Free Fall and Air Resistance
All objects (regardless of their mass) free-fall with the same acceleration – 10 m/s2 rounded up. This acceleration value is so important in physics that it has its own peculiar name – the acceleration of gravity – and its own peculiar symbol – "g." But why do all objects free-fall at the same rate of acceleration regardless of their mass? Is it because they all weigh the same? ... because they all have the same gravity? ... because the air resistance is the same for each?
Why do objects which encounter air resistance ultimately reach a terminal velocity?
In situations in which there is air resistance, why do massive objects fall faster than less massive objects?
To answer the above questions, Newton's second law of motion (Fnet = m*a) will be applied to analyze the motion of objects which are falling under the influence of gravity only (free-fall) and under the dual influence of gravity and air resistance.
Free Fall Motion
Free-fall is a special type of motion in which the only force acting upon an object is gravity. Objects, which are said to be undergoing free-fall, do not encounter 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. Why? Consider the free-falling motion of a 10-kg rock and a 1-kg rock.
If Newton's second law were applied to their falling motion, and if free-body diagrams were constructed, you would see that the 10-kg rock experiences a greater force of gravity. This greater force of gravity would have a direct effect upon the rock's acceleration; thus, based on force alone, you might think that the 10-kg rock would accelerate faster. But acceleration depends upon two factors: force and mass. The 10-kg rock obviously has more mass (or inertia) than the 1-kg rock. This increased mass has an inverse effect upon the rock's acceleration. Thus, the direct effect of greater force on the 10-kg rock is offset by the inverse effect of its greater mass; and so each rock accelerates at the same rate – 10 m/s2. The ratio of force to mass (Fnet/m) is the same for each rock in situations involving free fall; this ratio (Fnet/m) is equivalent to the acceleration of the object.
Falling with Air Resistance
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 an object depends upon a variety of factors. The two most common factors which have a direct effect upon the amount of air resistance present are the speed of the object and the cross-sectional area of the object. Increased speeds result in an increased amount of air resistance. Increased cross-sectional areas result in an increased amount of air resistance.
Terminal Velocity
Why does an object which encounters air resistance eventually reach a terminal velocity? To answer this question, apply Newton's second law to the motion of a falling skydiver.
As an object falls, it picks up speed. This increase in speed leads to an increase in the amount of air resistance. Eventually, the force of air resistance becomes large enough to balance the force of gravity. At this instant in time, the net force is 0 Newtons — the object stops accelerating. The object is said to have "reached a terminal velocity." Any change in velocity terminates as a result of the balancing of the individual forces acting upon the object. The velocity at which this occurs is called the "terminal velocity."
In situations in which there is air resistance, massive objects fall faster than less massive objects. Why? To answer this question. Consider the falling motion of two skydivers: one with a mass of 100 kg (skydiver plus parachute) and the other with a mass of 150 kg (skydiver plus parachute). The amount of air resistance depends upon the speed of the object. Objects like the skydivers above will continue to accelerate to higher speeds until they encounter an amount of air resistance which is equal to their weight. Since the 150-kg skydiver weighs more (experiences a greater force of gravity), he will have to accelerate to a higher speed before reaching his terminal velocity. Thus, massive objects fall faster than less massive objects because they are acted upon by a larger force of gravity; for this reason, they accelerate to higher speeds until the air resistance force equals their gravity force.
So after some research I was wrong, I'll hold my hands up to that. I did discover that nearly every physics book I looked in said to disregard air resistance as being negligable except where objects differed greatly in mass and/or cross sectional area.
Still my experience of physics comes from school and putting little lead pills through targets at long range.
Ho Hum
Sniper8052