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Here is a Mythbusters clip showing that you actually can blow your own sail. They install a sail on a swamp boat and reverse the direction of the fan. There are other examples that the ideas works, like, notably, thrust reversers on jet airplanes.

https://www.youtube.com/watch?v=uKXMTzMQWjo

This initially strikes most people (Including Mythbuster's resident engineer, Grant Imahara (may he rest in peace) as violating Newton's Third Law. Grant did not succeed in explaining away the contradiction at the end of the clip.

There are some related answers to a similar question here on the Stack Exchange:

Blowing your own sail?

But those answers imply that since the phenomenon can be explained in terms of the conservation laws, Newton's Third Law isn't violated. This is not satisfying. To be satisfying, an explanation would have to state the Third Law in one or more of its forms, explain why it appears to be contradicted in terms of the statement of the law itself, and then go on to explain why it is not contradicted in terms of the statement itself.

Can the valid application of Newton's Third Law to the the phenomenon in the Mythbusters swamp boat video be explained in terms of Newton's Laws, as applied to the actual objects in the video, without reference to conservation laws?

D. Ennis
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    You would first have to explain why you think this situation violates the third law. – Javier Oct 28 '20 at 16:50
  • The question does not say that I think the law is violated. – D. Ennis Oct 28 '20 at 18:03
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    The difficulty for me here is that I find it so immediately clear what is happening that there is no mystery to explain. It is like a magician's trick that goes wrong because you know what he did. Here you stand in the boat and blow the air; the air goes somewhere else (not in the boat); job done. – Andrew Steane Oct 28 '20 at 18:16
  • What you say in your last sentence would be true with or without a sail, so what job is done? And I agree that there is no mystery, I just seek a vigorous description of specific forces on specific objects in this specific example, with some continuity of how they relate. – D. Ennis Oct 28 '20 at 18:34
  • Using the conservation of momentum is a valid application of Newton's Third Law. – Emilio Pisanty Oct 28 '20 at 18:35
  • Then that would appear to be a "no" to the question. – D. Ennis Oct 28 '20 at 18:49
  • What do you mean by Can the valid application of Newton's Third Law to the phenomenon in the Mythbusters swamp boat video be explained in terms of the law itself, as applied to the actual objects in the video? – Deschele Schilder Oct 29 '20 at 00:00
  • You say that an answer should explain why the third law appears to be contradicted. This is hard to do if I don't think it appears to be contradicted! – Javier Oct 29 '20 at 01:43

3 Answers3

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Because the boat (the rigid structure holding the fan and sail) does not describe the entire force system, the third law does not prohibit net forces from arising that create motion. Motion of the boat is countered by (untracked) motion of the air in the vicinity of the boat.

If all the forces were internal to the boat, then we would expect the thrust from the fan and the impact on the sail would be equal and there would be no motion.

But that's not the case here. The fan doesn't have perfect directionality, it entrains nearby air, and the sail doesn't absorb the airstream but redirects it. Any of these can create a net force on vessel, causing acceleration.

The third law does't prevent motion here because the all the force couples do not act on the same object. If you instead put the fan and the sail inside a closed room on a similar boat preventing these effects, I would expect a different outcome.

BowlOfRed
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  • I must repeat the response I used below: With all due respect, is this intended as "yes" to the question or a "no?" – D. Ennis Oct 28 '20 at 18:22
  • I thought the final paragraph was pretty clear about summarizing why the third law should not be seen as a restriction on the motion here. Do you think that the answer would be improved if I added a "yes it can", or is there something else missing? – BowlOfRed Oct 28 '20 at 19:05
  • I agree that the last paragraph is good. I do think that readers would benefit from beginning the answer to a yes/no-explain question with a yes or no statement (no sarcasm intended). The other paragraphs don't lead to clear visualizations for me. – D. Ennis Oct 28 '20 at 19:46
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Imagine that instead of a fan and a sail inside the boat, you have a ball cannon and a wall. If the cannon fires to the wall and the ball bounces back into the cannon, the net motion after that will be zero, but if the ball hits the wall at an angle and bounces back leaving the boat, then the boat will move forward, as you basically are shooting backwards.

Thus the answer to your question is yes. once the wind bounces back it leaves the system, applying an external force to the sail.

  • it does not violate newton's law, because the ball (or the wind) are not part of the system after in bounces from the wall (sail), so there is an external force (the system is not closed) –  Oct 28 '20 at 17:41
  • With all due respect, would that be a "yes" or a "no" to the question? It appears to invoke conservation of momentum, but why would the cannonball bounce back? The cannonball would be moving forward and the cannon-Earth object moving backward, at a speed with inverse proportion to the proportion of the masses. When the ball hit the wall, both would stop. – D. Ennis Oct 28 '20 at 17:50
  • yes to the question, I though that was pretty clear. I added a phrase to make it more clear –  Oct 28 '20 at 17:50
  • Your answer doesn't address the backwards motion resulting from initially firing the ball though. – BioPhysicist Oct 29 '20 at 13:44
  • @BioPhysicist how not? the ship moves initially backwards and it stops once the ball reaches the wall, then moves forward when the ball moves backwards, but this time will not stop because the ball leaves the ship instead of getting caught back by the cannon –  Oct 29 '20 at 14:36
  • @Wolphramjonny I don't see that in your answer. And I guess the assumption is that the wall imparts a larger impulse on the ball than the cannon does? – BioPhysicist Oct 29 '20 at 14:45
  • @BioPhysicist I guess I was pretty unclear. no it can bounce back with the same momentum, as in an elastic collision. Do you understand the difference between the case in which the ball remains in the system and that in which it does not? –  Oct 29 '20 at 15:09
  • @Wolphramjonny I do understand.. But if the wall gives an impulse to the ball that is less than or equal to the impulse imparted by the cannon when the ball is launched then there will not be net forward movement after the collision. The wall needs to exert a larger impulse on the ball so that the ball is moving backwards relative to the initial position of the boat (and by momentum conservation, this would allow the boat to be moving forward relative to the initial position). – BioPhysicist Oct 29 '20 at 15:44
  • @BioPhysicist if the ball gets attached to the wall, it imparts its initial momentum (and the ship stops), if it bounces back, it imparts twice that (in the limit the wall has infinite mass), so the ship moves forwards unless it is trapped back –  Oct 29 '20 at 15:54
  • @Wolphramjonny Yes, that is correct, but it has to bounce backwards relative to the initial position, not just relative to the wall. – BioPhysicist Oct 29 '20 at 16:05
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The easiest explanation I have heard for this study is to replace the fan and sail with a ducted fan that has a fan blowing "forwards," and a U shaped duct in front of it which redirects that air stream "backwards." For most people, this will intuitively cause the boat to move forward. They can see that the air is coming from all directions into the fan (net 0 momentum), and then being directed out backwards, with a strong backwards momentum.

As such, we have a simple Newton's third law situation: air is forced backwards, and the equal and opposite reaction drives the boat forward.

Thus the only thing which is causing the problem in our minds is the sail. We think of the sail as being a sort of "wall," so that the air coming off of it has 0 net momentum, which should mean that we don't go forward. However, we shape the curve of the sail with the expressed intent of directing air. When the air leaves the sail, it isn't leaving it in all directions. It's leaving it in a predominantly backwards direction.

Cort Ammon
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  • I agree with all of this, but you invoked the momentum concept. – D. Ennis Oct 29 '20 at 13:16
  • @D.Ennis You could remove the mention of momentum, although I think it requires changing the last sentence of the first paragraph to "... with a strong backwards force." I think the reason it's difficult to remove the concept of conservation of momentum is that the fundamental rationale for why you can't blow your own sail is a momentum one. The language has to seep in, even if the final physical description doesn't use momentum. Otherwise it becomes a rather unsatisfactory refutation, failing to challenge the central tenent of the problem. – Cort Ammon Oct 29 '20 at 14:56
  • Particularly in the sail case, the directions of the forces involved are constantly changing over the surface of the sail and the volume of the airspace in front of it. That is a very complex fluid dynamics problem, so we look to conservation laws to limit what could happen. The ducted fan simplifies that geometry, but the rationale for why it applies in the sail case is tricky without conservation – Cort Ammon Oct 29 '20 at 15:01