Post
by smutek » Tue Mar 22, 2005 6:56 pm
Acceleration of gravity
If you drop an object relatively near the Earth, it will speed up according to the acceleration of gravity (g).
Object speeds up
When you let go of the object, its velocity is zero.
Since g = 32 ft/s2 = 9.8 m/s2, the velocity will be 32 ft/s (9.8 m/s) after one second.
Because the object is accelerating, the velocity after 2 seconds will be 2 x 32 ft/s = 64 ft/s (19.6 m/s).
After 10 seconds, the velocity will be 10 x 32 ft/s = 320 ft/s or 98 m/s.
You can see how the velocity of the object gets faster and faster.
Terminal velocity
Although a falling object will continue to accelerate until it is made to stop, like when it hits the ground, air resistance will slow down that acceleration. Air resistance is approximately proportional to the square of the velocity, so as the object falls faster, the air resistance increases until it equals the force of gravity. The object has reached what is called its terminal velocity.
There have been many calculations on what the terminal velocity would be for a penny dropped from a high building or airplane. Because a penny would probably tumble, the calculations can become highly complex. One estimate is that a penny dropped from a high building will accelerate until it reaches around 230 mph.
Some dispute such a high terminal velocity. A better example of terminal velocity is that of dropping a baseball. Once a falling baseball reaches 94 miles per hour or 42 meters/second, it would remain at the velocity and no longer accelerate.
Acceleration independent of mass
One surprising characteristic of the force of gravity is that the acceleration it causes in falling bodies it independent of the mass of the object.
In other words, a 5 pound weight would fall at the same rate as a 10 pound weight. If dropped from the same height, they would take the same time to hit the ground. Of course, in dropping a light weight object, air resistance often will slow the object down more than a heavier object.
Not only does is the acceleration of gravity independent of the mass of an object, but it is also independent of the velocity of the object parallel to the ground.
In other words, it an object is traveling at some velocity parallel to the ground, it will fall at the same rate as a stationary object. Thus a bullet shot from a gun will hit the ground at the same time as one that was simply dropped from the same height.
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