People and earth pull on each other, so why do people fall?

[Taharok]

Homework Statement

Daniel's weight is 800 Newtons. According to Newton's Third Law, if the Earth pulls on Daniel with a force of 800 Newtons, then Daniel pulls on Earth with a force of 800 Newtons in the opposite direction. Why then is Daniel able to trip and fall down to the ground?

Homework Equations

None

The Attempt at a Solution

Well, I've been stuck on this for a while now. I remember learning something about this with a leaf falling, but I can't remember/find it anymore.

I do have one theory, however. Even though I said there are no relevant equations, I believe I can use Newton's Second Law (F = ma) to figure out this problem. I need to rearrange this equation to solve for acceleration, as so: a = F / m. If force F is the same for both the Earth and for Daniel, then the only changing variable is m. The Earth has an extremely higher mass than Daniel, so the acceleration for the small force of 800 Newtons is so small, it's nearly nonexistent. However, Daniel's mass is much smaller, so the force of 800 Newtons causes his acceleration to be considerably higher than the earth's, so much as to make him fall down.

 

[DaveC426913]

I think you've got the right idea.

But I wonder about the wording of the question. Intuitively, why would Daniel not fall down? i.e. Why would the mutual attraction of Earth and boy adversely affect his movement toward the Earth upon tripping?

 

[jumbogala]

Your reasoning is right. If Daniel trips, he falls towards the Earth with a noticeable acceleration. Although the Earth DOES move up towards Daniel, its acceleration when it does that is so tiny that you can't tell it's happening.

 

[CompuChip]

Luckily, or I would be bouncing up and down and the solar system would probably get disrupted every time someone in Australia (hey guys!) jumps up and down or someone takes an elevator from the basement to the 20th floor.

PS Taharok, it might be "fun" for you to actually calculate the acceleration of the Earth due to Daniel falling, and its (relative) change in velocity if this fall took, say, half a second. :)