I got ahead of myself by using forces I had not yet introduced. I was using friction to push me horizontally across the floor! Here is the complete story:
When I tossed the ball upward and it was rising, gravity was pulling downward on it and it was accelerating downward. But when I obtained a force from the ground, it was not gravity that exerted that force on me; it was friction! As we will discuss in a few days, whenever you try to slide your foot across the floor toward the left, friction pushes your foot toward the right. In class, I traveled toward the right because I was being pushed by friction toward the right. I was actually accelerating in the direction I was pushed, just as you expect.
Weight and mass are proportional to one another and the bowling ball's increased mass does effectively cancel out its increased weight. Let's suppose that the bowling ball is 100 times as massive as the tennis ball—meaning that it takes 100 times as much force to make the bowling ball accelerate at a certain rate as it does to make the tennis ball accelerate at that same rate. Because weight is proportional to mass, the bowling ball also weighs 100 times as much as the tennis ball. So if the only force on each ball is its weight, each ball will accelerate at the same rate. The bowling ball will experience 100 times the force but it will be 100 times as hard to accelerate. The two factors of 100 will cancel and it will accelerate together with the tennis ball.
The statement of inertia contains the word "tends" (an object in motion tends to continue in motion and object at rest tends to remain at rest) because it doesn't deal with the presence or absence of forces. If forces were outlawed, then the word "tends" could be dropped from the statement.
However, Newton's first law is not ambivalent and does not contain the word "tends." It states directly that an object that's free of outside forces moves at constant velocity. No ifs, ands, or buts. If I have inserted the word "tends" into this law in class, it was a mistake on my part.
That observation, known as Newton's first law of motion, is one of the fundamental characteristics of the universe. I could answer simply that that's the way the universe works. But a more specific answer is that the universe exhibits translational symmetry—meaning that the laws of physics are the same from your current vantage point as they would be if you shifted a meter to your left. Shifting your vantage point along some linear path—a process called translation—doesn't affect the laws of physics. The laws of physics are said to be symmetric with respect to translations and, because translations of any size are possible, this symmetry is considered to be continuous in character (as opposed to mirror reflection, which is a discrete symmetry). Whenever the laws of physics exhibit a continuous symmetry of this sort, there is a related conserved quantity. The conserved quantity that accompanies translational symmetry is known as momentum. An isolated object's momentum can't change because momentum is a conserved quantity—it can't be created or destroyed. Since momentum is related to motion, an isolated object that's at rest and has no momentum must remain at rest with no momentum. And an isolated object that's moving and has a certain momentum must remain in motion with that same momentum.
Incidentally, the laws of physics also exhibit rotational symmetry—meaning that turning your head doesn't change the laws of physics—and this symmetry leads to the existence of a conserved quantity known as angular momentum. The laws of physics also don't change with the passage of time, a temporal symmetry that leads to the existence of a conserved quantity known as energy.
Yes, if the hole were drilled from the north pole to the south pole, the ball would behave just as you say. Assuming that there were no air resistance, the ball would drop through the center of the earth and rise to the surface on the other side. It would then return via the same path and travel all the way back to your hand. This motion would repeat over and over again, with the ball taking 84 minutes to go from your hand to your hand. That time is the same as it would take a satellite to orbit the earth once at sea level. In effect, the ball is orbiting through the earth rather than around it!
However, because there would be air resistance unless you maintained a vacuum inside the hole, the ball wouldn't rise to its original height after each passage through the earth. It would gradually loss energy and speed, and would eventually settle down at the very center of the earth.Finally, the reason for drilling the hole from the north pole to south pole is to avoid complications due to the earth's rotation. If you were to drill the hole anywhere but through the earth's rotational axis, the ball would hit the sides of the hole as it fell and its behavior would be altered.
No, I don't think that anti-gravity is possible. The interpretation of gravity found in Einstein's General Theory of Relativity is as a curvature of space-time around a concentration of mass/energy. That curvature has a specific sign, leading to what can be viewed as an attractive force. There is no mechanism for reversing the sign of the curvature and creating a repulsive force—anti-gravity. I know of only one case, involving a collision between two rapidly spinning black holes, in which two objects repel one another through gravitational effects. But that bizarre case is hardly the anti-gravity that people would hope to find.
In effect, you would be a skydiver without a parachute and would survive up until the moment of impact with the ground. Like any skydiver who has just left a forward-moving airplane, you would initially accelerate downward (due to gravity) and backward (due to air resistance). In those first few seconds, you would lose your forward velocity and would begin traveling downward rapidly. But soon you would be traveling downward so rapidly through the air that air resistance would keep you from picking up any more speed. You would then coast downward at a constant speed and would feel your normal weight. If you closed your eyes at this point, you would feel as though you were suspended on a strong upward stream of air. Unfortunately, this situation wouldn't last forever—you would eventually reach the ground. At that point, the ground would exert a tremendous upward force on you in order to stop you from penetrating into its surface. This upward force would cause you to decelerate very rapidly and it would also do you in.
When you stand on the floor, the floor exerts two different kinds of forces on you—an upward support force that balances your downward weight and horizontal frictional forces that prevent you from sliding across the floor. Ultimately, both forces involve electromagnetic forces between the charged particles in the floor and the charged particles in your feet. The support force develops as the atoms in the floor act to prevent the atoms in your feet from overlapping with them. The frictional forces have a similar origin, although they involve microscopic structure in the surfaces.
Inertia is everywhere. Left to itself, an object will obey inertia and travel at constant velocity. In deep space, far from any planet or star that exerts significant gravity, an object will exhibit this inertial motion. But on earth, the earth's gravity introduces complications that make it harder to observe inertial motion. A ball that's thrown up in the air still exhibits inertial effects, but its downward weight prevents the ball from following its inertia alone. Instead, the ball gradually loses its upward speed and eventually begins to descend instead. So inertia is the basic underlying principle of motion while gravity is a complicating factor.
It's very important to distinguish velocity from acceleration. Acceleration is caused only by forces, so while a ball is falling freely it is accelerating according to gravity alone. In that case it accelerates downward at 9.8 m/s2 throughout its fall (neglecting air resistance). But while the ball's acceleration is constant, its velocity isn't. Instead, the ball's velocity gradually increases in the downward direction, which is to say that the ball accelerates in the downward direction. Velocity doesn't "act"—only forces "act." Instead, a ball's velocity shifts more and more toward the downward direction as it falls.
About terminal velocity: when an object descends very rapidly through the air, it experiences a large upward force of air resistance. This new upward force becomes stronger as the downward speed of the object becomes greater. Eventually this upward air resistance force balances the object's downward weight and the object stops accelerating downward. It then descends at a constant velocity—obeying its inertia alone. This special downward speed is known as "terminal velocity." An object's terminal velocity depends on the strength of gravity, the shape and other characteristics of the object, and the density and other characteristics of the air.
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