Understanding Momentum Conservation in a Closed System: A Question Explained

[pete5383]

Ok, so I was pondering something as I lie in bed...so in a system with no outside forces, momentum has to be conserved, correct? So let's say me and the Earth are the system, and initially at rest, so we have zero momentum. I jump up in the air, giving myself momentum in the positive y direction, while the Earth has momentum equal to mine in the negative y direction (going down, even though it's very very slight). No, once I reach the peak of my jump, I start coming down, that is, the sign of my momentum has changed. Does this mean that at that moment the Earth starts to move back towards me to maintain a net momentum of zero? Also, it seems to me when I land I will be pushing the Earth down even more, making the net momentum afterwards non-zero. Can anyone explain to me where my thinking is wrong?

 

[Andrew Mason]

Ok, so I was pondering something as I lie in bed...so in a system with no outside forces, momentum has to be conserved, correct? So let's say me and the Earth are the system, and initially at rest, so we have zero momentum. I jump up in the air, giving myself momentum in the positive y direction, while the Earth has momentum equal to mine in the negative y direction (going down, even though it's very very slight). No, once I reach the peak of my jump, I start coming down, that is, the sign of my momentum has changed. Does this mean that at that moment the Earth starts to move back towards me to maintain a net momentum of zero?

Yes

Also, it seems to me when I land I will be pushing the Earth down even more, making the net momentum afterwards non-zero. Can anyone explain to me where my thinking is wrong?

When you jump up, the Earth recoils a very small amount. But as you move away from the earth, there is a gravitational force between you and the Earth that slows and eventually reverses the motion of the Earth and of you. You and the Earth then move toward each other and collide, thereby providing an impulse to each sufficient to stop further motion so that each has 0 momentum. I am not sure why you think that when this collision occurs, you will be pushing the Earth even more than when you jumped. You necessarily have the same speed when you left the Earth as when you collided with it.

AM

 

[HallsofIvy]

When pete5382 said "pushing the Earth down even more" he didn't mean that the force landing on the Earth was greater than that jumping. He meant that there was a force, downward) when he jumped and then the same force(downward) again when he landed (so he was applying "even more" force). Of course, as you say, he is missing the pull of gravity. The reason he stops going up and starts coming down is because the force of gravity is pulling him toward the earth. At the same time, the mass of his body is pulling the Earth toward him. It's very small of course, but then the push he gives the Earth when he jumps is very small. Anyway, the two downward pushes he gives the Earth when he jumps and when he lands are exactly offset by the gravitational force his mass applies to the earth.

 

[pete5383]

Ahhhhhh, I was forgetting about the gravitational attraction between us...duh...hehe. That makes sense to me now. That's what I get for posting at 2 in the morning. But thank you all very much!