Describing Motion With Words - Intro

Lesson 3: Newton's Second Law of Motion

Free Fall and Air Resistance

All objects (regardless of their mass) free-fall with the same acceleration - 10 m/s/s. This particular 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? This question will be explored in this section of Lesson 3.

In addition to an exploration of free-fall, the motion of objects which encounter air resistance will also be analyzed. In particular, two questions will be explored:

To answer the above questions, Newton's second law of motion (F net = m*a) will be applied to analyze the motion of object which are falling under the sole influence of gravity (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, 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 10-kg rock and a 1-kg rock.

If Newton's second law were applied to their falling motion, were constructed, then it would be seen that the 10-kg rock would 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, it might be thought 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). This increased mass has a inverse effect upon the rock's acceleration. And thus, the direct effect of greater force on the 10-kg rock is offset by the inverse effect of the greater mass of the 10-kg mass; and so each rock accelerates at the same rate - 10 m/s/s. The ratio of force to mass (Fnet/m) is the same for each rock under 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 the object is dependent upon a variety of factors. To keep the topic simple, it can be said that the two most common factors which 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. Increased cross-sectional areas result in an increased amount of air resistance.

Why does an object which encounters air resistance eventually reach a terminal velocity? To answer this questions, Newton's second law will be applied to the motion of a falling skydiver. In the diagrams below, free-body diagrams showing the forces acting upon a 100-kg skydiver are shown. For each case, use the diagrams to determine the net force and acceleration of the skydiver at each instant in time. Then use the "pop-up menus" to view the answers.

 

 

 





 

The diagrams above illustrate a key principle. As an object falls, it picks up speed. The increase in speed leads to an increase in the amount of air resistance. Eventually, the force of air resistance becomes large enough to balances the force of gravity. At this instant in time, the net force is 0 Newtons; the object will stop accelerating. The object is said to have "reached a terminal velocity." The change in velocity terminates as a result of the balance of forces; the velocity at which this happens is called the "terminal velocity."

In situations in which there is air resistance, more massive objects fall faster than less massive objects. But why? To answer the why question, it is necessary to consider the free-body diagrams for objects of different mass. 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 free-body diagrams are shown below for the instant in time in which they have reached terminal velocity.

As learned above, the amount of air resistance depends upon the speed of the object. Objects like those 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), it will accelerate to higher speeds before reaching a terminal velocity. Thus, more massive object 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 the gravity force.

 

Lesson 3: Newton's Second Law of Motion

 

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