Ultramiler wrote:
I recently talked to Isaac Newton with my time machine. Here's what he said.
Here are my three laws of motion. They apply because we're dealing with a problem in which the more advanced, modern theories of gravity tend to correspond extremely closely with my own initial approximation to the truth. All other considerations tend to be negligible, so we can assume that my theory applies. Einstein ended up being more correct than I was, with his warped-space, speed-of-light-is-the-limit approach, but he isn't all that necessary under these conditions.
"I. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it."
So if an object orbits the earth (meaning it always possesses tangential velocity), and gravity is removed, it flies off due to the lack of continual acceleration back towards the earth, formerly provided by gravity.
"II. The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma. Acceleration and force are vectors (as indicated by their symbols being displayed in slant bold font); in this law the direction of the force vector is the same as the direction of the acceleration vector."
Combined with the first law, this tells us that a runner's velocity in any direction cannot be changed except by the application of a force that has a component in that direction.
To simplify things, we can draw a free-body diagram to show the forces that act on our runner. Do it yourself. You'll end up seeing that three forces act on our runner. One of these is gravity. Due to my Law of Universal Gravitation (not shown here, but look it up, you ignoramus--even if you think you know it), that force is directed toward the Earth's center of mass. Straight down. This means it has no horizontal component. If the runner is moving horizontally (as said runner would, if running on a flat surface), this means that gravity does not affect this runner's motion. Wrong direction. See the previous paragraph.
"III. For every action there is an equal and opposite reaction."
What does affect our runner's motion? Remember the other two forces? Air resistance is one. When you move, you're pushing against air. According to my Law III, this means air also pushes against you, slowing you down.
But if you're going to run forward, you have to maintain a forward velocity. You do this through a third force. The ground applies a force to you.
Wait, what? Why would it do that? Because you push against it with your leg. My Law III says that this means it pushes against you. And since you're less massive than the object you're pushing against (the Earth tends to outmass any human being, so we'll assume this is true), you end up being the one that accelerates more. The forces are equal, but the actual acceleration is inversely proportional to the mass of the object that accelerates. So you accelerate the Earth by some small quantity, and it accelerates you by an amount that's rather larger.
And to forestall any complaints that the ground can't push against us in a horizontal direction, I'd call upon you to remember friction. Our leg pushes down, yes, which causes us to move upward. But that's only one component of the force our leg produces. The leg pushes at an angle, and so would tend to slide across the ground, but for friction, which keeps it stationary on the ground. Gravity ends up countering the vertical motion--we don't tend to become significantly airborne when we run--but not the horizontal motion.
The upshot of it all is that gravity doesn't pull you forward. My laws of motion, which apply in this case, prevent this. What lets you go forward is a push from your leg on the ground.
you could have saved yourself the time it took you to write all that if you were smart enough to realize that i was not arguing anything in contradiction to your post.
nothing like a thread on physics to bring out all the wannabe know-it-alls