## How can a basketball weigh 7.5 to 8.5 pounds when blown up but much less when deflated?

### How can a basketball weigh 7.5 to 8.5 pounds when blown up but much less when deflated? What is it filled with when deflated?

I will answer your question in two parts. First, the actual weight of a basketball is dominated by its skin and, which weighs about 22 ounces (about 1.4 pounds). The air inside a properly inflated basketball weighs only about 0.03 pounds. Of that 0.03 pounds of air, only about 0.01 are measurable on a scale because buoyant effects due to the surrounding air support the other 0.02 pounds of air. That’s because the first 0.02 pounds of air put into the basketball simply fill it so that it’s spherical– air has gone from outside the basketball to inside the basketball and the scale won’t notice this change in location. Once you pump extra air into the ball, packing the air more tightly than normal and stiffening the ball’s surface, that additional air will appear on the scale’s weight measurement. A properly inflated basketball has about 0.01 pounds of extra air in it, so it’ll weigh an extra 0.01 pounds on a scale.

So what is the 7.5 to 8.5 pounds that a basketball is supposed to contain? Or the 13 pounds that a football is supposed to contain? Those aren’t weights at all. In fact, they are careless abbreviations for a different physical quantity: pressure. They should actually be written “7.5 to 8.5 pounds-per-square-inch” and “13-pounds-per-square inch” respectively.

Fluids such as air have pressures — the forces they exert on each unit of surface area they contact. For example, air that is listed as having a pressure of 7.5 pounds per square inch exerts a force of 7.5 pounds on each square inch of surface it touches. That means that the air in a properly inflated basketball pushes outward with a force of 7.5 to 8.5 pounds on each square inch of the inner surface of that ball. That outward push stretches the ball tight and gives it its feel and bounciness. Similarly, a properly inflated football has a pressure of 13 pounds per square inch and thus the air inside it exerts an outward  force of 13 pounds on each square inch of surface inside the ball. Again, this outward push stretches the ball taut and gives it its bounciness and feel.

An underinflated basketball or football weighs just slightly less than a properly inflated ball because its skin hasn’t changed and the weight of the air it contains is so insignificant. But the decrease in outward forces on the skin of the ball significantly changes its feel and bounciness.

## Why does a diving bounce up and down after the diver jumps off its surface?

### Why does a diving bounce up and down after the diver jumps off its surface?

When left alone, the diving board settles down to its equilibrium shape and position — arrangement at which all of its parts are experiencing zero net force and are therefore not accelerating. If the board is disturbed from that arrangement and released, it will vibrate back and forth about that equilibrium arrangement until it settles down again.

When the diver leaves the diving board, the board is usually far from its equilibrium arrangement and its parts are usually moving as well. It consequently vibrates back and forth. Whenever it is above the equilibrium arrangement, the springiness of the board, assisted slightly by gravity, causes its parts to experience downward net forces and those parts accelerate downward. If the board was rising, it slows to a stop and then begins to descend toward the equilibrium. Whenever the board is below the equilibrium arrangement, its springiness, opposed slight by gravity, causes its parts to experience upward net forces and those parts accelerate upward. If the board was descending, it slows to a stop and then begins to rise toward equilibrium.

So whenever the board is away from equilibrium, it is accelerating toward that equilibrium and will soon be moving toward equilibrium. When it reaches equilibrium, however, it will be moving and will thus coast through equilibrium and overshoot. That’s why it bounces up and down — it keeps coasting through equilibrium, turning around, heading back toward equilibrium, and coasting through again. But with each bounce, the board wastes some of its energy as thermal energy via internal friction and air resistance. Its bounces get weaker and weaker until it eventually settles at equilibrium and stops moving altogether.

## Does a rocket push up on itself?

### Does a rocket push up on itself?

No. An object cannot push on itself, meaning that the entire rocket cannot push on the entire rocket.

But part of the rocket can push on another part of the rocket, and that’s exactly what it does. The ship-part of the rocket pushes on the fuel-part of the rocket and the two parts accelerate in opposite directions as a result. The plume of exhaust rushing out of the tail of the rocket is the fuel-part that has accelerated downward to an exceptionally high speed. That fuel-part has been pushed downward hard by the ship-part of the rocket. The ship-part of the rocket has been pushed upward equally hard and it accelerates upward. Gravity introduces a complication, in that it pulls all of the parts downward, but the upward push on the ship-part typically dwarfs gravity and so the ship-part accelerates upward rapidly.

## Why does a ball fall only about 5 meters in its first second of falling?

### After one second of falling, a ball’s velocity is about 10 meters per second downward. So why does it travel only about 5 meters downward during that one second?

If the ball traveled steadily at 10 meters per second downward for one second, it would travel 10 meters downward. But a falling ball does not move steadily. Instead, it accelerates downward and its velocity changes with time. When dropped from rest, its velocity starts at 0 and steadily increases to about 10 meters per second downward after 1 second of falling. Its average velocity during that 1 second interval is only about 5 meters per second (the average of 0 and 10 meters per second) downward. Therefore, the ball only moves downward about 5 meters.

## Why does a sheet of paper fall faster when it’s above a falling book?

### Why does a sheet of paper on top of a large book fall and land at the same time as the book?

By itself, a falling sheet of paper experiences severe air resistance as it moves downward through stationary air. It soon reaches a small terminal velocity — the downward speed at which the upward force of air resistance cancels its downward weight and it stops accelerating downward. The falling book protects the sheet from that air resistance, so the sheet can fall unimpeded.

All objects that move downward through stationary air experience upward air resistance forces, but heavy compact objects (e.g., books) are less affected by those forces than light, fluffy ones (e.g., sheets of paper). Although a book falls mostly unimpeded through stationary air, it does affect the air it encounters. Most importantly, it drags a pocket of air with it. The air just above the book is moving downward at approximately the book’s velocity. When a sheet of paper is located in this special region of downward-moving air, it can fall with the book and experience virtually no forces due to the air.

This behavior is known as drafting and is important in many types of races, including running, bicycling, skating, and swimming. For example, a bicyclist drags a pocket of air with her and a second bicyclist following close behind her and located in that pocket of forward-moving air experiences less air resistance. Consequently, a group of bicyclists traveling in a tight line makes easier forward progress through stationary air than separated bicyclists each fighting air resistance in their own. The lead bicyclist in the line gets the air moving for the others and exhausts first, so they typically take turns as the lead bicyclist. Some races forbid drafting because it provides such an advantage for the following bicyclist.

Drafting while skydiving is actually dangerous and is normally avoided. A descending skydiver creates a pocket of downward-moving air above them and when a second skydiver enters that pocket of downward-moving air, the upward air resistance decreases dramatically. The second skydiver suddenly accelerates downward due to weight and can drop onto the first skydiver. This is usually a bad idea and can lead to disaster. Similarly, the sheet of paper drops onto the book below it, but the only possibility of injury is if they land on your foot.

## Why doesn’t a moving wagon fall through a sidewalk?

### If a wagon is moving on a sidewalk, why doesn’t that wagon fall through the sidewalk?

The wagon and sidewalk cannot occupy the same space at the same time. Although the wagon’s weight pulls it downward, the sidewalk pushes the wagon upward with a force that prevents the wagon from moving into the sidewalk.

The type of force the sidewalk exerts on the wagon is known by several different names: support force, contact force, or normal force. It derives from the repulsive forces that atoms experience when they are too close together. When the wagon and sidewalk are pushed together by the wagon’s weight, the atoms of the wagon and sidewalk become too closely spaced and they push apart.

When solid objects are pressed into one another, they always respond with support forces that act to separate them. The harder they are pressed together, the more their atoms overlap and the harder they push apart. There are limits, however, beyond which the objects begin to break apart. Pressing them together causes them to dent or deform, a large-scale behavior related to the small-scale overlapping of their atoms. They can only dent or deform so much before they break.

## Which ball lands first: one thrown up or one thrown forward?

### If a ball is thrown horizontally, will it still land at the same moment as a ball thrown straight up?

The ball thrown horizontally will land first. Its velocity immediately begins to develop a downward component and it moves downward faster and faster until lands on the ground. In contrast, the ball throw straight up starts with an upward component to its velocity and it rises to a peak height before it begins to develop a downward component to its velocity. Its travel time to the ground is much longer.

A more sophisticated way to look at this question is to recognize that you can separate the horizontal and vertical motions of a falling ball. Since the ball’s weight is purely vertical, it has no effect on the ball’s horizontal motion. The ball’s horizontal motion is that of a coasting: the ball’s horizontal component of velocity never changes. If the ball had any forward component of velocity when you released it, that ball will make steady progress in its forward direction.

The ball’s vertical motion, however, is that of falling: the ball’s vertical component of velocity changes with time as the ball accelerates downward at the acceleration due to gravity. The ball thrown horizontally begins its fall with zero vertical component to its velocity. It’s effectively falling from rest in terms of its vertical motion. It drops faster and faster and soon lands on the ground. The ball thrown upward, however, beings its fall with an upward vertical component to its velocity. It travels upward at first, rising more and more slowly until it reaches its peak height momentarily, and then it descends more and more quickly until it reaches the ground. That second motion, up and then down, takes far longer than the first motion, down only.

## How do the new Cyclonic Wave Microwave Ovens work?

### How do the new Panasonic Cyclonic Wave Microwave Ovens work and are they better than ordinary microwave ovens?

I just did a quick check of the patent literature to see if I can figure out what those new Panasonic ovens are doing differently. I found an international patent application WO 2009011111 A1 and 5 national applications, including US 20100176123 A1. Assuming that these patent applications describe the new microwave ovens, they look interesting.

One of the basic problems with microwave cooking is that the microwaves reflect from the metal walls of the cooking chamber and establish a standing wave pattern. Standing waves appear whenever vibrations are confined to limited region of space, such as in musical instruments on the surface of water in your drinking glass. The vibrations “dance in place,” which is why they’re called standing waves. In some places, the motion of a standing wave is strong and in other places, it’s weak.

The standing waves that form in a microwave oven’s cooking chamber aren’t vibrations; they’re electromagnetic standing waves. Nonetheless, they have that same characteristic of having more intensity in some places than in others. Those variations in microwave intensity produce uneven cooking and are thus a nuisance. Two conventional solutions to the uneven cooking problem are to move the food about, typically on a rotating platform, or “stirring” the microwaves with moving metal objects that dither the standing waves about.

What Panasonic appears to have done is develop a more sophisticated microwave source, one that can steer the microwaves as they first enter the cooking chamber. The technique they’re using is similar to that used in phased-array radar; both devices steer their microwave emissions by adjusting the relative phases of their many emitting antennas. If they swirl the emitted wave around rapidly, calling it a “cyclonic wave” would seem appropriate.

By changing that microwave steering rapidly, the Panasonic oven can vary the standing wave pattern inside the cooking chamber so that each region of space has approximately the same average microwave intensity. Food should therefore cook relatively evenly in this oven.

The approach makes sense and should be effective. As to whether the technique is cost effective and how it compares to the other techniques for improving the uniformity of cooking, that’s beyond what I can predict myself.

## How can you calculate the position of a falling ball?

### When you drop a ball, its position changes in a complicated way. How would you calculate that position?

When you drop a ball, its altitude decreases by larger and larger increments as the seconds pass. If we call the altitude from which you drop it zero, then its altitude after 1 second is -4.9 m (-4.9 meters or about -16 feet), after 2 seconds is -19.6 m, and after 3 seconds is – 44.1 m. Here is one way to calculate those values.

First, note that the ball is accelerating downward steadily at 9.8 m/s2. The ball’s initial velocity was zero, so its velocity after falling for time t is 9.8 m/s2 * t downward.

Next, let’s find the ball’s average velocity while falling for time t. The ball’s velocity has been changing steadily from 0 when you dropped it to 9.8 m/s2 * t downward after falling for time t, so it’s average velocity is simply the average of those two individual values: 0 and 9.8 m/s2 * t downward. That average is 4.9 m/s2 downward.

Lastly, let’s determine how far downward the ball has traveled after falling for time t. Since it’s average velocity was 4.9 m/s2 * t downward and it has traveled for time t with that average velocity, its change in position is 4.9 m/s2 * t downward * t or simply 4.9 m/s2 * t2 downward. As you can see, its change in position is proportional to the square of its fall time t. With each passing second, it is moving downward faster and covering more distance. As stated above, its altitude after 1 second of falling is -4.9 m, after 2 seconds of falling is -19.6 m, and after 3 seconds of falling is -44.1 m.

## If an object is moving, how could nothing be pushing on it?

### How can an object with a constant velocity have zero net force acting on it? The object is moving, so how could nothing be pushing on it?

This important question is addressed by the concept and the observation of inertia. An object that is free of all external forces continues moving as it was. You don’t have to push on something to keep it moving. That is its nature. Left to itself, an object that’s moving will keep moving in a straight line at a steady pace. That’s ultimately the observation that’s called Newton’s first law of motion. Forces, therefore, don’t cause velocity. Velocity is a matter of history; if an object was already moving that’s what it’s going to tend to keep doing.

What forces cause are changes in velocity. In other words, they cause accelerations. So, if an object happens to be, at the point you are paying attention, moving to your right, at some particular velocity, in the absence of any pushes, that’s what it’s going to keep doing. That is its nature. That’s the observation of behaviors in our universe, without exception. The velocity they have is the velocity they keep. You don’t have to push on them to keep them moving; they do that for free. You have to push on them to bring them to a stop, to speed them up, or to change their direction.