throw a bottle and let go what happens to my body momentum question

Question

I weigh 200lbs im holding a bottle that weighs 5lbs. I go to through the bottle at a velocity of 5mph at someone and at the last possible moment i change my mind and simply drop the bottle. How far backwards or foward did my body go.

Answer 1

Hi Richard!

 

One of the nice things about conservation of momentum is that it ignores the internal actions of the system.  The only thing that matters is that no net external force acts on it.  I will therefore assume no horizontal friction is involved in this scenario.

 

In this case, no net force acts on the you-bottle system in the horizontal direction.  If (as the problem seems to suggest) you and the bottle start at rest, with zero momentum in the horizontal, you should end up with zero net momentum in the horizontal after the bottle is released.  Since the bottle is dropped, it has zero horizontal momentum after release.  Therefore, if the you-bottle system is to have zero final horizontal momentum, and the bottle has zero final horizontal momentum, you must have zero final horizontal momentum, as well.  Since you have mass, this means you must have zero velocity; i.e. remain stationary.  So, overall, you should have no change in position

 

What this means is that whatever force you gave to the bottle to start throwing it away from you, you must have given an equal force in the other direction to hold it back.  So, as you throw, it might be that you start to move opposite the direction of the throw a little as you accelerate the bottle away, but then you would slide an equal amount back as you pull the bottle back to keep it from moving horizontally.

 

But conservation of momentum does not care about the details of any internal interaction.  You can jump right over those details to connect the initial state of the system to its final state.  That is one of the most useful qualities of conservation of momentum, when it can be invoked (which is when no net external force is applied to the system).

 

I hope this helps!  Just let me know if you have any questions about this, or want to talk more about it.