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How is momentum conserved in this example?
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Suppose a sticky substance is thrown at wall. The initial momentum of the wall and substance system is only due to velocity of the substance but the final momentum is 0. Why is momentum not conserved?
newtonian-mechanics reference-frames momentum conservation-laws collision
edited 8 mins ago
Captain Man
1053
asked 4 hours ago
Vedansh Agrawal
383
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up vote
4
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Suppose a sticky substance is thrown at wall. The initial momentum of the wall and substance system is only due to velocity of the substance but the final momentum is 0. Why is momentum not conserved?
newtonian-mechanics reference-frames momentum conservation-laws collision
edited 8 mins ago
Captain Man
1053
asked 4 hours ago
Vedansh Agrawal
383
6
The final momentum is not $0$!
– tfb
4 hours ago
add a comment |Â
up vote
4
down vote
favorite
up vote
4
down vote
favorite
Suppose a sticky substance is thrown at wall. The initial momentum of the wall and substance system is only due to velocity of the substance but the final momentum is 0. Why is momentum not conserved?
newtonian-mechanics reference-frames momentum conservation-laws collision
edited 8 mins ago
Captain Man
1053
asked 4 hours ago
Vedansh Agrawal
383
Suppose a sticky substance is thrown at wall. The initial momentum of the wall and substance system is only due to velocity of the substance but the final momentum is 0. Why is momentum not conserved?
newtonian-mechanics reference-frames momentum conservation-laws collision
newtonian-mechanics reference-frames momentum conservation-laws collision
edited 8 mins ago
Captain Man
1053
asked 4 hours ago
Vedansh Agrawal
383
edited 8 mins ago
Captain Man
1053
asked 4 hours ago
Vedansh Agrawal
383
edited 8 mins ago
Captain Man
1053
edited 8 mins ago
Captain Man
1053
edited 8 mins ago
Captain Man
1053
1053
asked 4 hours ago
Vedansh Agrawal
383
asked 4 hours ago
Vedansh Agrawal
383
asked 4 hours ago
Vedansh Agrawal
383
383
6
The final momentum is not $0$!
– tfb
4 hours ago
add a comment |Â
6
The final momentum is not $0$!
– tfb
4 hours ago
6
6
The final momentum is not $0$!
– tfb
4 hours ago
The final momentum is not $0$!
– tfb
4 hours ago
add a comment |Â
4 Answers
4
active
oldest
votes
up vote
8
down vote
accepted
You should also consider what the wall is attached to. And obviously it is the Earth. If we assume the Earth's velocity is zero after the substance is thrown, since there is the force that slow down the substance at the moment of impact, there is also the reaction force on Earth with the same magnitude and opposite direction. So Earth will gain velocity and final momentum of combined Earth and substance system will be equal to the intial momentum of the substance.
And also we can look at the situation in a bit different way. When we stand on the floor and throw the substance, there appears a friction force between our feet and the floor and it acts on us in the throw direction. So the friction force on Earth will be opposite to the throw direction and Earth will pick up speed towards the substance, too. And at any moment, Earth plus substance system will have zero momentum. The substance and the Earth will move towards each other and after the impact their speed will be zero.
answered 3 hours ago
physicsguy19
483114
add a comment |Â
up vote
5
down vote
If you assume that you throw the sticky substance from rest at the wall then your assertion that the total final momentum of the Earth/wall/you and sticky substance system is correct. Indeed that is also the initial momentum of the Earth/wall/you and sticky substance system before you threw the sticky substance.
In the act of throwing the sticky substance, the Earth/wall/you impart momentum on the sticky substance $vec p_rm ss$, and as a consequence of Newton's third law, the sticky substance exerts an equal magnitude opposite direction momentum on the Earth/wall/you $vec p_rm Ewy$ such that the initial momentum of the system $0$ is equal to the final momentum of the system, i.e.
$$0 = vec p_rm ss+vec p_rm EwyRightarrow vec p_rm ss=-vec p_rm Ewy$$
Assuming no air resistance, etc. the reverse happens when the sticky substance hits and sticks to the wall with $$vec p_rm ss+vec p_rm Ewy=0.$$
Of course you do not notice the movement of the Earth, etc. because it is so much more massive than the mass of the sticky substance.
In terms of magnitudes: $$m_rm ss V_rm ss= M_rm Ewy v_rm Ewy Rightarrow v_rm Ewy = frac m_rm ssM_rm Ewytimes V_rm sstext and frac m_rm ssM_rm Ewyll1.$$
If you just consider the sticky substance already in motion, and the Earth/wall/you not moving before the sticky substance hits the wall, you have in terms of magnitudes:
$$m_rm ss V_rm ss= M_rm Ewyss v_rm Ewyss Rightarrow v_rm Ewyss = frac m_rm ssm_rm ss+ M_rm Ewytimes V_rm sstext and frac m_rm ssm_rm ss+ M_rm Ewyll 1$$
with there being no noticeable movement after the collision.
Mind you, would you notice if the wall, still intact and connected to the Earth, did move given that you would also be moving whilst standing on the Earth?
edited 1 hour ago
Kyle Kanos
21.3k114791
answered 3 hours ago
Farcher
45.2k33388
add a comment |Â
up vote
0
down vote
The wall will move a little bit as well as exert a small force on whatever it's attached to, etc., etc., until you get to applying a force to the Earth. Everything else is so massive, so we can't see this happening. You are assuming an immovable wall, which is not physically the case.
answered 4 hours ago
Aaron Stevens
4,1411624
add a comment |Â
up vote
0
down vote
Remember Newton’s 3rd law. The change in momentum is $F : Delta t$ (also known as impulse). So, since by Newton’s 3rd law the forces are equal and opposite then the change in momentum must also be equal and opposite.
Therefore, Newton’s laws guarantee conservation of momentum, and to see where the momentum goes all you have to do is look for the Newton’s 3rd law pair. So here momentum is transferred between the sticky substance and the wall, and the wall (being so massive) gains a little momentum which makes it move imperceptibly.
answered 3 hours ago
Dale
1,877415
add a comment |Â
4 Answers
4
active
oldest
votes
4 Answers
4
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
8
down vote
accepted
You should also consider what the wall is attached to. And obviously it is the Earth. If we assume the Earth's velocity is zero after the substance is thrown, since there is the force that slow down the substance at the moment of impact, there is also the reaction force on Earth with the same magnitude and opposite direction. So Earth will gain velocity and final momentum of combined Earth and substance system will be equal to the intial momentum of the substance.
And also we can look at the situation in a bit different way. When we stand on the floor and throw the substance, there appears a friction force between our feet and the floor and it acts on us in the throw direction. So the friction force on Earth will be opposite to the throw direction and Earth will pick up speed towards the substance, too. And at any moment, Earth plus substance system will have zero momentum. The substance and the Earth will move towards each other and after the impact their speed will be zero.
answered 3 hours ago
physicsguy19
483114
add a comment |Â
up vote
8
down vote
accepted
You should also consider what the wall is attached to. And obviously it is the Earth. If we assume the Earth's velocity is zero after the substance is thrown, since there is the force that slow down the substance at the moment of impact, there is also the reaction force on Earth with the same magnitude and opposite direction. So Earth will gain velocity and final momentum of combined Earth and substance system will be equal to the intial momentum of the substance.
And also we can look at the situation in a bit different way. When we stand on the floor and throw the substance, there appears a friction force between our feet and the floor and it acts on us in the throw direction. So the friction force on Earth will be opposite to the throw direction and Earth will pick up speed towards the substance, too. And at any moment, Earth plus substance system will have zero momentum. The substance and the Earth will move towards each other and after the impact their speed will be zero.
answered 3 hours ago
physicsguy19
483114
add a comment |Â
up vote
8
down vote
accepted
up vote
8
down vote
accepted
You should also consider what the wall is attached to. And obviously it is the Earth. If we assume the Earth's velocity is zero after the substance is thrown, since there is the force that slow down the substance at the moment of impact, there is also the reaction force on Earth with the same magnitude and opposite direction. So Earth will gain velocity and final momentum of combined Earth and substance system will be equal to the intial momentum of the substance.
And also we can look at the situation in a bit different way. When we stand on the floor and throw the substance, there appears a friction force between our feet and the floor and it acts on us in the throw direction. So the friction force on Earth will be opposite to the throw direction and Earth will pick up speed towards the substance, too. And at any moment, Earth plus substance system will have zero momentum. The substance and the Earth will move towards each other and after the impact their speed will be zero.
answered 3 hours ago
physicsguy19
483114
You should also consider what the wall is attached to. And obviously it is the Earth. If we assume the Earth's velocity is zero after the substance is thrown, since there is the force that slow down the substance at the moment of impact, there is also the reaction force on Earth with the same magnitude and opposite direction. So Earth will gain velocity and final momentum of combined Earth and substance system will be equal to the intial momentum of the substance.
And also we can look at the situation in a bit different way. When we stand on the floor and throw the substance, there appears a friction force between our feet and the floor and it acts on us in the throw direction. So the friction force on Earth will be opposite to the throw direction and Earth will pick up speed towards the substance, too. And at any moment, Earth plus substance system will have zero momentum. The substance and the Earth will move towards each other and after the impact their speed will be zero.
answered 3 hours ago
physicsguy19
483114
answered 3 hours ago
physicsguy19
483114
answered 3 hours ago
physicsguy19
483114
answered 3 hours ago
physicsguy19
483114
483114
add a comment |Â
add a comment |Â
up vote
5
down vote
If you assume that you throw the sticky substance from rest at the wall then your assertion that the total final momentum of the Earth/wall/you and sticky substance system is correct. Indeed that is also the initial momentum of the Earth/wall/you and sticky substance system before you threw the sticky substance.
In the act of throwing the sticky substance, the Earth/wall/you impart momentum on the sticky substance $vec p_rm ss$, and as a consequence of Newton's third law, the sticky substance exerts an equal magnitude opposite direction momentum on the Earth/wall/you $vec p_rm Ewy$ such that the initial momentum of the system $0$ is equal to the final momentum of the system, i.e.
$$0 = vec p_rm ss+vec p_rm EwyRightarrow vec p_rm ss=-vec p_rm Ewy$$
Assuming no air resistance, etc. the reverse happens when the sticky substance hits and sticks to the wall with $$vec p_rm ss+vec p_rm Ewy=0.$$
Of course you do not notice the movement of the Earth, etc. because it is so much more massive than the mass of the sticky substance.
In terms of magnitudes: $$m_rm ss V_rm ss= M_rm Ewy v_rm Ewy Rightarrow v_rm Ewy = frac m_rm ssM_rm Ewytimes V_rm sstext and frac m_rm ssM_rm Ewyll1.$$
If you just consider the sticky substance already in motion, and the Earth/wall/you not moving before the sticky substance hits the wall, you have in terms of magnitudes:
$$m_rm ss V_rm ss= M_rm Ewyss v_rm Ewyss Rightarrow v_rm Ewyss = frac m_rm ssm_rm ss+ M_rm Ewytimes V_rm sstext and frac m_rm ssm_rm ss+ M_rm Ewyll 1$$
with there being no noticeable movement after the collision.
Mind you, would you notice if the wall, still intact and connected to the Earth, did move given that you would also be moving whilst standing on the Earth?
edited 1 hour ago
Kyle Kanos
21.3k114791
answered 3 hours ago
Farcher
45.2k33388
add a comment |Â
up vote
5
down vote
If you assume that you throw the sticky substance from rest at the wall then your assertion that the total final momentum of the Earth/wall/you and sticky substance system is correct. Indeed that is also the initial momentum of the Earth/wall/you and sticky substance system before you threw the sticky substance.
In the act of throwing the sticky substance, the Earth/wall/you impart momentum on the sticky substance $vec p_rm ss$, and as a consequence of Newton's third law, the sticky substance exerts an equal magnitude opposite direction momentum on the Earth/wall/you $vec p_rm Ewy$ such that the initial momentum of the system $0$ is equal to the final momentum of the system, i.e.
$$0 = vec p_rm ss+vec p_rm EwyRightarrow vec p_rm ss=-vec p_rm Ewy$$
Assuming no air resistance, etc. the reverse happens when the sticky substance hits and sticks to the wall with $$vec p_rm ss+vec p_rm Ewy=0.$$
Of course you do not notice the movement of the Earth, etc. because it is so much more massive than the mass of the sticky substance.
In terms of magnitudes: $$m_rm ss V_rm ss= M_rm Ewy v_rm Ewy Rightarrow v_rm Ewy = frac m_rm ssM_rm Ewytimes V_rm sstext and frac m_rm ssM_rm Ewyll1.$$
If you just consider the sticky substance already in motion, and the Earth/wall/you not moving before the sticky substance hits the wall, you have in terms of magnitudes:
$$m_rm ss V_rm ss= M_rm Ewyss v_rm Ewyss Rightarrow v_rm Ewyss = frac m_rm ssm_rm ss+ M_rm Ewytimes V_rm sstext and frac m_rm ssm_rm ss+ M_rm Ewyll 1$$
with there being no noticeable movement after the collision.
Mind you, would you notice if the wall, still intact and connected to the Earth, did move given that you would also be moving whilst standing on the Earth?
edited 1 hour ago
Kyle Kanos
21.3k114791
answered 3 hours ago
Farcher
45.2k33388
add a comment |Â
up vote
5
down vote
up vote
5
down vote
If you assume that you throw the sticky substance from rest at the wall then your assertion that the total final momentum of the Earth/wall/you and sticky substance system is correct. Indeed that is also the initial momentum of the Earth/wall/you and sticky substance system before you threw the sticky substance.
In the act of throwing the sticky substance, the Earth/wall/you impart momentum on the sticky substance $vec p_rm ss$, and as a consequence of Newton's third law, the sticky substance exerts an equal magnitude opposite direction momentum on the Earth/wall/you $vec p_rm Ewy$ such that the initial momentum of the system $0$ is equal to the final momentum of the system, i.e.
$$0 = vec p_rm ss+vec p_rm EwyRightarrow vec p_rm ss=-vec p_rm Ewy$$
Assuming no air resistance, etc. the reverse happens when the sticky substance hits and sticks to the wall with $$vec p_rm ss+vec p_rm Ewy=0.$$
Of course you do not notice the movement of the Earth, etc. because it is so much more massive than the mass of the sticky substance.
In terms of magnitudes: $$m_rm ss V_rm ss= M_rm Ewy v_rm Ewy Rightarrow v_rm Ewy = frac m_rm ssM_rm Ewytimes V_rm sstext and frac m_rm ssM_rm Ewyll1.$$
If you just consider the sticky substance already in motion, and the Earth/wall/you not moving before the sticky substance hits the wall, you have in terms of magnitudes:
$$m_rm ss V_rm ss= M_rm Ewyss v_rm Ewyss Rightarrow v_rm Ewyss = frac m_rm ssm_rm ss+ M_rm Ewytimes V_rm sstext and frac m_rm ssm_rm ss+ M_rm Ewyll 1$$
with there being no noticeable movement after the collision.
Mind you, would you notice if the wall, still intact and connected to the Earth, did move given that you would also be moving whilst standing on the Earth?
edited 1 hour ago
Kyle Kanos
21.3k114791
answered 3 hours ago
Farcher
45.2k33388
If you assume that you throw the sticky substance from rest at the wall then your assertion that the total final momentum of the Earth/wall/you and sticky substance system is correct. Indeed that is also the initial momentum of the Earth/wall/you and sticky substance system before you threw the sticky substance.
In the act of throwing the sticky substance, the Earth/wall/you impart momentum on the sticky substance $vec p_rm ss$, and as a consequence of Newton's third law, the sticky substance exerts an equal magnitude opposite direction momentum on the Earth/wall/you $vec p_rm Ewy$ such that the initial momentum of the system $0$ is equal to the final momentum of the system, i.e.
$$0 = vec p_rm ss+vec p_rm EwyRightarrow vec p_rm ss=-vec p_rm Ewy$$
Assuming no air resistance, etc. the reverse happens when the sticky substance hits and sticks to the wall with $$vec p_rm ss+vec p_rm Ewy=0.$$
Of course you do not notice the movement of the Earth, etc. because it is so much more massive than the mass of the sticky substance.
In terms of magnitudes: $$m_rm ss V_rm ss= M_rm Ewy v_rm Ewy Rightarrow v_rm Ewy = frac m_rm ssM_rm Ewytimes V_rm sstext and frac m_rm ssM_rm Ewyll1.$$
If you just consider the sticky substance already in motion, and the Earth/wall/you not moving before the sticky substance hits the wall, you have in terms of magnitudes:
$$m_rm ss V_rm ss= M_rm Ewyss v_rm Ewyss Rightarrow v_rm Ewyss = frac m_rm ssm_rm ss+ M_rm Ewytimes V_rm sstext and frac m_rm ssm_rm ss+ M_rm Ewyll 1$$
with there being no noticeable movement after the collision.
Mind you, would you notice if the wall, still intact and connected to the Earth, did move given that you would also be moving whilst standing on the Earth?
edited 1 hour ago
Kyle Kanos
21.3k114791
answered 3 hours ago
Farcher
45.2k33388
edited 1 hour ago
Kyle Kanos
21.3k114791
edited 1 hour ago
Kyle Kanos
21.3k114791
edited 1 hour ago
Kyle Kanos
21.3k114791
21.3k114791
answered 3 hours ago
Farcher
45.2k33388
answered 3 hours ago
Farcher
45.2k33388
answered 3 hours ago
Farcher
45.2k33388
45.2k33388
add a comment |Â
add a comment |Â
up vote
0
down vote
The wall will move a little bit as well as exert a small force on whatever it's attached to, etc., etc., until you get to applying a force to the Earth. Everything else is so massive, so we can't see this happening. You are assuming an immovable wall, which is not physically the case.
answered 4 hours ago
Aaron Stevens
4,1411624
add a comment |Â
up vote
0
down vote
The wall will move a little bit as well as exert a small force on whatever it's attached to, etc., etc., until you get to applying a force to the Earth. Everything else is so massive, so we can't see this happening. You are assuming an immovable wall, which is not physically the case.
answered 4 hours ago
Aaron Stevens
4,1411624
add a comment |Â
up vote
0
down vote
up vote
0
down vote
The wall will move a little bit as well as exert a small force on whatever it's attached to, etc., etc., until you get to applying a force to the Earth. Everything else is so massive, so we can't see this happening. You are assuming an immovable wall, which is not physically the case.
answered 4 hours ago
Aaron Stevens
4,1411624
The wall will move a little bit as well as exert a small force on whatever it's attached to, etc., etc., until you get to applying a force to the Earth. Everything else is so massive, so we can't see this happening. You are assuming an immovable wall, which is not physically the case.
answered 4 hours ago
Aaron Stevens
4,1411624
answered 4 hours ago
Aaron Stevens
4,1411624
answered 4 hours ago
Aaron Stevens
4,1411624
answered 4 hours ago
Aaron Stevens
4,1411624
4,1411624
add a comment |Â
add a comment |Â
up vote
0
down vote
Remember Newton’s 3rd law. The change in momentum is $F : Delta t$ (also known as impulse). So, since by Newton’s 3rd law the forces are equal and opposite then the change in momentum must also be equal and opposite.
Therefore, Newton’s laws guarantee conservation of momentum, and to see where the momentum goes all you have to do is look for the Newton’s 3rd law pair. So here momentum is transferred between the sticky substance and the wall, and the wall (being so massive) gains a little momentum which makes it move imperceptibly.
answered 3 hours ago
Dale
1,877415
add a comment |Â
up vote
0
down vote
Remember Newton’s 3rd law. The change in momentum is $F : Delta t$ (also known as impulse). So, since by Newton’s 3rd law the forces are equal and opposite then the change in momentum must also be equal and opposite.
Therefore, Newton’s laws guarantee conservation of momentum, and to see where the momentum goes all you have to do is look for the Newton’s 3rd law pair. So here momentum is transferred between the sticky substance and the wall, and the wall (being so massive) gains a little momentum which makes it move imperceptibly.
answered 3 hours ago
Dale
1,877415
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Remember Newton’s 3rd law. The change in momentum is $F : Delta t$ (also known as impulse). So, since by Newton’s 3rd law the forces are equal and opposite then the change in momentum must also be equal and opposite.
Therefore, Newton’s laws guarantee conservation of momentum, and to see where the momentum goes all you have to do is look for the Newton’s 3rd law pair. So here momentum is transferred between the sticky substance and the wall, and the wall (being so massive) gains a little momentum which makes it move imperceptibly.
answered 3 hours ago
Dale
1,877415
Remember Newton’s 3rd law. The change in momentum is $F : Delta t$ (also known as impulse). So, since by Newton’s 3rd law the forces are equal and opposite then the change in momentum must also be equal and opposite.
Therefore, Newton’s laws guarantee conservation of momentum, and to see where the momentum goes all you have to do is look for the Newton’s 3rd law pair. So here momentum is transferred between the sticky substance and the wall, and the wall (being so massive) gains a little momentum which makes it move imperceptibly.
answered 3 hours ago
Dale
1,877415
answered 3 hours ago
Dale
1,877415
answered 3 hours ago
Dale
1,877415
answered 3 hours ago
Dale
1,877415
1,877415
add a comment |Â
add a comment |Â
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6
The final momentum is not $0$!
– tfb
4 hours ago