                            It is in fact the work done by all the forces plus some constants. These constants are just formalisms which are of no use in dynamical problems. In fact you don't even need the potential formalisms as long as you make sure to include the work done by those forces separately. In that case the work done on the system would correspond just to the change in kinetic energy of the system. The potential concept is there so that you don't need to integrate the force with x again and again, you can just use a formula. As long as you don't want to lose the sense of causality, I recommend not to use the potential; you can still get the same results by using only kinetic energy but including work by all forces.







                            share|cite|improve this answer












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                            share|cite|improve this answer










                            answered 4 hours ago









                            Yash Agarwal

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