Why does energy conservation give me the wrong answer in this inelastic collision problem?












2












$begingroup$


Suppose there are two objects. The first object is stationary and has the next parameters: v1=0 m/s, m1= 4kg. The second object is heading towards the first one with speed v2= 8m/s and mass m2= 60 kg. Due to collision, objects merge into one and continue to move with the velocity v3. Suppose all the energy gets converted into speed. I want to know the magnitude of velocity v3. My question is : Why do we get slightly different results when using kinetic energy compared to conservation of momentum when solving for v3. If we assume no energy gets converted into heat, couldn't we set up equations like : Ek1=0 J and Ek2=$frac{m_2*v_2^2}{2}$ . E3=E2+E1=$frac{v_3^2}{2}*(m_1+m_2)$ . v3=$sqrt{frac{(E_1+E_2)*2}{(m_1+m_2)}}$ ? Why do we get different result this way comparing to the result when we calculate v3 using conservation of momentum?










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$endgroup$








  • 2




    $begingroup$
    Energy is not conserved in your setup.
    $endgroup$
    – Jasper
    15 hours ago






  • 2




    $begingroup$
    @knzhou With this edit, the answer is right in the title...
    $endgroup$
    – Jasper
    7 hours ago






  • 1




    $begingroup$
    @Jasper Not at all! If somebody doesn't understand why inelastic collisions (i.e. sticking together) don't conserve energy, the title edit doesn't change anything. All it does is make the answer easier to see for people who do know mechanics.
    $endgroup$
    – knzhou
    7 hours ago












  • $begingroup$
    Imagine the two objct being cars. When they collide, they change their outer form (alas!), and that takes up some energy you don't get back. That's where the "missing energy" from the correct momentum-based calculation goes into.
    $endgroup$
    – Ralf Kleberhoff
    7 hours ago






  • 1




    $begingroup$
    @RalfKleberhoff This is where the energy could go, but in general the objects to not need to deform for the collision to be perfectly inelastic.
    $endgroup$
    – Aaron Stevens
    5 hours ago
















2












$begingroup$


Suppose there are two objects. The first object is stationary and has the next parameters: v1=0 m/s, m1= 4kg. The second object is heading towards the first one with speed v2= 8m/s and mass m2= 60 kg. Due to collision, objects merge into one and continue to move with the velocity v3. Suppose all the energy gets converted into speed. I want to know the magnitude of velocity v3. My question is : Why do we get slightly different results when using kinetic energy compared to conservation of momentum when solving for v3. If we assume no energy gets converted into heat, couldn't we set up equations like : Ek1=0 J and Ek2=$frac{m_2*v_2^2}{2}$ . E3=E2+E1=$frac{v_3^2}{2}*(m_1+m_2)$ . v3=$sqrt{frac{(E_1+E_2)*2}{(m_1+m_2)}}$ ? Why do we get different result this way comparing to the result when we calculate v3 using conservation of momentum?










share|cite|improve this question











$endgroup$








  • 2




    $begingroup$
    Energy is not conserved in your setup.
    $endgroup$
    – Jasper
    15 hours ago






  • 2




    $begingroup$
    @knzhou With this edit, the answer is right in the title...
    $endgroup$
    – Jasper
    7 hours ago






  • 1




    $begingroup$
    @Jasper Not at all! If somebody doesn't understand why inelastic collisions (i.e. sticking together) don't conserve energy, the title edit doesn't change anything. All it does is make the answer easier to see for people who do know mechanics.
    $endgroup$
    – knzhou
    7 hours ago












  • $begingroup$
    Imagine the two objct being cars. When they collide, they change their outer form (alas!), and that takes up some energy you don't get back. That's where the "missing energy" from the correct momentum-based calculation goes into.
    $endgroup$
    – Ralf Kleberhoff
    7 hours ago






  • 1




    $begingroup$
    @RalfKleberhoff This is where the energy could go, but in general the objects to not need to deform for the collision to be perfectly inelastic.
    $endgroup$
    – Aaron Stevens
    5 hours ago














2












2








2





$begingroup$


Suppose there are two objects. The first object is stationary and has the next parameters: v1=0 m/s, m1= 4kg. The second object is heading towards the first one with speed v2= 8m/s and mass m2= 60 kg. Due to collision, objects merge into one and continue to move with the velocity v3. Suppose all the energy gets converted into speed. I want to know the magnitude of velocity v3. My question is : Why do we get slightly different results when using kinetic energy compared to conservation of momentum when solving for v3. If we assume no energy gets converted into heat, couldn't we set up equations like : Ek1=0 J and Ek2=$frac{m_2*v_2^2}{2}$ . E3=E2+E1=$frac{v_3^2}{2}*(m_1+m_2)$ . v3=$sqrt{frac{(E_1+E_2)*2}{(m_1+m_2)}}$ ? Why do we get different result this way comparing to the result when we calculate v3 using conservation of momentum?










share|cite|improve this question











$endgroup$




Suppose there are two objects. The first object is stationary and has the next parameters: v1=0 m/s, m1= 4kg. The second object is heading towards the first one with speed v2= 8m/s and mass m2= 60 kg. Due to collision, objects merge into one and continue to move with the velocity v3. Suppose all the energy gets converted into speed. I want to know the magnitude of velocity v3. My question is : Why do we get slightly different results when using kinetic energy compared to conservation of momentum when solving for v3. If we assume no energy gets converted into heat, couldn't we set up equations like : Ek1=0 J and Ek2=$frac{m_2*v_2^2}{2}$ . E3=E2+E1=$frac{v_3^2}{2}*(m_1+m_2)$ . v3=$sqrt{frac{(E_1+E_2)*2}{(m_1+m_2)}}$ ? Why do we get different result this way comparing to the result when we calculate v3 using conservation of momentum?







newtonian-mechanics energy momentum energy-conservation collision






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share|cite|improve this question













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share|cite|improve this question








edited 12 hours ago









knzhou

45k11122218




45k11122218










asked 16 hours ago









ToTheSpace 2ToTheSpace 2

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221








  • 2




    $begingroup$
    Energy is not conserved in your setup.
    $endgroup$
    – Jasper
    15 hours ago






  • 2




    $begingroup$
    @knzhou With this edit, the answer is right in the title...
    $endgroup$
    – Jasper
    7 hours ago






  • 1




    $begingroup$
    @Jasper Not at all! If somebody doesn't understand why inelastic collisions (i.e. sticking together) don't conserve energy, the title edit doesn't change anything. All it does is make the answer easier to see for people who do know mechanics.
    $endgroup$
    – knzhou
    7 hours ago












  • $begingroup$
    Imagine the two objct being cars. When they collide, they change their outer form (alas!), and that takes up some energy you don't get back. That's where the "missing energy" from the correct momentum-based calculation goes into.
    $endgroup$
    – Ralf Kleberhoff
    7 hours ago






  • 1




    $begingroup$
    @RalfKleberhoff This is where the energy could go, but in general the objects to not need to deform for the collision to be perfectly inelastic.
    $endgroup$
    – Aaron Stevens
    5 hours ago














  • 2




    $begingroup$
    Energy is not conserved in your setup.
    $endgroup$
    – Jasper
    15 hours ago






  • 2




    $begingroup$
    @knzhou With this edit, the answer is right in the title...
    $endgroup$
    – Jasper
    7 hours ago






  • 1




    $begingroup$
    @Jasper Not at all! If somebody doesn't understand why inelastic collisions (i.e. sticking together) don't conserve energy, the title edit doesn't change anything. All it does is make the answer easier to see for people who do know mechanics.
    $endgroup$
    – knzhou
    7 hours ago












  • $begingroup$
    Imagine the two objct being cars. When they collide, they change their outer form (alas!), and that takes up some energy you don't get back. That's where the "missing energy" from the correct momentum-based calculation goes into.
    $endgroup$
    – Ralf Kleberhoff
    7 hours ago






  • 1




    $begingroup$
    @RalfKleberhoff This is where the energy could go, but in general the objects to not need to deform for the collision to be perfectly inelastic.
    $endgroup$
    – Aaron Stevens
    5 hours ago








2




2




$begingroup$
Energy is not conserved in your setup.
$endgroup$
– Jasper
15 hours ago




$begingroup$
Energy is not conserved in your setup.
$endgroup$
– Jasper
15 hours ago




2




2




$begingroup$
@knzhou With this edit, the answer is right in the title...
$endgroup$
– Jasper
7 hours ago




$begingroup$
@knzhou With this edit, the answer is right in the title...
$endgroup$
– Jasper
7 hours ago




1




1




$begingroup$
@Jasper Not at all! If somebody doesn't understand why inelastic collisions (i.e. sticking together) don't conserve energy, the title edit doesn't change anything. All it does is make the answer easier to see for people who do know mechanics.
$endgroup$
– knzhou
7 hours ago






$begingroup$
@Jasper Not at all! If somebody doesn't understand why inelastic collisions (i.e. sticking together) don't conserve energy, the title edit doesn't change anything. All it does is make the answer easier to see for people who do know mechanics.
$endgroup$
– knzhou
7 hours ago














$begingroup$
Imagine the two objct being cars. When they collide, they change their outer form (alas!), and that takes up some energy you don't get back. That's where the "missing energy" from the correct momentum-based calculation goes into.
$endgroup$
– Ralf Kleberhoff
7 hours ago




$begingroup$
Imagine the two objct being cars. When they collide, they change their outer form (alas!), and that takes up some energy you don't get back. That's where the "missing energy" from the correct momentum-based calculation goes into.
$endgroup$
– Ralf Kleberhoff
7 hours ago




1




1




$begingroup$
@RalfKleberhoff This is where the energy could go, but in general the objects to not need to deform for the collision to be perfectly inelastic.
$endgroup$
– Aaron Stevens
5 hours ago




$begingroup$
@RalfKleberhoff This is where the energy could go, but in general the objects to not need to deform for the collision to be perfectly inelastic.
$endgroup$
– Aaron Stevens
5 hours ago










5 Answers
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Momentum is conserved if there are no external forces involved. This is the case in your setup, so the final velocity you get from conservation of momentum is right.



If you start with conservation of energy, you'll see that you get a different velocity.



Since physicists strongly believe in conservation of energy, this means that some of the mechanical energy went somewhere. This is a strong hint that you can not assume conservation of mechanical energy at will. If you assume both conservation of momentum and energy, the bodies can't stick together and move as one.



The "sticking" eats up some energy that is lost on the mechanical side.






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$endgroup$









  • 2




    $begingroup$
    Since physicists strongly believe in conservation of energy... I don't think the belief in it makes the conclusions true. Conservation of energy isn't like Tinker Bell :)
    $endgroup$
    – Aaron Stevens
    5 hours ago



















4












$begingroup$

The other answers are correct in saying that energy is not conserved, but I feel like they are lacking in truly showing why this is the case. So let's assume energy and momentum are both conserved in this process and see that we arrive at a contradiction.



So we have object 1 at rest and object 2 hits it and they stick together. Using momentum conservation:
$$m_2v_2=m_1v+m_2v$$



Using energy conservation (cancelling $1/2$ from each term):
$$m_2v_2^2=m_1v^2+m_2v^2$$



Now for fun tricks. In each of the above equations let's get all terms involving object 2 on the left and all terms involving object 1 on the right and then divide the energy equation by the momentum equation:



$$frac{m_2(v_2^2-v^2)}{m_2(v_2-v)}=frac{m_1v^2}{m_1v}$$



Now, $v_2^2-v^2=(v_2-v)(v_2+v)$, therefore (cancelling many things)



$$v_2+v=v$$
or
$$v_2=0$$



Uh oh. We see that before the collision object 2 is at rest. But object 1 was at rest also$^*$. Therefore no collision with these properties could have occurred. Therefore something is wrong with our assumptions of both energy and momentum conservation.



Momentum has to be conserved since there are no external forces on the system. Therefore it must be that energy is not conserved. There is nothing saying energy must be conserved here, but we have now shown that it actually cannot be conserved.





$^*$ In general if we had specified the velocity of $m_1$ by $v_1$ we would have arrived at $v_1=v_2$ using similar methods used above. This just means the objects started out with the same velocity and never actually collide. Therefore, the only way our system can conserve both energy and momentum and have equal "final" velocities is if no collision happened.






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$endgroup$





















    2












    $begingroup$

    The objects are merged, and an inelastic collision is one in which objects stick together after impact: kinetic energy is not conserved. Therefore, you can't assume that kinetic energy is conserved; merging takes a little bit of energy.



    If this system is isolated, and no force acted upon neither of the two objects, then, momentum is conserved; hence, you can calculate the final velocity using the momentum's equation.






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    Busy Minder is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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    $endgroup$





















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      $begingroup$


      Suppose all the energy gets converted into speed.




      Uh oh! That's your error. You can't just suppose that something that doesn't happen, happens.



      The collision was inelastic. That means some of the energy gets converted to heat, as the objects merge. This is the difference between your total before and after energy.






      share|cite|improve this answer









      $endgroup$





















        0












        $begingroup$

        I think that the hypothesis of momentum conservation is flawed since the problem really doesn't state that. Also there's nothing saying that the system is isolated at all.



        Hence you calculated what you can (assuming that "energy" in the problem statement refers only to the kinetic energy itself).
        If the hypothesis of kinetic energy conversion is correct (I would assume so since it's stated) then your energy-based calculation is correct :) and the missing momentum is due to an external source.






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        New contributor




        user3155984 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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        $endgroup$









        • 2




          $begingroup$
          Momentum is conserved in collisions. Why would you assume external forces? It seems like you are the one making additional assumptions, not the OP.
          $endgroup$
          – Aaron Stevens
          5 hours ago












        • $begingroup$
          @Aaron: I know what is momentum/energy conservation. I'm not making any additional assumptions and just using the conditions stated in the problem. If the problem is badly formulated this is another situation.
          $endgroup$
          – user3155984
          5 hours ago






        • 1




          $begingroup$
          The problem isn't poorly formulated. Just before and just after the collision momentum has to be conserved. If there are external forces then you just have to look just before and just after. Momentum will not be lost due to the collision, and it seems like the OP is interested in the collision, not unspecified external forces that aren't involved with the collision.
          $endgroup$
          – Aaron Stevens
          5 hours ago











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        5 Answers
        5






        active

        oldest

        votes








        5 Answers
        5






        active

        oldest

        votes









        active

        oldest

        votes






        active

        oldest

        votes









        4












        $begingroup$

        Momentum is conserved if there are no external forces involved. This is the case in your setup, so the final velocity you get from conservation of momentum is right.



        If you start with conservation of energy, you'll see that you get a different velocity.



        Since physicists strongly believe in conservation of energy, this means that some of the mechanical energy went somewhere. This is a strong hint that you can not assume conservation of mechanical energy at will. If you assume both conservation of momentum and energy, the bodies can't stick together and move as one.



        The "sticking" eats up some energy that is lost on the mechanical side.






        share|cite|improve this answer









        $endgroup$









        • 2




          $begingroup$
          Since physicists strongly believe in conservation of energy... I don't think the belief in it makes the conclusions true. Conservation of energy isn't like Tinker Bell :)
          $endgroup$
          – Aaron Stevens
          5 hours ago
















        4












        $begingroup$

        Momentum is conserved if there are no external forces involved. This is the case in your setup, so the final velocity you get from conservation of momentum is right.



        If you start with conservation of energy, you'll see that you get a different velocity.



        Since physicists strongly believe in conservation of energy, this means that some of the mechanical energy went somewhere. This is a strong hint that you can not assume conservation of mechanical energy at will. If you assume both conservation of momentum and energy, the bodies can't stick together and move as one.



        The "sticking" eats up some energy that is lost on the mechanical side.






        share|cite|improve this answer









        $endgroup$









        • 2




          $begingroup$
          Since physicists strongly believe in conservation of energy... I don't think the belief in it makes the conclusions true. Conservation of energy isn't like Tinker Bell :)
          $endgroup$
          – Aaron Stevens
          5 hours ago














        4












        4








        4





        $begingroup$

        Momentum is conserved if there are no external forces involved. This is the case in your setup, so the final velocity you get from conservation of momentum is right.



        If you start with conservation of energy, you'll see that you get a different velocity.



        Since physicists strongly believe in conservation of energy, this means that some of the mechanical energy went somewhere. This is a strong hint that you can not assume conservation of mechanical energy at will. If you assume both conservation of momentum and energy, the bodies can't stick together and move as one.



        The "sticking" eats up some energy that is lost on the mechanical side.






        share|cite|improve this answer









        $endgroup$



        Momentum is conserved if there are no external forces involved. This is the case in your setup, so the final velocity you get from conservation of momentum is right.



        If you start with conservation of energy, you'll see that you get a different velocity.



        Since physicists strongly believe in conservation of energy, this means that some of the mechanical energy went somewhere. This is a strong hint that you can not assume conservation of mechanical energy at will. If you assume both conservation of momentum and energy, the bodies can't stick together and move as one.



        The "sticking" eats up some energy that is lost on the mechanical side.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered 15 hours ago









        JasperJasper

        1,0941517




        1,0941517








        • 2




          $begingroup$
          Since physicists strongly believe in conservation of energy... I don't think the belief in it makes the conclusions true. Conservation of energy isn't like Tinker Bell :)
          $endgroup$
          – Aaron Stevens
          5 hours ago














        • 2




          $begingroup$
          Since physicists strongly believe in conservation of energy... I don't think the belief in it makes the conclusions true. Conservation of energy isn't like Tinker Bell :)
          $endgroup$
          – Aaron Stevens
          5 hours ago








        2




        2




        $begingroup$
        Since physicists strongly believe in conservation of energy... I don't think the belief in it makes the conclusions true. Conservation of energy isn't like Tinker Bell :)
        $endgroup$
        – Aaron Stevens
        5 hours ago




        $begingroup$
        Since physicists strongly believe in conservation of energy... I don't think the belief in it makes the conclusions true. Conservation of energy isn't like Tinker Bell :)
        $endgroup$
        – Aaron Stevens
        5 hours ago











        4












        $begingroup$

        The other answers are correct in saying that energy is not conserved, but I feel like they are lacking in truly showing why this is the case. So let's assume energy and momentum are both conserved in this process and see that we arrive at a contradiction.



        So we have object 1 at rest and object 2 hits it and they stick together. Using momentum conservation:
        $$m_2v_2=m_1v+m_2v$$



        Using energy conservation (cancelling $1/2$ from each term):
        $$m_2v_2^2=m_1v^2+m_2v^2$$



        Now for fun tricks. In each of the above equations let's get all terms involving object 2 on the left and all terms involving object 1 on the right and then divide the energy equation by the momentum equation:



        $$frac{m_2(v_2^2-v^2)}{m_2(v_2-v)}=frac{m_1v^2}{m_1v}$$



        Now, $v_2^2-v^2=(v_2-v)(v_2+v)$, therefore (cancelling many things)



        $$v_2+v=v$$
        or
        $$v_2=0$$



        Uh oh. We see that before the collision object 2 is at rest. But object 1 was at rest also$^*$. Therefore no collision with these properties could have occurred. Therefore something is wrong with our assumptions of both energy and momentum conservation.



        Momentum has to be conserved since there are no external forces on the system. Therefore it must be that energy is not conserved. There is nothing saying energy must be conserved here, but we have now shown that it actually cannot be conserved.





        $^*$ In general if we had specified the velocity of $m_1$ by $v_1$ we would have arrived at $v_1=v_2$ using similar methods used above. This just means the objects started out with the same velocity and never actually collide. Therefore, the only way our system can conserve both energy and momentum and have equal "final" velocities is if no collision happened.






        share|cite|improve this answer











        $endgroup$


















          4












          $begingroup$

          The other answers are correct in saying that energy is not conserved, but I feel like they are lacking in truly showing why this is the case. So let's assume energy and momentum are both conserved in this process and see that we arrive at a contradiction.



          So we have object 1 at rest and object 2 hits it and they stick together. Using momentum conservation:
          $$m_2v_2=m_1v+m_2v$$



          Using energy conservation (cancelling $1/2$ from each term):
          $$m_2v_2^2=m_1v^2+m_2v^2$$



          Now for fun tricks. In each of the above equations let's get all terms involving object 2 on the left and all terms involving object 1 on the right and then divide the energy equation by the momentum equation:



          $$frac{m_2(v_2^2-v^2)}{m_2(v_2-v)}=frac{m_1v^2}{m_1v}$$



          Now, $v_2^2-v^2=(v_2-v)(v_2+v)$, therefore (cancelling many things)



          $$v_2+v=v$$
          or
          $$v_2=0$$



          Uh oh. We see that before the collision object 2 is at rest. But object 1 was at rest also$^*$. Therefore no collision with these properties could have occurred. Therefore something is wrong with our assumptions of both energy and momentum conservation.



          Momentum has to be conserved since there are no external forces on the system. Therefore it must be that energy is not conserved. There is nothing saying energy must be conserved here, but we have now shown that it actually cannot be conserved.





          $^*$ In general if we had specified the velocity of $m_1$ by $v_1$ we would have arrived at $v_1=v_2$ using similar methods used above. This just means the objects started out with the same velocity and never actually collide. Therefore, the only way our system can conserve both energy and momentum and have equal "final" velocities is if no collision happened.






          share|cite|improve this answer











          $endgroup$
















            4












            4








            4





            $begingroup$

            The other answers are correct in saying that energy is not conserved, but I feel like they are lacking in truly showing why this is the case. So let's assume energy and momentum are both conserved in this process and see that we arrive at a contradiction.



            So we have object 1 at rest and object 2 hits it and they stick together. Using momentum conservation:
            $$m_2v_2=m_1v+m_2v$$



            Using energy conservation (cancelling $1/2$ from each term):
            $$m_2v_2^2=m_1v^2+m_2v^2$$



            Now for fun tricks. In each of the above equations let's get all terms involving object 2 on the left and all terms involving object 1 on the right and then divide the energy equation by the momentum equation:



            $$frac{m_2(v_2^2-v^2)}{m_2(v_2-v)}=frac{m_1v^2}{m_1v}$$



            Now, $v_2^2-v^2=(v_2-v)(v_2+v)$, therefore (cancelling many things)



            $$v_2+v=v$$
            or
            $$v_2=0$$



            Uh oh. We see that before the collision object 2 is at rest. But object 1 was at rest also$^*$. Therefore no collision with these properties could have occurred. Therefore something is wrong with our assumptions of both energy and momentum conservation.



            Momentum has to be conserved since there are no external forces on the system. Therefore it must be that energy is not conserved. There is nothing saying energy must be conserved here, but we have now shown that it actually cannot be conserved.





            $^*$ In general if we had specified the velocity of $m_1$ by $v_1$ we would have arrived at $v_1=v_2$ using similar methods used above. This just means the objects started out with the same velocity and never actually collide. Therefore, the only way our system can conserve both energy and momentum and have equal "final" velocities is if no collision happened.






            share|cite|improve this answer











            $endgroup$



            The other answers are correct in saying that energy is not conserved, but I feel like they are lacking in truly showing why this is the case. So let's assume energy and momentum are both conserved in this process and see that we arrive at a contradiction.



            So we have object 1 at rest and object 2 hits it and they stick together. Using momentum conservation:
            $$m_2v_2=m_1v+m_2v$$



            Using energy conservation (cancelling $1/2$ from each term):
            $$m_2v_2^2=m_1v^2+m_2v^2$$



            Now for fun tricks. In each of the above equations let's get all terms involving object 2 on the left and all terms involving object 1 on the right and then divide the energy equation by the momentum equation:



            $$frac{m_2(v_2^2-v^2)}{m_2(v_2-v)}=frac{m_1v^2}{m_1v}$$



            Now, $v_2^2-v^2=(v_2-v)(v_2+v)$, therefore (cancelling many things)



            $$v_2+v=v$$
            or
            $$v_2=0$$



            Uh oh. We see that before the collision object 2 is at rest. But object 1 was at rest also$^*$. Therefore no collision with these properties could have occurred. Therefore something is wrong with our assumptions of both energy and momentum conservation.



            Momentum has to be conserved since there are no external forces on the system. Therefore it must be that energy is not conserved. There is nothing saying energy must be conserved here, but we have now shown that it actually cannot be conserved.





            $^*$ In general if we had specified the velocity of $m_1$ by $v_1$ we would have arrived at $v_1=v_2$ using similar methods used above. This just means the objects started out with the same velocity and never actually collide. Therefore, the only way our system can conserve both energy and momentum and have equal "final" velocities is if no collision happened.







            share|cite|improve this answer














            share|cite|improve this answer



            share|cite|improve this answer








            edited 6 hours ago

























            answered 14 hours ago









            Aaron StevensAaron Stevens

            13k42248




            13k42248























                2












                $begingroup$

                The objects are merged, and an inelastic collision is one in which objects stick together after impact: kinetic energy is not conserved. Therefore, you can't assume that kinetic energy is conserved; merging takes a little bit of energy.



                If this system is isolated, and no force acted upon neither of the two objects, then, momentum is conserved; hence, you can calculate the final velocity using the momentum's equation.






                share|cite|improve this answer








                New contributor




                Busy Minder is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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                $endgroup$


















                  2












                  $begingroup$

                  The objects are merged, and an inelastic collision is one in which objects stick together after impact: kinetic energy is not conserved. Therefore, you can't assume that kinetic energy is conserved; merging takes a little bit of energy.



                  If this system is isolated, and no force acted upon neither of the two objects, then, momentum is conserved; hence, you can calculate the final velocity using the momentum's equation.






                  share|cite|improve this answer








                  New contributor




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






                  $endgroup$
















                    2












                    2








                    2





                    $begingroup$

                    The objects are merged, and an inelastic collision is one in which objects stick together after impact: kinetic energy is not conserved. Therefore, you can't assume that kinetic energy is conserved; merging takes a little bit of energy.



                    If this system is isolated, and no force acted upon neither of the two objects, then, momentum is conserved; hence, you can calculate the final velocity using the momentum's equation.






                    share|cite|improve this answer








                    New contributor




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






                    $endgroup$



                    The objects are merged, and an inelastic collision is one in which objects stick together after impact: kinetic energy is not conserved. Therefore, you can't assume that kinetic energy is conserved; merging takes a little bit of energy.



                    If this system is isolated, and no force acted upon neither of the two objects, then, momentum is conserved; hence, you can calculate the final velocity using the momentum's equation.







                    share|cite|improve this answer








                    New contributor




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









                    share|cite|improve this answer



                    share|cite|improve this answer






                    New contributor




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                    answered 15 hours ago









                    Busy MinderBusy Minder

                    213




                    213




                    New contributor




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                    New contributor





                    Busy Minder is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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                    Busy Minder is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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                        2












                        $begingroup$


                        Suppose all the energy gets converted into speed.




                        Uh oh! That's your error. You can't just suppose that something that doesn't happen, happens.



                        The collision was inelastic. That means some of the energy gets converted to heat, as the objects merge. This is the difference between your total before and after energy.






                        share|cite|improve this answer









                        $endgroup$


















                          2












                          $begingroup$


                          Suppose all the energy gets converted into speed.




                          Uh oh! That's your error. You can't just suppose that something that doesn't happen, happens.



                          The collision was inelastic. That means some of the energy gets converted to heat, as the objects merge. This is the difference between your total before and after energy.






                          share|cite|improve this answer









                          $endgroup$
















                            2












                            2








                            2





                            $begingroup$


                            Suppose all the energy gets converted into speed.




                            Uh oh! That's your error. You can't just suppose that something that doesn't happen, happens.



                            The collision was inelastic. That means some of the energy gets converted to heat, as the objects merge. This is the difference between your total before and after energy.






                            share|cite|improve this answer









                            $endgroup$




                            Suppose all the energy gets converted into speed.




                            Uh oh! That's your error. You can't just suppose that something that doesn't happen, happens.



                            The collision was inelastic. That means some of the energy gets converted to heat, as the objects merge. This is the difference between your total before and after energy.







                            share|cite|improve this answer












                            share|cite|improve this answer



                            share|cite|improve this answer










                            answered 10 hours ago









                            Neil_UKNeil_UK

                            1605




                            1605























                                0












                                $begingroup$

                                I think that the hypothesis of momentum conservation is flawed since the problem really doesn't state that. Also there's nothing saying that the system is isolated at all.



                                Hence you calculated what you can (assuming that "energy" in the problem statement refers only to the kinetic energy itself).
                                If the hypothesis of kinetic energy conversion is correct (I would assume so since it's stated) then your energy-based calculation is correct :) and the missing momentum is due to an external source.






                                share|cite|improve this answer








                                New contributor




                                user3155984 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                                Check out our Code of Conduct.






                                $endgroup$









                                • 2




                                  $begingroup$
                                  Momentum is conserved in collisions. Why would you assume external forces? It seems like you are the one making additional assumptions, not the OP.
                                  $endgroup$
                                  – Aaron Stevens
                                  5 hours ago












                                • $begingroup$
                                  @Aaron: I know what is momentum/energy conservation. I'm not making any additional assumptions and just using the conditions stated in the problem. If the problem is badly formulated this is another situation.
                                  $endgroup$
                                  – user3155984
                                  5 hours ago






                                • 1




                                  $begingroup$
                                  The problem isn't poorly formulated. Just before and just after the collision momentum has to be conserved. If there are external forces then you just have to look just before and just after. Momentum will not be lost due to the collision, and it seems like the OP is interested in the collision, not unspecified external forces that aren't involved with the collision.
                                  $endgroup$
                                  – Aaron Stevens
                                  5 hours ago
















                                0












                                $begingroup$

                                I think that the hypothesis of momentum conservation is flawed since the problem really doesn't state that. Also there's nothing saying that the system is isolated at all.



                                Hence you calculated what you can (assuming that "energy" in the problem statement refers only to the kinetic energy itself).
                                If the hypothesis of kinetic energy conversion is correct (I would assume so since it's stated) then your energy-based calculation is correct :) and the missing momentum is due to an external source.






                                share|cite|improve this answer








                                New contributor




                                user3155984 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                                Check out our Code of Conduct.






                                $endgroup$









                                • 2




                                  $begingroup$
                                  Momentum is conserved in collisions. Why would you assume external forces? It seems like you are the one making additional assumptions, not the OP.
                                  $endgroup$
                                  – Aaron Stevens
                                  5 hours ago












                                • $begingroup$
                                  @Aaron: I know what is momentum/energy conservation. I'm not making any additional assumptions and just using the conditions stated in the problem. If the problem is badly formulated this is another situation.
                                  $endgroup$
                                  – user3155984
                                  5 hours ago






                                • 1




                                  $begingroup$
                                  The problem isn't poorly formulated. Just before and just after the collision momentum has to be conserved. If there are external forces then you just have to look just before and just after. Momentum will not be lost due to the collision, and it seems like the OP is interested in the collision, not unspecified external forces that aren't involved with the collision.
                                  $endgroup$
                                  – Aaron Stevens
                                  5 hours ago














                                0












                                0








                                0





                                $begingroup$

                                I think that the hypothesis of momentum conservation is flawed since the problem really doesn't state that. Also there's nothing saying that the system is isolated at all.



                                Hence you calculated what you can (assuming that "energy" in the problem statement refers only to the kinetic energy itself).
                                If the hypothesis of kinetic energy conversion is correct (I would assume so since it's stated) then your energy-based calculation is correct :) and the missing momentum is due to an external source.






                                share|cite|improve this answer








                                New contributor




                                user3155984 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                                Check out our Code of Conduct.






                                $endgroup$



                                I think that the hypothesis of momentum conservation is flawed since the problem really doesn't state that. Also there's nothing saying that the system is isolated at all.



                                Hence you calculated what you can (assuming that "energy" in the problem statement refers only to the kinetic energy itself).
                                If the hypothesis of kinetic energy conversion is correct (I would assume so since it's stated) then your energy-based calculation is correct :) and the missing momentum is due to an external source.







                                share|cite|improve this answer








                                New contributor




                                user3155984 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                                Check out our Code of Conduct.









                                share|cite|improve this answer



                                share|cite|improve this answer






                                New contributor




                                user3155984 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                                Check out our Code of Conduct.









                                answered 5 hours ago









                                user3155984user3155984

                                1




                                1




                                New contributor




                                user3155984 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                                Check out our Code of Conduct.





                                New contributor





                                user3155984 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                                Check out our Code of Conduct.






                                user3155984 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                                Check out our Code of Conduct.








                                • 2




                                  $begingroup$
                                  Momentum is conserved in collisions. Why would you assume external forces? It seems like you are the one making additional assumptions, not the OP.
                                  $endgroup$
                                  – Aaron Stevens
                                  5 hours ago












                                • $begingroup$
                                  @Aaron: I know what is momentum/energy conservation. I'm not making any additional assumptions and just using the conditions stated in the problem. If the problem is badly formulated this is another situation.
                                  $endgroup$
                                  – user3155984
                                  5 hours ago






                                • 1




                                  $begingroup$
                                  The problem isn't poorly formulated. Just before and just after the collision momentum has to be conserved. If there are external forces then you just have to look just before and just after. Momentum will not be lost due to the collision, and it seems like the OP is interested in the collision, not unspecified external forces that aren't involved with the collision.
                                  $endgroup$
                                  – Aaron Stevens
                                  5 hours ago














                                • 2




                                  $begingroup$
                                  Momentum is conserved in collisions. Why would you assume external forces? It seems like you are the one making additional assumptions, not the OP.
                                  $endgroup$
                                  – Aaron Stevens
                                  5 hours ago












                                • $begingroup$
                                  @Aaron: I know what is momentum/energy conservation. I'm not making any additional assumptions and just using the conditions stated in the problem. If the problem is badly formulated this is another situation.
                                  $endgroup$
                                  – user3155984
                                  5 hours ago






                                • 1




                                  $begingroup$
                                  The problem isn't poorly formulated. Just before and just after the collision momentum has to be conserved. If there are external forces then you just have to look just before and just after. Momentum will not be lost due to the collision, and it seems like the OP is interested in the collision, not unspecified external forces that aren't involved with the collision.
                                  $endgroup$
                                  – Aaron Stevens
                                  5 hours ago








                                2




                                2




                                $begingroup$
                                Momentum is conserved in collisions. Why would you assume external forces? It seems like you are the one making additional assumptions, not the OP.
                                $endgroup$
                                – Aaron Stevens
                                5 hours ago






                                $begingroup$
                                Momentum is conserved in collisions. Why would you assume external forces? It seems like you are the one making additional assumptions, not the OP.
                                $endgroup$
                                – Aaron Stevens
                                5 hours ago














                                $begingroup$
                                @Aaron: I know what is momentum/energy conservation. I'm not making any additional assumptions and just using the conditions stated in the problem. If the problem is badly formulated this is another situation.
                                $endgroup$
                                – user3155984
                                5 hours ago




                                $begingroup$
                                @Aaron: I know what is momentum/energy conservation. I'm not making any additional assumptions and just using the conditions stated in the problem. If the problem is badly formulated this is another situation.
                                $endgroup$
                                – user3155984
                                5 hours ago




                                1




                                1




                                $begingroup$
                                The problem isn't poorly formulated. Just before and just after the collision momentum has to be conserved. If there are external forces then you just have to look just before and just after. Momentum will not be lost due to the collision, and it seems like the OP is interested in the collision, not unspecified external forces that aren't involved with the collision.
                                $endgroup$
                                – Aaron Stevens
                                5 hours ago




                                $begingroup$
                                The problem isn't poorly formulated. Just before and just after the collision momentum has to be conserved. If there are external forces then you just have to look just before and just after. Momentum will not be lost due to the collision, and it seems like the OP is interested in the collision, not unspecified external forces that aren't involved with the collision.
                                $endgroup$
                                – Aaron Stevens
                                5 hours ago


















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