Pitchers throw curveballs, making batters swing wildly. Football players throw perfect spirals, the balls spinning rapidly as they land in the arms of receivers. And skydivers hang below parachutes, drifting slowly to Earth.
We’ve learned that the only force acting on a ballistic object is gravity. But that’s not completely true! There’s something else: air. Fortunately for us, we live on a planet with an atmosphere. It protects us from harmful radiation and gives us oxygen to breath. But the air also affects projectiles in weird and interesting ways.
ESSENTIAL QUESTION
What are some different ways of manipulating the motion of a projectile through the air, and why are these useful?
Remember Galileo’s experiment atop the leaning tower of Pisa? Suppose you were to drop a feather and bowling ball at the same time. According to Galileo’s experiment, they should hit the ground at the same time.
atmosphere: the mixture of gases surrounding Earth.
radiation: energy transmitted in the form of rays, waves, or particles from a source, such as the sun.
drag: the force air exerts on a body moving through it.
surface area: a measure of the total area that the surface of an object occupies.
aeronautical engineer: a person who designs and tests aircraft.
aerodynamic: having a shape that reduces the amount of drag created by air passing around or over it.
streamlined: designed with a smooth surface that minimizes resistance through air or water
But do they? If they don’t, does it mean Galileo was wrong? Or is something else going on?
Imagine standing on a chair and dropping a flat piece of paper and a crumpled piece of paper at the same time. Do they hit the ground together? The two pieces of paper have the same mass, but they fall at different rates. According to Galileo, that shouldn’t happen!
Is gravity really affecting the two objects differently, or is there some other force at work?
The flat piece of paper is experiencing more drag, or air resistance. Air resistance is the force of friction between an object and the air it’s moving through. The amount of air resistance on a projectile depends on the projectile’s size and speed. When you drop a flat piece of paper, it has a lot of surface area facing the direction it’s traveling.
A Feather on the Moon
What would happen if you repeated the paper experiment on the moon? During one of his moonwalks, Apollo 15 commander David Scott (1932– ) demonstrated Galileo’s discovery by dropping a feather and a hammer at the same time.
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This creates a lot of drag, slowing the paper’s acceleration. The crumpled paper experiences drag, too, but the amount of air resistance is less because the paper has a smaller surface area in the direction it’s moving.
For most things, including slingshots and basketballs, air resistance is so small that it can be ignored. But when objects are really big or move very fast, even a little bit of surface area can create a lot of drag and change their ballistic trajectories.
DID YOU KNOW?
Aerodynamics is a part of physics that studies how air moves around things such as airplane wings and rockets. Scientists who study aerodynamics to design better and more efficient airplanes are called aeronautical engineers.
To lessen the amount of air resistance, things such as arrows, airplanes, rockets, and even cars are designed to be more aerodynamic or streamlined. The more streamlined a projectile is, the less drag it has—and the farther and faster it can fly!
Although making objects more aerodynamic can help them reach amazing speeds, sometimes slowing a projectile down is important, too.
PARACHUTES
While most things that move through the air try to keep the amount of drag as small as possible, lots of air resistance can sometimes be very helpful. Suppose you wanted to deliver something fragile by firing it from a cannon or dropping it from an airplane? It probably wouldn’t survive its flight unless you could find a way to slow it down before it’s smashed to bits.
Parachutes are used to deliver important supplies to hard-to-reach places and softly return astronauts to Earth. How do they work?
In the 1470s, the famous artist and inventor Leonardo da Vinci (1452–1519) designed a “tented roof” to carry a person underneath it. There’s no record of it ever being tested, but many historians consider it the first parachute!
Instead of having a streamlined shape, parachutes are large and open. They’re designed with lots of surface area. This lets them catch as much air as possible and create a lot of air resistance as they fall.
By pushing against so much air, parachutes use the force of drag to slow down and safely land payloads such as space capsules and skydivers.
Alan Eustace (1957– ) is an engineer who holds the record for the highest jump back to Earth. He rose more than 135,000 feet attached to a balloon, and then jumped back to Earth with a parachute.
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And watch a video of him at this website. |
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When skydivers leap from airplanes, they experience air resistance as they fall to Earth. As the force of gravity accelerates the skydiver, Earth’s atmosphere pushes back. When the force of drag equals the force of gravity, the skydiver no longer accelerates. This is called terminal velocity. A skydiver reaches terminal velocity at about 125 miles per hour!
But parachutes aren’t the only things that use air resistance and drag in interesting ways. There are other projectiles that can use these powerful forces.
THROWING A CURVE
A batter swings at a pitch, only to watch it curve under the bat at the last second. A striker scores a spectacular goal, and the replay shows the fantastic shot curling past the goalie’s outstretched hands into the back of the net. How does this happen?
Dick Rudolph (1887–1949), who was known for throwing curveballs, used this grip on the ball.
credit: Library of Congress
optical illusion: a trick of the eyes that makes people see something differently than it really is.
turbulent: unsteady or violent movement.
Magnus effect: when air pressure on one side of a ball is greater than on the other side, making the ball move toward the side where there is less pressure.
After a ball is thrown or kicked, it follows a ballistic trajectory, with gravity and air resistance the only forces acting on it. Newton’s first law says that an object needs a force to change speed or direction, so how do baseballs and soccer balls manage to curve?
For years, people thought that curve balls in sports were a trick of the eye, used to fool the other team. Is a curve ball an optical illusion or is it real?
A special kind of ball can help us sort this out—the Wiffle ball. How does a Wiffle ball move through the air? Instead of flying steadily like a baseball or tennis ball, it wiggles and waggles its way across the field. You can see for yourself by doing the activity on page 90.
The holes of the Wiffle ball are important to its wild turns and sudden wobbles. As air flows over and through the holes, it becomes turbulent. Because the air doesn’t flow smoothly around the ball, the air resistance is unequal on different parts of the ball. And thanks to Newton’s first law, we know that unbalanced forces can cause things to change direction or speed. When the Wiffle ball is thrown, these unbalanced forces cause the ball to curve, dip, and dive dramatically!
DID YOU KNOW?
The Wiffle ball was originally created out of perfume packaging! In 1953, a dad named David Mullany used a razor blade to slice holes into a hard plastic ball so his son could make balls serve and curve with ease.
And it turns out that you don’t need holes to make projectiles move in strange ways—you can do it with spin!
When a pitcher throws a curveball, they grip the ball in such a way that it spins very quickly when it’s released toward home plate. As the ball spins, a thin layer of air spins with it.
As the ball sails toward the plate, it runs into air pushing it in the opposite direction.
The thin layer of air speeds up the oncoming air on one side of the ball but slows it down on the other. This causes a difference in pressure on either side of the ball, pushing the ball in the direction of its spin.
Different grips and kicks can spin balls in different ways, making balls curve left, right, and even up or down! This is called the Magnus effect, and it gives curveballs their curve, causes golf balls to slice, and lets soccer players’ shots seem to avoid the goalkeeper on their way into the back of the net!
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When you throw or toss something, you usually can’t help but give it a little spin. Athletes who put a lot of spin on balls can make their sport’s projectiles do some amazing things. But have you wondered what can happen when there’s no spin on a ball?
knuckleball: a baseball thrown with as little spin as possible.
spiral: winding in a continuous and gradually widening or tightening curve.
KNUCKLING
Have you heard of a knuckleball? In baseball, only a few pitchers have mastered the knuckleball’s unpredictable movements. Unlike other pitches, knuckleballs are thrown so that the ball has as little spin as possible.
The result is a pitch that moves in ways that make it hard for a batter to hit, and difficult for a catcher to catch!
So how does it work? Scientists aren’t completely sure. Researchers think that as a knuckleball is thrown, the stitches on the baseball’s surface cause turbulence in the thin layer of air around the ball. But unlike with a curveball, this turbulence causes forces to push the knuckleball in different directions instead of one.
Good Pitchin’
Have you heard of R.A. Dickey (1974– )? In 2012, he won the Cy Young baseball award as the best pitcher in the National League. His knuckleballs are amazing to watch!
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This strange knuckling effect is also seen in soccer, when a ball is kicked so that it has very little spin. But soccer balls don’t have stitches sticking out the way baseballs do, so there must be something else going on. Maybe you’ll be the person to figure it out!
In many sports, spin is used to change the ballistic trajectory of projectiles. But spin can also keep a projectile headed in the right direction.
Do you watch or play American football? A football has an interesting shape. Instead of being round like a soccer ball, it’s wide in the middle and pointed on both ends.
Good quarterbacks can throw footballs incredible distances with amazing accuracy. But if you tried to throw a football without practice, it probably wouldn’t get very far.
Inexperienced players can get frustrated as the ball tumbles end over end as soon as it leaves their hand. So how do football players make it look so easy?
Just like a baseball pitcher, quarterbacks spin the ball as it leaves their hands. This is called “throwing a spiral.”
DID YOU KNOW?
The mathematical name for the shape of an American football is a “prolate spheroid.” Playing a game of prolate spheroid would sound a little strange. No wonder they just call it a football!
axis: an imaginary line down the middle of a sphere around which it rotates.
angular momentum: an object’s resistance to either start or stop spinning due to inertia.
gyroscope: a spinning wheel or disk used to measure or maintain orientation.
orientation: the direction and position of something compared to something else.
gyroscopic stabilization: when a spinning object stays pointed in the direction it was thrown.
fletching: feather-like material at the end of an arrow.
To throw a spiral, the player must spin the football around an imaginary line called an axis that connects its two pointy ends. Throwing a spiral is not easy—it takes a lot of practice to throw the perfect spiral like a professional football player. Even the best athletes can struggle to throw it correctly! So why do they throw it in such a difficult way?
In baseball, pitchers put spin on the ball to make it harder to hit. But in football, quarterbacks put spin on the ball to make it easier to catch! That’s because a spinning football has angular momentum.
According to Newton’s first law, when something is in motion, it resists changing its motion due to its inertia.
What’s a Gyroscope?
Because spinning objects resist a change in their orientation, they can be made to do all kinds of interesting things. A gyroscope can be easily balanced on a string or the tip of a finger and is even used to help airplanes and spacecraft know which way they’re pointed!
credit: Misko (CC by 2.0)
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That happens with spinning objects, too! When you spin a top, it wants to keep spinning the same way and resists falling over. As a football spins around its axis, it acts like a top and resists any change in its orientation. That means the ball stays pointed in the direction it’s thrown. This is called gyroscopic stabilization.
A well-thrown spiral makes the football less wobbly and it also makes it more aerodynamic. Maybe more importantly, it also makes the ball much easier for someone to catch!
If a football is thrown without spin, it can tumble end over end. That tumbling makes it really hard to catch a last-minute, game-winning touchdown pass!
Gyroscopic stabilization isn’t used just by quarterbacks and archers, however. It turns out that bullets spin, too.
DID YOU KNOW?
In archery, arrows are designed to spin, too. At the rear of the arrow, feather-like material called fletching is made with a slight twist. This causes the arrow to spin as it flies and increases the archer’s accuracy!
THE RIFLE
The earliest bullets were small metal balls that bounced around inside the gun barrel, making their trajectories unpredictable. Marksmen had to be close to their targets to be sure they could hit their marks. Otherwise, chances were good that they’d miss!
In the sixteenth century, an important improvement made guns much more accurate. The carving of grooves on the inside of a gun’s barrel made it much easier for a marksman to strike a target, and do so from a far greater distance. As the bullet traveled along the barrel, the grooves gave the projectile spin—just like a spiral pass from a quarterback! This technique was called rifling, and it’s how the rifle got its name.
DID YOU KNOW?
The first widespread use of modern, streamlined bullets in battle was during the American Civil War (1861–1865).
These are bullets from a Civil War battle found in the ground of Fredericksburg, Virginia.
In all recent wars, firearms such as guns and rifles have played a large part in battles, big and small. Firearms are also a controversial topic in many countries. Some countries have strict laws limiting who can own firearms and what kind they can own. In the United States, the Second Amendment to the U.S. Constitution states:
“A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.”
Many Americans believe the Second Amendment gives them the right to keep and own firearms without limits, while others argue that the writers of the Constitution meant for these weapons to be restricted. It is a very controversial topic. What do you think?
Finally, in the nineteenth century, the bullet was given a cone-like shape, making it more aerodynamic. All these improvements made rifles even more accurate—and deadlier.
Although they’ve advanced a lot in the last century, the basic design and physics behind firearms and bullets has stayed the same.
For most projectiles, thinking about drag or orientation isn’t necessary. But the bigger and faster the projectile, the more important these elements become. Rockets are just about the biggest and fastest projectiles there are! We’ll learn about these machines in the next chapter.
ESSENTIAL QUESTION
What are some different ways of manipulating the motion of a projectile through the air, and why are these useful?
GALILEO’S EXPERIMENT, PART 3
When you first did Galileo’s famous experiment, you saw that gravity pulls on everything the same way, causing things such as tennis balls and dump trucks to fall at the same rate and hit the ground at the same time. The second time, you used it to prove that horizontal and vertical motion are independent. Now you’re going to put a wrinkle into the same experiment one more time—using paper!
›Take two pieces of paper and crumple one into a ball. Leave the other flat.
›Hold the flat piece of paper in one hand parallel to the ground. Hold the crumpled piece of paper in the other hand.
›At the same time, drop both the crumpled and the flat paper pieces of paper. What happens? Record your observations in your engineering notebook.
Questions to think about
Compare the motions of the two pieces of paper. How are they different?
Use a timer to record the rate of fall for each piece of paper. How can you explain the differences?
What forces are affecting the motion of the pieces of paper?
What would Newton and Galileo say about this experiment?
Try This!
Does holding the flat piece of paper vertically change how it falls? Can you fold or shape the paper in a different way to cause it to fall at a different rate? Try dropping an object that’s the same size and shape as a sheet of paper (such as a large book) along with a single flat sheet. How do they compare?
Do you have an important payload you want to deliver by slingshot, catapult, rocket, or just a hard throw? Then you might need a parachute to help it land!
›For the parachute, choose thin, light material to work with, such as cloth, paper, or plastic that can be cut. Cut your material into a circle.
›Cut at a least four evenly spaced, small holes around the edge of the parachute.
›Cut the same number of strings as holes. They should all be the same length.
›Tie a string to each hole. You might want to use tape to help reinforce the holes.
›Tie the strings together at the bottom and attach them to your payload. Use tape, glue, or another string.
›Test your parachute! Drop your payload from a safe height and see how it works. Does your valuable cargo survive?
Questions to think about
How does the parachute keep the payload from falling as it normally would? What forces are at work?
How does the mass of the payload affect the parachute?
Does the height of the drop change how the parachute works?
Try This!
Try different shapes for your parachutes. Is there a best shape? Why or why not? Try placing a small hole in the center of your parachute. Does this affect how the parachute works?
WHAT MAKES WIFFLE BALLS WAFFLE?
Have you ever played Wiffle ball? The crazy plastic ball is famous for seeming to defy the laws of physics with its crazy curves and dramatic drops. What makes the Wiffle ball behave the way it does?
›Wrap a few Wiffle balls with tape. Try to use the same amount of tape for each ball. Cut through the tape of one Wiffle ball so that the holes are open but leave the other Wiffle balls covered.
›Outdoors, throw one covered ball and the open ball several times each at a target. Carefully observe how they move.
›Try your best to throw each ball the same way, and from the same distance. What happens? Draw the ballistic trajectory of each experiment in your engineering notebook.
Questions to think about
Is there a difference in how the two balls move? If there is, what do you think is causing the difference? If not, why not?
Why wrap the Wiffle balls with about the same amount of tape? And why try to throw them the same way each time?
Try This!
Try using something to throw the balls—a catapult or slingshot, for example. Does the way the projectiles are accelerated affect their motion? Try cutting the holes just on one side of one of the covered balls and throwing the ball with holes facing in different directions. Does this affect the ball’s motion? Record the motion of the balls in slow-motion video and compare their trajectories. How do they differ? How are they the same? Can you think of ways to measure the differences using the camera?
Football players make throwing a spiral look easy, but it certainly is not! So, why bother spinning a football in the first place? Is there something about spinning that helps quarterbacks throw those winning passes?
›Use a top or a fidget spinner if you have one, or make one yourself.
›To make your own top, glue a bead to a washer. The hole of the bead should be right over the center of the washer.
›Trim a bamboo skewer to about 2 inches long. Push the skewer through the washer and the hole in the bead, leaving about one-quarter of an inch sticking out of the bottom of the bead. Glue the skewer to the bead.
›Now, try to balance your top without spinning it. Can you do it?
›Spin it! What is the motion like? What observations can you make? What is it doing? What isn’t it doing?
Questions to think about
What do you notice about the motion of the top or spinner as it’s spinning?
Think about Newton’s laws of motion. Can you use them to explain how the top keeps from falling over?
What happens when it stops spinning?
Does playing with your top or spinner give you any ideas as to why it might be helpful to spin a football when it’s thrown?
Consider This!
What is important for something to spin like a top? Does the shape, weight, or size change how long it spins? Can you spin other objects like a top? Experiment with different materials to see what makes a good top or spinner.
Throwing something like a football so that it spins isn’t easy, but with practice you can do it!
›Place your target in a wide-open space outside. Give yourself at least 4 to 6 feet of space between you and the target.
›Throw an empty paper towel roll at your target. First, try throwing it without spin. Can you hit your target? Give yourself one point for each success.
›Next, try spinning it along its length as you throw it. This will take practice! Try rolling it off your fingers. Does spin help you hit your target? Give yourself two points each time you succeed.
Questions to think about
What happened when the tube was thrown without spin? What was the motion like? Was it predictable? Were you able to hit the target?
What happened when you spun the tube? What was the motion like this time? Did it make it easier or harder to hit the target than throwing the tube with no spin?
Which is more accurate, throwing with or without spin?
Explain your answer. Can you think of another example?
What laws of motion are at work?
Try This!
Try your hand at throwing a football. It’s not easy! What other projectiles can you spin?
NASA hammer feather