Suppose that I have a box in space and it is filled with air in it. I keep a fan at one end and blew the air to other end. The air will hit the box with some velocity, so it should move.

I know that this is completely false because the momentum of the system remains constant. But somehow I cannot explain that clearly.

Fan in box


2 Answers 2


If you use Newton's 3rd law of motion, which states that for every action, there is a equal and opposite reaction i.e. when the fan accelerate the air particles by a force, it also experiences a backward reaction force and according to 3rd law of motion these action and reaction force must be equal.Hence the net force acting of the box is zero . That's why it is not moving by the fan.

$F_{reaction} = F_{action}$

If you want to explain it by the momentum conservation theorem then you have to consider the change of the fan and air particles and the summation of change of momentum of all particles must be zero. Since here the velocity of the fan and the air particles are opposite directed, hence the summation becomes zero.

$\sum^n_{k=1}$ $ m_i\bar{v}_i$

  • 1
    $\begingroup$ Excellent. Now let's twist the OP's head by pointing out that you can mount a fan on a sailboat, aim it at the sail, and make headway. :-) $\endgroup$ Nov 11, 2014 at 14:20
  • $\begingroup$ Actually in case of a sailboat, the fan and the boat is one system since they are rigidly bound with each other. According to Newton's 3rd law of motion the action and reaction must be occurred between two different objects. That's why it's not possible to sail a boat with a fan running on it. $\endgroup$ Nov 11, 2014 at 14:29
  • $\begingroup$ Except that it is possible to sail a boat with a fan. Look it up (hint: vectors) $\endgroup$ Nov 11, 2014 at 14:35
  • $\begingroup$ Would u please give me the question in a little details ? $\endgroup$ Nov 11, 2014 at 14:43
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    $\begingroup$ The Mythbusters proved that you can "blow your own sail" with a fan. discovery.com/tv-shows/mythbusters/videos/… It only works under certain conditions (sail size, fan size and output, etc.), and you would be better off taking down the sail and just using the fan. $\endgroup$
    – JRE
    Nov 11, 2014 at 15:57

No! You have to make an opening in the front and in the back. The theory is that the sum of the momentum of all moving particles and things $\displaystyle\sum_{k=1}^nm_i\mathbf{v}_i$ should be zero.

If some particles are accelerated by the fan and moving backwards a force will be applied to the box in direction forward.

If it wasn't a smooth stream of moving molecules, but for instance rather heavy balls, the box would be shaking forward and backward when the balls was thrown and when they hitting against the sealed box.

  • $\begingroup$ That's not a theory- it's a fact. And you only really need one opening. See the famous "can you reverse a lawn sprinkler underwater" question. $\endgroup$ Nov 11, 2014 at 13:58
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    $\begingroup$ It's a fact and a theory, @Carl. The fact is that it works. But there is no fact about a final truth in physics, so we better call the theory for a theory. $\endgroup$
    – Lehs
    Nov 11, 2014 at 15:26
  • $\begingroup$ OK, well, I think it's better called "the law of conservation of momentum," but point taken. $\endgroup$ Nov 11, 2014 at 17:08
  • $\begingroup$ @Carl Witthoft: Yes, and we also have Ohm's law. But as we know it's fact of the type 'well functioning approximation'. $\endgroup$
    – Lehs
    Nov 12, 2014 at 9:04

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