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We are here to mess with your mind. Let's get that straight from the start. One of the lessons that we have both learned at the Exploratorium is: Take no one's word for the truth. Experiment. Make your own observations.
We are here to pass those lessons along. But first, we are here to mess with your mind.
The Way You Think It Is
At the Exploratorium, we have an exhibit that consists of a clear plastic tube that's about 5 feet long, hooked up to a vacuum pump. Inside the tube is a small plastic chicken and a brightly colored feather. You can flip the tube over and watch the two objects fall.
If the tube is filled with air, the feather floats gently downward and the chicken drops like--well, like a plastic chicken. But if you use the vacuum pump to evacuate most of the air from the tube and then repeat the experiment, you get a very different result. The feather and the chicken fall side by side, hitting the bottom of the tube at exactly the same time.
When astronaut David Scott stood on the moon and dropped a geologist's hammer and a falcon feather side by side, he demonstrated the same principle. The hammer and the feather struck the lunar surface at the same time.
Scott's lunar antics and the Exploratorium exhibit both relate to some of the stuff with which Galileo was messing back in 1604. If you took high school physics, you probably learned the principle derived from Galileo's work. It's usually summed up as something like this: in the absence of air resistance, anything you drop will accelerate toward the ground at the acceleration of gravity, usually abbreviated as g. At the surface of the earth, g is just shy of 10 meters per second per second (32 feet per second squared).. That means that anything you drop will accelerate from 0 mph to 60 mph (0 to 100 km/hr) in about 3 seconds. That's what your physics teacher probably told you. And if you're a good science fiction reader, you probably believed your physics teacher.
Not so fast. Take no one's word for the truth. Is what your physics teacher told you really true?
Taking the Plunge
To prepare for writing this article, Paul suggested that Pat experience freefall by riding "The Drop Zone" at Great America, a nearby amusement park. On this ride, you are strapped into a seat, hauled to the top of an 80+ meter tower (higher than a 20 story building), and dropped.
Paul likes this ride. After all, you can make some interesting physics observations during the 2+ seconds of free fall. For example, he says, you can watch the ground as it approaches and note the high acceleration. You can release a penny and notice how how it falls in relation to your fall. You can pay attention to the feeling in your innards as the springy windings of your intestines relax as you go into freefall.
So Paul suggested that Pat, in the interest of science, ride the Drop Zone--maybe ride it more than once, so she could make detailed observations. Pat, being a diligent researcher, did ride the Drop Zone, but her experiments did not go exactly as planned.
As readers of this magazine know, Pat is usually more concerned with character development than with science. At Great America, character development (or perhaps the lack of character development) interfered with physics research, though Pat did make a number of observations. Pat reported that she closed her eyes as soon as she was strapped into her seat. She observed that she swore a blue streak the entire time the seats were being lifted to the top of the tower, then noted that she screamed all the way down. She did report strange sensations in her intestines, though she refused to describe them as in any way relaxed.
Dave, Pat's research companion, did complete one of Paul's experiments. He placed a penny on his open hand and watched what happened to the coin as he fell. "Did you see that?" he asked Pat, when they reached the ground. "The penny roseaway from my hand as we fell."
"See what?" asked Pat, as she opened her eyes for the first time since leaving the ground.
According to Galileo, that penny should have fallen with the exact same acceleration as Pat and Dave. Dave's hand was shielding the coin from the effects of wind resistance so the coin should have stayed right with Dave's hand. What gives? Do the riders on the drop zone accelerate faster than g, or does the the coin accelerate more slowly? Is Galileo spinning in his grave?
To figure this one out, Paul rode the drop zone a number of times. As he repeatedly plummeted to earth, he tried the coin experiment and observed the same strange behavior that Dave had noticed. He also made a few other observations. He noticed the restraining straps pushed down onto his shoulders as he went into freefall. That didn't make sense. Since the seat and Paul went into freefall at the same time, the car should be falling at the same rate as Paul and the straps shouldn't be pulling him down.
So Paul had two puzzles to figure out--the strange behavior of the coin and the push of the shoulder straps. He started experimenting around home, and figured a few things out, if you have a slinky vailable you can do his experiments too.
Faster than a Falling Slinky
Try this. Find a slinky. Hold it by the top turn and let it dangle down from your hand. The bottom should be above the floor. (We had to cut off part of an older plastic slinky to make it short enough.) With your other hand, hold a set of car keys next to the top of the slinky.
Before you drop the keys and the slinky at the same time, try to predict what will happen. Are you going to vote with Galileo and say that the top of the slinky and the keys will reach the ground at the same time? Or are you a bit more suspicious now?
OK--now try the experiment.
Ha! Take that, Galileo! The top of the slinky beat the keys to the ground.The top of the slinky accelerated downward much faster than the keys! Faster than the acceleration of gravity.
Now hold the slinky as you did before and hold the keys next to the bottom of the slinky. (If your arms are not long enough bunch up a few turns of the slinky at the top where you hold it.) Drop them at the same time. This time the keys fall faster, the bottom of the slinky appears to just stay in place, and the keys beat the slinky to the ground. Weird.
One last experiment. Fold the slinky up tight and mark the middle with a piece of tape. This spot is the slinky's center of mass. (You have to mark it, because when the slinky stretches under its own weight, the center of mass won't be in the center of the stretched slinky.) Hold the slinky by its top again and drop the keys next to the center of mass of the slinky. The keys and the center of mass fall together, the slinky and the keys hit the floor together.
In freefall, the center of mass of an object accelerates at g. But if the object can change shape elastically as it falls, some parts may accelerate faster than g and some parts slower.
So what's going on here? Well, gravity isn't the only force working on all parts of the slinky. The top turn of the slinky, or the top "slink" (as Paul calls it) is pulled down by gravity, but it's also pulled down by the tension forces from the rest of the stretched slinky. When you are holding the slinky, the top turn is pulled up by your hand. The downward and upward forces add to zero so the top turn has zero acceleration. When you first let go, the slinky is still stretched. The top is being pulled down by gravity as well as by the stretched spring below. So the top slink accelerates down faster than it would with the pull of gravity alone---faster than g acceleration.
The bottom of the slinky is being pulled down by gravity and up by the stretched slinky above. When you first let go, the slinky begins to pull itself together starting at the top. It takes a while for the change in tension to propagate to the bottom. So the bottom remains at rest for a while.
The slinky experiment helped us to understand why the shoulder straps on the ride pulled down on Paul, not because the car was falling faster than g. Paul's spine is elastic, like a slinky! When Paul was sitting at rest at the top of the ride, his acceleration was zero. Gravity was pulling down on every bit of Paul and the seat was pushing up on his butt. In particular, Paul's head and shoulders were pushing down on his spine and the seat was pushing up so his spine was compressed. When Paul went into free fall, his spine was no longer pushed down by his head, so his spine expanded. He grew more than a centimeter taller in a fraction of a second. His expanding spine pushed his shoulders into the shoulder straps and Paul felt the reaction force of the shoulder straps on his body.
The human spine expands in free fall, which is something NASA has known for a long time. When astronauts go into free fall they grow, so their space suits have to have room for the lengthened spines. The same phenomenon explains why you are a little taller in the morning after lying down all night. Once you stand up and that massive head of yours squashes down on your spine, you shrink back down. You don't have to take our word for it. (Remember what we said at the beginning of the article?) Measure your height before you go to bed and before you get up and you'll find a difference.
The mysterious behavior of the penny can also be explained by examining what happens to your body when it is suddenly freed from the constraints of gravity. When Paul's arm was extended, holding the penny, the muscles were pulling up against gravity, keeping the arm still. When Paul went into free fall, his arm accelerated down with his body and the muscle no longer needed to pull upward to keep the arm in place. But it took a moment for Paul to get that message to his muscles, and the muscles kept pulling up for fraction of a second. As a result, his arm jerked up involuntarily launching the penny up out of his hand to where the effects of air resistance cause it to lag gently behind him as he fell.
The Problem of the Bungee Jumpers
Folks at the Exploratorium are not the only ones performing odd experiments in free fall. A group of bungee-jumping high school student experimentalists, led by their teacher Clarence Bakken, decided to record their acceleration during a jump.
Before we tell you what happened, think about the situation. Before we started messing with your mind, you might have figured that they would all accelerate at g. What do you say now?
Well, every one of them accelerated at least 10% faster than g. How could this be?
Here's a clue. The bungee cord they used was tied to the bridge at foot level, hung down over the edge of the bridge and then came back up to them. bungee cords are stretchy--if they weren't, the sudden stop at the end of the jump would probably kill the jumper. The bungee cord hanging off the bridge was stretched under its own weight. Think about what happened with the slinky, and you'll be able to figure out why the bungee jumpers accelerated at a rate greater than g.
When the jumpers stepped off the bridge, they were not only pulled down by gravity. They were pulled down by the elastic forces from the stretched bungee cord.
Here's a slinky model of the bungee jumpers. Hold both ends of the slinky at the same height so that the middle sags down toward the floor in a U shape. Hold a set of keys in the hand that holds one end of the slinky. Drop the keys and that end of the slinky at the same time. Notice that the end of the slinky accelerates down faster than the keys!
Peeling the Onion
Physics professors spend a great deal of time and effort to convince students of that in the absence of air resistance all objects fall at g. Understand this simple concept, and you are far ahead of most of the population in understanding how the universe works. However, you have to be careful not to extend simple models too far. In the case of our falling objects, there were elastic forces which increased the acceleration of parts of the object to greater than g.
As a teacher, Paul always begins with the simplest possible model that answers a question or explains an experiment. Modify the question and he may have to shift to a more complicated model. For example, ask how far a baseball drops as it is pitched across the front of a classroom and he'll use Newton's laws to figure it out. Ask how far light falls and he'll use general relativity (which gives exactly double the answer predicted by Newton.) So he tells his classes that every answer he gives contains an asterisk*, and the invisible footnote says *"But it's more complicated than that."
When it comes to falling, the important physics idea is that everything falls at g. However we have just shown you one of the asterisks. Elastic forces within an object can produce accelerations greater than g.
(Optional experiment put in separate box)
Not So Fast, Galileo!
Here's a simple experiment that you can use to demonstrate that not all objects fall at the same rate.
Find a yardstick. (Paul says find a meter stick, but he went metric decades ago. Don't worry about it---a yardstick will do just fine.)
Lay the yardstick on the floor and lift one end up so that the stick makes a 45 degree angle with the floor.
Now hold a coin next to the end of the yardstick and drop both at the same time. The end of the stick will hit the floor before the coin. Notice that the coin always falls on top of the stick. If you watch from the side, you can see the coin lag behind. That's because the end of the stick is accelerating faster than g.
In freefall, the center of mass of an object accelerates at g. But the meter stick isn't in freefall because the floor is pushing up on the bottom of the stick. Also, the stick rotates as it falls. The combination of the force from the floor and the rotation of the stick leads to an acceleration of the tip that is greater than g. The complete explanation is another asterisk.
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Copyright © 1998–2019 Fantasy & Science Fiction All Rights Reserved Worldwide