Why do falling objects incur terminal velocity?
Falling objects incur terminal velocity because of air resistance.
Example and Discussion: Imagine two objects are falling from the top of a very tall building. For sake of argument say that they are a man and a small stone. They are under the influence of two forces: Their weight (which ties in with gravity) and air resistance. Its probably not much of a surprise but as expected the man does strike the ground before the stone. What we are concerned with is Why?
The man and the stone are both being pulled down by the forces of their respective weights (W = Mass * Acceleration due to gravity). At the point of being dropped initially, the forces due to gravity is not balanced by any other forces and therefore acts alone in pulling the two objects towards the earth at a rate of 9.8 m/s2. As they begin to gain speed however they start to encounter the upward acting force of air resistance. air resistance is the result of an object plowing through the air and colliding with air molecules. The more air molecules an object collides with, the greater the force of air resistance. Therefore we can summarize now that the amount of air resistance is dependent not only on the speed of the falling object but also on its surface area. Based on this information alone we can make our first prediction that the air resistance (for the same speed) would be more for the man as he has a larger surface area and therefore collides with more molecules of air. This however might confuse you. If the man encounters more air resistance, why and how does he reach the ground before the stone.
To answer these questions, we turn to Newton's first and second laws and combine them with our knowledge of terminal velocity. According to Newton's laws, an object accelerates until the force acting on it is unbalanced, or disturbed in some way that the overall acceleration is proportional to the overall force acting on the object and its mass. Falling objects initially accelerate because there is no net force big enough to counteract the downward force of their weights. As they continue to fall however, they gain speed and thereby encounter an increasing amount of air resistance force, acting upward. In fact, objects in free fall will continue to accelerate until the force of air resistance becomes a large enough value to balance the downward acting force of the objects weight(W = mg) or as we also call it, the gravitational force. The man has more mass, weighs more and therefore experiences a greater gravitational force pulling it towards the earth than the stone. It will therefore have to accelerate for a longer period of time to build up the air resistance to balance this larger gravitational force. If the object reaches this stage at which the speed it has built up gives it the air resistance to balance the force of gravity, it is said to be at terminal velocity.
Once an object reaches its terminal velocity it does not accelerate anymore. It will continue to fall toward the earth at this velocity for the remainder of its drop. Taking the case in point, we now realize that the man has a much greater terminal velocity than the stone. Since it takes a much greater speed to accumulate sufficient air resistance force to balance the force of gravity, we can pretty safely make the assumption that the man accelerated for a longer period of time. What happens in fact is that, the man never really reaches his terminal velocity because the distance he fell was too short. Given enough free fall time, the man would have accelerated enough, to high enough speeds to build up air resistance strong enough to counterbalance the effects of gravity. But in this case he doesn't. So in fact, he never really stops accelerating. The stone on the other hand, weighs considerably less, and therefore only needs a lower speed to reach its terminal velocity. The distance it travelled during the fall was enough for it to achieve this. It was therefore travelling at terminal velocity(acceleration = 0 m/s2.), when it hit the ground.
In conclusion, the man falls faster than the stone because he never stops accelerating at any point before reaching the ground(accumulating more and more air resistance as he goes along). The stone on the other hand quickly reaches its terminal velocity. Not requiring much air resistance, the stone obtains its state of terminal velocity in an early stage of the fall.
Alternate case:
Just to make the point clearer, consider an alternate situation in which both the objects fall under identical conditions, in a "vacuum". Yes! This might surprise you, but without the force of air resistance, they both accelerate toward the earth under the same gravitational force(9.8m/s2). They therefore will reach the ground at the same time.