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Skydiving & Air Resistance

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Galileo drops the ball
Why is Galileo wearing a space suit?
Click on the picture to find out.

Skydiving is a great activity for experiencing some key laws of physics. Skydivers jump from planes flying high above the earth. Immediately, and in a rather dramatic way, they become keenly aware of the force of gravity. At a certain point, their parachutes open, giving them, on top of a tremendous feeling of relief, a sensation of deceleration caused by friction with the air, or drag.
Below is additional information to help understand how this works, along with some historical notes.

Galileo Drops the Ball – Drag

In around 1590 Galileo Galilei (1564-1642) climbed up the Leaning Tower of Pisa and dropped some balls to the ground. Two balls of different masses, but of similar shape and density that were released together hit the ground at the same time. Until then it was commonly believed that heavy things fall faster than light things. Many people still believe this, and casual observation of everyday phenomena often does tend to confirm this view.
If you drop a brick and a feather at the same time the brick will probably hit the ground first. But this is because of differences in the amount of friction between these objects and the air around them, not because their masses are different. If there were no air, the feather and the brick would hit the ground at the same time.

Newton and the Apple – Gravity

According to legend, Isaac Newton (1642-1727) learned about gravity when an apple fell on his head while he was sitting under a tree. He realized that there was a force -- the "force of gravity" -- that caused objects to accelerate toward earth.
Drag – the friction between an object and a fluid, such as air, that it is moving through – is a force that acts opposite to the direction that the object is moving, slowing it down. When an object is falling, drag is an upwards force. Unlike the force of gravity, drag increases with speed. When an object is not moving through the air drag is zero. As it moves faster, drag increases.
The mass of a skydiver is the same with the parachute folded up in the backpack as it is when it is open. But the open parachute causes much more drag. If you took a feather and squashed it into a small ball it would fall through the air with less drag and therefore fall faster.

More About Friction

Aristotle (384-322 BC) believed that in order to keep something moving it was necessary to continually apply a force to it. In our friction-filled world, this is not an unreasonable theory.

  • When you push a book across the table it only moves as long as you push. When you stop pushing, the book stops moving.
  • If you are riding a bicycle on level ground, you have to keep peddling to keep moving. If you stop peddling you will slow down and eventually come to a stop.

But his theory did not hold up. Both the book and the bike slow down and stop because of friction, not because of the lack of a force to keep them going. If there were no friction, the book would speed up as long as you pushed it and then continue to move at a constant velocity when you stop pushing. Peddling the bike would cause it to speed up. When you stop peddling you would coast forever at the same speed. After its engines have been turned off, a space ship will continue to move at constant velocity through empty space, where it experiences no friction. Galileo understood and described this with his concept of inertia. Newton worked out the details and the math.
Aristotle's incorrect law of motion can be spelled out as

F = m v

Where F is the force acting on an object, m is its mass and v is its velocity. In other words for a given object (m is constant), the more you push (more F) the faster you go (more v). If you stop pushing (F = 0) you stop moving (v = 0).
Newton tells it this way in his second law of motion:

F = ma

Where F is the force acting on an object, m is its mass and a is its acceleration.
It turns out that Newton's theory had some limitations as well. When it comes to very strong gravitational fields and speeds approaching that of light Einstein's Theory of Relativity is a more accurate description of the way the Universe works. And in the tiny world inside atoms, Quantum Physics applies, but that's another story! For things in our everyday experience, Newton's laws of motion remain in force.
Another look at fractions
Skydiving provides an illustration of the friction that occurs when a large solid object moves through a gas such as air. Friction with the air, called drag, is proportional to the square of velocity

D = kv2

where D is drag, v is velocity and k is a constant. The constant k is determined by the density of the gas and the shape of the object. A person with an open parachute is presenting a larger surface area to the air than when the parachute is closed. The weight is the same in either case.
For objects moving slowly through liquids, such as the pebbles we dropped through water and corn syrup in the Viscosity of Liquids experiment, a standard approximation is to assume that friction is proportional to velocity. In general, a formula

f = kv

where f is friction, v is velocity and k is a constant, would apply.
Another type of friction involves solid objects sliding against each other, such as a book being pushed across a table. In such situations, the force of friction depends upon two factors:

  1. the force that presses the surfaces of the two objects together, called the "normal force," in this case, the weight of the book. If you had a pile of ten books instead of just one book, the normal force would be greater and it would be harder to push.
  2. the roughness of the surfaces. If the book and the table were both covered with sandpaper there would be more friction and it would be harder to push the book. The nature of the surfaces determines the "coefficient of friction" usually represented by the Greek letter µ (pronounced "mu")

For sliding objects

f = µN

Where f is the force of friction, µ is the coefficient of friction and N is the normal force. But it's not quite so simple. The force of friction differs depending upon whether or not the book is moving. While the book is moving the force resisting your push is called kinetic friction, fk.

fk = µkN

where µk is the coefficient of kinetic friction.
If you push very gently on the book while it is sitting still it will not move. The force ofstatic friction is equal to the force of your push. If you push a little harder, the book still doesn't move, but the force of static friction is greater, again equaling the force of your push. You can keep pushing harder until the book starts to move. At the point just before it does

fs = µsN

where fs is static friction and µs is the coefficient of static friction.
For a given object on a given surface, the coefficient of kinetic friction is generally less than the coefficient of static friction. You may have experienced this when you try to push a heavy object. It's harder to get it moving than to keep it moving.
 

The book is sitting still on the table. The force of gravity is pulling downward, but the table exerts an equal and opposite force upward. The total of all forces acting on the book is zero so it does not accelerate. Book on a table
If you push hard enough, you will overcome static friction. The red arrow indicates the force of your push. The green arrow is the force of friction. The book accelerates. Pushi the book
Once in motion, if the force  of your push equals kinetic friction, the book will move at a constant velocity. Forces on the book
When you stop pushing the book still moves, but now friction is the only sideways force on the book so it decelerates rapidly... Forces on the book
...and comes to a stop. Forces on the book
We have created an interactive applet for you to play with to get a feel for how this works. Click on the image to the right to begin. Friction example 

Skydiving and Gliding – More about Gravity and Drag

Our discussion of the physics of skydiving in Gravity and Drag assumes that the skydiver is falling straight down. In fact, there is also horizontal movement. Our description more closely fits what happened when Phillipe Theys began skydiving in 1970 and "...parachutes were round like mushrooms." These chutes tended to fall straight down through the air. Modern parachutes are more like airplane wings and skydiving is actually like gliding. You move both forward and downward as indicated by the green arrow. Drag, shown by the read arrow, acts opposite to the direction of motion -- upward, but also backward.*
GlidingThere are other air sports that are related to skydiving. Hang gliding is similar, but the hang glider has a rigid frame supporting the fabric wing, and instead of jumping out of a plane one generally launches by jumping from a hill or cliff.
In the sport of soaring, people fly airplanes without engines. These gliders, or sailplanes, have rigid, smooth wings and bodies. This results in much lower drag than is the case with parachutes and hang gliders. They glide at a shallow angle and can ride upward moving air currents just as sea gulls and eagles do, remaining aloft for hours at a time. The Related Links page has links to web sites with information about these exciting sports.
If you want to learn more about this topic go to the Related Links page and click on the link to the HyperPhysics web site.
*We are talking about motion through the air. But unless it is a very calm day with no wind, the air is also moving across the ground. This has no effect on how the parachute descends through the air, but it will affect how and where you land.

In the Science Lab

The Air Resistance experiment illustrates how drag depends upon the surface area of an object compared to its weight. We start with two identical pieces of paper and fold one very tightly while loosely crumpling the other. When dropped, there is more drag on the loosely crumpled paper because it presents a greater surface area to the air it is moving through. The two pieces of paper weigh the same. If there were no air, they would fall at the same rate.
In Make a Parachute we offer plans for a small parachute. There are many possible designs and many different materials that could be used.


This content has been re-published with permission from SEED. Copyright © 2024 Schlumberger Excellence in Education Development (SEED), Inc.