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

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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=$fracm_2*v_2^22$ . E3=E2+E1=$fracv_3^22*(m_1+m_2)$ . v3=$sqrtfrac(E_1+E_2)*2(m_1+m_2)$ ? Why do we get different result this way comparing to the result when we calculate v3 using conservation of momentum?










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  • 3




    $begingroup$
    Energy is not conserved in your setup.
    $endgroup$
    – Jasper
    Mar 16 at 9:30






  • 2




    $begingroup$
    @knzhou With this edit, the answer is right in the title...
    $endgroup$
    – Jasper
    Mar 16 at 17:40






  • 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
    Mar 16 at 17:41











  • $begingroup$
    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
    Mar 16 at 18:03






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    $begingroup$
    @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
    Mar 16 at 19:34















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=$fracm_2*v_2^22$ . E3=E2+E1=$fracv_3^22*(m_1+m_2)$ . v3=$sqrtfrac(E_1+E_2)*2(m_1+m_2)$ ? 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











$endgroup$







  • 3




    $begingroup$
    Energy is not conserved in your setup.
    $endgroup$
    – Jasper
    Mar 16 at 9:30






  • 2




    $begingroup$
    @knzhou With this edit, the answer is right in the title...
    $endgroup$
    – Jasper
    Mar 16 at 17:40






  • 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
    Mar 16 at 17:41











  • $begingroup$
    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
    Mar 16 at 18:03






  • 2




    $begingroup$
    @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
    Mar 16 at 19:34













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=$fracm_2*v_2^22$ . E3=E2+E1=$fracv_3^22*(m_1+m_2)$ . v3=$sqrtfrac(E_1+E_2)*2(m_1+m_2)$ ? 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=$fracm_2*v_2^22$ . E3=E2+E1=$fracv_3^22*(m_1+m_2)$ . v3=$sqrtfrac(E_1+E_2)*2(m_1+m_2)$ ? 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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edited Mar 16 at 12:44









knzhou

47k11127226




47k11127226










asked Mar 16 at 9:02









ToTheSpace 2ToTheSpace 2

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  • 3




    $begingroup$
    Energy is not conserved in your setup.
    $endgroup$
    – Jasper
    Mar 16 at 9:30






  • 2




    $begingroup$
    @knzhou With this edit, the answer is right in the title...
    $endgroup$
    – Jasper
    Mar 16 at 17:40






  • 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
    Mar 16 at 17:41











  • $begingroup$
    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
    Mar 16 at 18:03






  • 2




    $begingroup$
    @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
    Mar 16 at 19:34












  • 3




    $begingroup$
    Energy is not conserved in your setup.
    $endgroup$
    – Jasper
    Mar 16 at 9:30






  • 2




    $begingroup$
    @knzhou With this edit, the answer is right in the title...
    $endgroup$
    – Jasper
    Mar 16 at 17:40






  • 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
    Mar 16 at 17:41











  • $begingroup$
    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
    Mar 16 at 18:03






  • 2




    $begingroup$
    @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
    Mar 16 at 19:34







3




3




$begingroup$
Energy is not conserved in your setup.
$endgroup$
– Jasper
Mar 16 at 9:30




$begingroup$
Energy is not conserved in your setup.
$endgroup$
– Jasper
Mar 16 at 9:30




2




2




$begingroup$
@knzhou With this edit, the answer is right in the title...
$endgroup$
– Jasper
Mar 16 at 17:40




$begingroup$
@knzhou With this edit, the answer is right in the title...
$endgroup$
– Jasper
Mar 16 at 17:40




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
Mar 16 at 17:41





$begingroup$
@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
Mar 16 at 17:41













$begingroup$
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
Mar 16 at 18:03




$begingroup$
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
Mar 16 at 18:03




2




2




$begingroup$
@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
Mar 16 at 19:34




$begingroup$
@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
Mar 16 at 19:34










5 Answers
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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:



$$fracm_2(v_2^2-v^2)m_2(v_2-v)=fracm_1v^2m_1v$$



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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    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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    • 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
      Mar 16 at 19:36


















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    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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      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.






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        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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        • 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
          Mar 16 at 19:31











        • $begingroup$
          @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
          Mar 16 at 19:39






        • 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
          Mar 16 at 19:42










        • $begingroup$
          @AaronStevens The problem is badly formulated in the sense that it imposes two assumptions that contradict each other (given that there are no external forces), namely "objects merge into one" and "all the energy gets converted into speed."
          $endgroup$
          – Andreas Blass
          Mar 17 at 1:46










        • $begingroup$
          No... The OP is incorrectly assuming that energy is conserved when the objects stick together. The "problem" (or you could say system) is just a perfectly inelastic collision where the objects stick together. Any incorrect assumptions come from the OP, not from the "problem" or system.
          $endgroup$
          – Aaron Stevens
          Mar 17 at 2:00











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        5 Answers
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        active

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        5 Answers
        5






        active

        oldest

        votes









        active

        oldest

        votes






        active

        oldest

        votes









        6












        $begingroup$

        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:



        $$fracm_2(v_2^2-v^2)m_2(v_2-v)=fracm_1v^2m_1v$$



        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











        $endgroup$

















          6












          $begingroup$

          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:



          $$fracm_2(v_2^2-v^2)m_2(v_2-v)=fracm_1v^2m_1v$$



          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











          $endgroup$















            6












            6








            6





            $begingroup$

            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:



            $$fracm_2(v_2^2-v^2)m_2(v_2-v)=fracm_1v^2m_1v$$



            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:



            $$fracm_2(v_2^2-v^2)m_2(v_2-v)=fracm_1v^2m_1v$$



            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 Mar 16 at 18:53

























            answered Mar 16 at 10:29









            Aaron StevensAaron Stevens

            15.4k42555




            15.4k42555





















                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
                  Mar 16 at 19:36















                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
                  Mar 16 at 19:36













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                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 Mar 16 at 10:09









                JasperJasper

                1,2521517




                1,2521517







                • 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
                  Mar 16 at 19:36












                • 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
                  Mar 16 at 19:36







                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
                Mar 16 at 19:36




                $begingroup$
                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
                Mar 16 at 19:36











                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









                $endgroup$

















                  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









                  $endgroup$















                    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









                    $endgroup$



                    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












                    share|cite|improve this answer



                    share|cite|improve this answer










                    answered Mar 16 at 9:56









                    Busy MinderBusy Minder

                    213




                    213





















                        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 Mar 16 at 15:08









                            Neil_UKNeil_UK

                            1595




                            1595





















                                -2












                                $begingroup$

                                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









                                $endgroup$








                                • 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
                                  Mar 16 at 19:31











                                • $begingroup$
                                  @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
                                  Mar 16 at 19:39






                                • 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
                                  Mar 16 at 19:42










                                • $begingroup$
                                  @AaronStevens The problem is badly formulated in the sense that it imposes two assumptions that contradict each other (given that there are no external forces), namely "objects merge into one" and "all the energy gets converted into speed."
                                  $endgroup$
                                  – Andreas Blass
                                  Mar 17 at 1:46










                                • $begingroup$
                                  No... The OP is incorrectly assuming that energy is conserved when the objects stick together. The "problem" (or you could say system) is just a perfectly inelastic collision where the objects stick together. Any incorrect assumptions come from the OP, not from the "problem" or system.
                                  $endgroup$
                                  – Aaron Stevens
                                  Mar 17 at 2:00















                                -2












                                $begingroup$

                                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









                                $endgroup$








                                • 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
                                  Mar 16 at 19:31











                                • $begingroup$
                                  @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
                                  Mar 16 at 19:39






                                • 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
                                  Mar 16 at 19:42










                                • $begingroup$
                                  @AaronStevens The problem is badly formulated in the sense that it imposes two assumptions that contradict each other (given that there are no external forces), namely "objects merge into one" and "all the energy gets converted into speed."
                                  $endgroup$
                                  – Andreas Blass
                                  Mar 17 at 1:46










                                • $begingroup$
                                  No... The OP is incorrectly assuming that energy is conserved when the objects stick together. The "problem" (or you could say system) is just a perfectly inelastic collision where the objects stick together. Any incorrect assumptions come from the OP, not from the "problem" or system.
                                  $endgroup$
                                  – Aaron Stevens
                                  Mar 17 at 2:00













                                -2












                                -2








                                -2





                                $begingroup$

                                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









                                $endgroup$



                                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












                                share|cite|improve this answer



                                share|cite|improve this answer










                                answered Mar 16 at 19:24









                                user3155984user3155984

                                32




                                32







                                • 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
                                  Mar 16 at 19:31











                                • $begingroup$
                                  @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
                                  Mar 16 at 19:39






                                • 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
                                  Mar 16 at 19:42










                                • $begingroup$
                                  @AaronStevens The problem is badly formulated in the sense that it imposes two assumptions that contradict each other (given that there are no external forces), namely "objects merge into one" and "all the energy gets converted into speed."
                                  $endgroup$
                                  – Andreas Blass
                                  Mar 17 at 1:46










                                • $begingroup$
                                  No... The OP is incorrectly assuming that energy is conserved when the objects stick together. The "problem" (or you could say system) is just a perfectly inelastic collision where the objects stick together. Any incorrect assumptions come from the OP, not from the "problem" or system.
                                  $endgroup$
                                  – Aaron Stevens
                                  Mar 17 at 2:00












                                • 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
                                  Mar 16 at 19:31











                                • $begingroup$
                                  @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
                                  Mar 16 at 19:39






                                • 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
                                  Mar 16 at 19:42










                                • $begingroup$
                                  @AaronStevens The problem is badly formulated in the sense that it imposes two assumptions that contradict each other (given that there are no external forces), namely "objects merge into one" and "all the energy gets converted into speed."
                                  $endgroup$
                                  – Andreas Blass
                                  Mar 17 at 1:46










                                • $begingroup$
                                  No... The OP is incorrectly assuming that energy is conserved when the objects stick together. The "problem" (or you could say system) is just a perfectly inelastic collision where the objects stick together. Any incorrect assumptions come from the OP, not from the "problem" or system.
                                  $endgroup$
                                  – Aaron Stevens
                                  Mar 17 at 2:00







                                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
                                Mar 16 at 19:31





                                $begingroup$
                                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
                                Mar 16 at 19:31













                                $begingroup$
                                @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
                                Mar 16 at 19:39




                                $begingroup$
                                @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
                                Mar 16 at 19:39




                                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
                                Mar 16 at 19:42




                                $begingroup$
                                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
                                Mar 16 at 19:42












                                $begingroup$
                                @AaronStevens The problem is badly formulated in the sense that it imposes two assumptions that contradict each other (given that there are no external forces), namely "objects merge into one" and "all the energy gets converted into speed."
                                $endgroup$
                                – Andreas Blass
                                Mar 17 at 1:46




                                $begingroup$
                                @AaronStevens The problem is badly formulated in the sense that it imposes two assumptions that contradict each other (given that there are no external forces), namely "objects merge into one" and "all the energy gets converted into speed."
                                $endgroup$
                                – Andreas Blass
                                Mar 17 at 1:46












                                $begingroup$
                                No... The OP is incorrectly assuming that energy is conserved when the objects stick together. The "problem" (or you could say system) is just a perfectly inelastic collision where the objects stick together. Any incorrect assumptions come from the OP, not from the "problem" or system.
                                $endgroup$
                                – Aaron Stevens
                                Mar 17 at 2:00




                                $begingroup$
                                No... The OP is incorrectly assuming that energy is conserved when the objects stick together. The "problem" (or you could say system) is just a perfectly inelastic collision where the objects stick together. Any incorrect assumptions come from the OP, not from the "problem" or system.
                                $endgroup$
                                – Aaron Stevens
                                Mar 17 at 2:00

















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