Why neglect air resistance

You can see the difference between these pretty clearly in the clip: the soccer ball flies smoothly, the beach ball floats a little, and the balloon really seems to hang in the air. This is even more clear if you track the position of the objects over time, using something like Tracker Video Analysis. Which I did, because I'm a physics professor, and produced the following graph:.

Graphs showing the flight of a soccer ball, a beach ball, and a balloon from the video clip in the Figure by Chad Orzel. These look superficially similar in that they go up and come back down, but you can see a clear difference: the curve for the soccer ball looks the same coming down as going up, while the balloon clearly falls in a different way than it rose. Both the beach ball and the balloon take longer to rise and fall, reflecting the fact that air resistance slows them more significantly than the soccer ball.

We can see this even more clearly by trying to make these data points fit with the simple, elegant physics equation. In the absence of air resistance, an object falling near the surface of the Earth should trace out a parabola, with an acceleration of 9.

If we fit a parabola to the soccer ball's flight, we can see that this works really well:. A parabola fit to the motion of the soccer ball; the acceleration from this is 9.

The line goes nicely through nearly all the points, and the value of acceleration you get from this is amazingly close to the expected result: 9. Doing the same thing with the balloon, on the other hand Trying to fit a parabola to the flight of a balloon, and failing.

The line misses a bunch of the points on either side, and does so in a systematic way. That's because this curve isn't really a parabola at all-- it's pushed away from the elegant parabolic shape by the air resistance force, which produces an acceleration that's about 30 times greater for the balloon than the soccer ball.

In fact, if you look at the tail end of the balloon's flight, the points seem to fall along a straight line, not a parabola. A straight-line fit works great R 2 of 0. This is the phenomenon of "terminal speed"-- since the air resistance force increases as speed increases, as gravity pulls the balloon down the air resistance force increases until it's just as big as the gravitational force.

At which point, gravity pulling down and air resistance buoying the balloon up cancel each other out, and the balloon falls at a constant speed. This is critically important physics for things like skydiving or the re-entry of spacecraft coming down from orbit.

In fact, terminal velocity gives you a nice conceptual explanation of why spacecraft engineers have to work so hard to dissipate the tremendous heat generated by craft falling back to Earth. A falling object that reaches its terminal velocity does not increase its kinetic energy as it falls further kinetic energy depends only on mass and speed , but does continue to lose potential energy due to gravity which depends only on mass and height.

That energy has to go somewhere, and it gets turned into heat. It has to lose this energy somehow, and so the pilot will slow the engines down, but usually this is not enough.

The pilot will also extend the landing gear and the flaps on the wings, both of which increase the air resistance and slow the plane down. The more air resistance there is, the faster the plane can slow down to make a safe landing. On the runway, the pilot will even put the engines in reverse this is done with air diverters on the sides of the engines , blowing air in front of the airplane, to slow the plane down even faster. If there is too much air resistance, then the airplane will flutter like a feather in the wind, or like a piece of paper.

The reverse-engine trick works on the ground because the wheels help keep the plane rolling safely and stably while there is so much resistance to its motion. You may notice birds doing the same kind of thing when they land. They swoop down, and then just as they come in for a landing, they start flapping their wings backwards, pushing air in front of them so they come to a graceful stop and can grab onto a small branch.

As learned in an earlier unit, free fall is a special type of motion in which the only force acting upon an object is gravity. Objects that are said to be undergoing free fall , are not encountering a significant force of air resistance; they are falling under the sole influence of gravity. Under such conditions, all objects will fall with the same rate of acceleration, regardless of their mass.

But why? Consider the free-falling motion of a kg baby elephant and a 1-kg overgrown mouse. If Newton's second law were applied to their falling motion, and if a free-body diagram were constructed, then it would be seen that the kg baby elephant would experiences a greater force of gravity.

This greater force of gravity would have a direct effect upon the elephant's acceleration; thus, based on force alone, it might be thought that the kg baby elephant would accelerate faster. But acceleration depends upon two factors: force and mass. The kg baby elephant obviously has more mass or inertia. This increased mass has an inverse effect upon the elephant's acceleration. The gravitational field strength is a property of the location within Earth's gravitational field and not a property of the baby elephant nor the mouse.

All objects placed upon Earth's surface will experience this amount of force 9. Being a property of the location within Earth's gravitational field and not a property of the free falling object itself, all objects on Earth's surface will experience this amount of force per mass.

As such, all objects free fall at the same rate regardless of their mass. Because the 9. Gravitational forces will be discussed in greater detail in a later unit of The Physics Classroom tutorial.

As an object falls through air, it usually encounters some degree of air resistance. Air resistance is the result of collisions of the object's leading surface with air molecules.

The actual amount of air resistance encountered by the object is dependent upon a variety of factors. To keep the topic simple, it can be said that the two most common factors that have a direct effect upon the amount of air resistance are the speed of the object and the cross-sectional area of the object.

Increased speeds result in an increased amount of air resistance.