Category: falling balls

If there was a hole drilled directly through the center of the earth and a ball was dropped into it, what would happen to the ball? Would it oscillate up and down in the hole until it remained suspended in the center? — JC, Dallas, TX

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.

Why does a body at rest remain at rest and a body in motion remain in motion, in the absence of unbalanced force? — AW, Karachi, Pakistan

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.

With Newton’s first law, the word “tends” seems a bit ambivalent. Does this word suggest there are exceptions to the rule?

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.

Can you explain once again how the bowling ball and the tennis ball drop at the same time. Are weight and mass proportional? If mass is the resistance to acceleration and weight is a gravitational force pulling down on the ball, doesn’t the weight of the bowling ball make it fall faster? Or does the bowling ball’s increased mass in a way cancel out the bowling ball’s increased weight? – HC

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.

Warner Brothers has been misleading children! The coyote and the anvil hit the ground at the same time!

You’re exactly right. Occasionally one of those cartoons shows the coyote falling with the anvil directly above his head and the distance between them remaining constant, which is what should happen (ignoring air resistance). But more often, the coyote falls much faster than the anvil, hits the ground first, and is then pounded by the anvil. It sure would be neat to live in a cartoon—the laws of physics just wouldn’t apply.

When accelerating, can you decelerate by going in a direction that is not opposite (your velocity)? For example, going north can you decelerate by going east?

Decelerating is a very specific acceleration—always in the direction opposite your velocity. If you were heading north and accelerated toward the east, your velocity would soon point toward the northeast. It would have some northward aspect because you were initially heading north and hadn’t yet accelerated toward the south. It would have some eastward aspect because you had initially been heading neither eastward nor westward and had since accelerated toward the east.

On the other hand, if you were heading north and then turned toward the east, you would have lost your northward velocity and obtained an eastward velocity. This “turning” would have involved a southward acceleration (to get rid of the northward velocity) and an eastward acceleration (to acquire an eastward velocity).

You said that from the moment the ball leaves your hand (after you threw it upward), it accelerates downward even though you threw it upward. However you then said that the ground (gravity) pushed on your foot to make you accelerate, so why would you also not be accelerating in the opposite direction, like the ball? Why would you not accelerate in the direction in which you were pushed?

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.

How was Newton able to prove inertia with gravity and friction still being present? Why didn’t people think he was crazy? Did he have some type of vacuum or something? – JP

Actually, it was Galileo who first realized that objects have this tendency to continue moving at a steady rate in a straight-line path—what we call “inertia.” He deduced this fact by studying the motions of balls on ramps. He noted that a ball rolling down a slight incline steadily picked up speed while a ball rolling up a slight incline steadily lost speed. From these observations he realized that a ball rolling along a level surface would roll at a steady speed indefinitely, where it not for friction and air resistance. He was aware that friction, air resistance, and gravity were disturbing the natural motions of objects and had figured out a way to see beyond them. But it wasn’t until Newton took up this sort of study that the idea of forces and their effects was properly developed. Overall, it took almost two thousand years, from Aristotle to Newton, for the incorrect idea that objects tend to remain stationary when free of forces to be replaced with the correct idea that objects tend to continue at constant velocity when free of forces.

What is gravity and how do you define it?

There are two levels at which to work. First, there is Newtonian gravity—an attraction that exists between any two objects and that pulls each object toward the center of mass of the other object with a force that’s equal to the gravitational constant times the product of the two masses, divided by the square of the distance separating the two objects. For example, you are attracted toward the earth’s center of mass with a force equal to the gravitational constant times the product of the earth’s mass and your mass, divided by the square of the distance between the earth’s center of mass and your own center of mass. This force is usually called “your weight.” The earth is attracted toward your center of mass with exactly the same amount of force.

Second, there is the gravity of Einstein’s general relativity—a distortion of space/time that’s caused by the local presence of mass/energy. Space is curved around objects in such a way that two freely moving objects tend to accelerate toward one another. As long as those objects aren’t too large or too dense, this new description of gravity is equivalent to the Newtonian version—they both predict exactly the same effects. But when one or both of the objects is extremely massive or very dense, general relativity provides a more accurate prediction of what will happen. In reality, mass/energy really does warp space/time and general relativity does provide the correct view of gravity in our universe. The next level of theory, quantum gravity (which will reconcile the theory of general relativity with the theory of quantum physics), is still in the works.

If a projectile released or hit at a 45° angle above horizontal should go the farthest, then why, in the game of golf, does the three iron (20° loft) hit a golf ball so much farther in the air than, say, a seven iron (approximately 45° loft) if the same technique and force are produced by the golfer? Is it backspin, shaft length, etc.?

It’s backspin! Air pushes the spinning ball upward and it flies downfield in much the same way as a glider. When you throw a glider for distance, you concentrate your efforts on making it move horizontally because the air will help to keep the glider from hitting the ground too soon. Similarly, the air holds the spinning golf ball up for a remarkably long time so that giving the ball lots of downfield speed is most important for its distance. That’s why a low-loft club like a three iron sends the ball so far.