The diagrams above illustrate a key principle. When an object falls, it picks up speed. The increase in speed leads to an increase in air resistance. Eventually, the air resistance force becomes large enough to balance gravity. At this point, the net force is 0 newtons; The object stops accelerating. It is said that the object has reached a final speed. The gear shift ends with the balance of power. The speed at which this happens is called terminal velocity. As learned in an earlier unit, free fall is a special type of motion in which the only force acting on an object is gravity. Objects that are said to be in free fall do not encounter significant drag force; They fall under the sole influence of gravity. Under such conditions, all objects fall at the same rate of acceleration, regardless of their mass. But why? Consider the free-falling movement of a 1000kg baby elephant and a 1kg overgrown mouse. As learned above, the level of air resistance depends on the speed of the object.
A falling object continues to accelerate at higher speeds until it encounters air resistance equal to its weight. As the 150 kg skydiver weighs more (experiences greater gravity), it accelerates to higher speeds before reaching a final speed. For example, more massive objects fall faster than less massive objects because they are affected by greater gravity; For this reason, they accelerate to higher speeds until the drag force equals gravity. Once the upward force of drag on an object is large enough to compensate for the downward gravity, the object is said to have reached a terminal velocity. The final velocity is the final velocity of the object; The object will continue to fall to the ground at this final speed. In the case of the elephant and the feather, the elephant has a terminal velocity much greater than the feather. As mentioned above, the elephant should accelerate over a longer period of time. The elephant needs greater speed to accumulate enough upward drag to compensate for the downward gravity. In fact, the elephant never reaches terminal speed; The animation above shows that there is still acceleration on the elephant just before it hits the ground. If we were to represent the relative magnitude of the two forces acting on the elephant and feather at different times of their fall, it could look like the one shown below. (NOTE: The size of the force vector is indicated by the relative size of the arrow.) The final velocity equation tells us that an object with a large cross-section or a high drag coefficient falls more slowly than an object with a small area or a low drag coefficient.
(A large flat plate falls more slowly than a small ball of the same weight.) And if we had two objects with the same surface area and drag coefficient (two spheres of the same size), the lighter object would fall more slowly. This seems to contradict Galileo`s conclusions that all free-falling objects would fall at the same speed with the same drag. But Galileo`s principle only applies in vacuum, where there is NO air resistance and air resistance is zero. When an object falls into the air, it usually encounters some air resistance. Air resistance is the result of collisions of the object`s attack surface with air molecules. The actual resistance of the air encountered by the object depends on a variety of factors. To keep the subject simple, it can be said that the two most common factors that directly affect the height of air resistance are the speed of the object and the cross-section of the object. Increasing speeds leads to an increase in air resistance. Enlarged cross-sections result in increased air resistance. But what if there was no air resistance? If the drag could be eliminated in some way (by running the experiment in a vacuum), which object – the elephant or the feather – would touch the ground first? Study these questions by following the corresponding links to Elephant and Feather (Free Fall) in multimedia physics studios. In air resistance situations, more massive objects fall faster than less massive objects.
But why? To answer the question of why, it is necessary to consider free-body diagrams for objects of different masses. Consider the falling movement of two paratroopers: one with a mass of 100 kg (parachutist plus parachute) and the other with a mass of 150 kg (parachutist plus parachute). The free body diagrams are shown below for the moment they have reached the final speed. In addition to the study of free fall, the movement of objects that encounter air resistance is also analyzed. In particular, two issues are examined: Using the above diagrams and the animation above, observe that the spring quickly reaches the balance of forces and therefore zero acceleration (i.e. the final velocity). On the other hand, the elephant never reaches terminal speed when falling; The forces are never completely balanced and so there is still an acceleration. If given enough time, the elephant could eventually accelerate to speeds high enough to respond to a drag force large enough upwards to reach a final speed. If it were to reach a final speed, this speed would be extremely high – much greater than the final speed of the spring.
To answer these questions, one must understand Newton`s first and second laws and the concept of final velocity. According to Newton`s laws, an object accelerates when the forces acting on it are unbalanced; In addition, the amount of acceleration is directly proportional to the amount of net force (unbalanced force) acting on it. Falling objects initially accelerate (gain velocity) because no force is large enough to compensate for the downward gravity. However, as an object gains speed, it encounters an increasing upward drag force. In fact, objects will continue to accelerate (gain speed) until the drag reaches a value large enough to compensate for the descending gravity. As the elephant has more mass, it weighs more and experiences a greater downward impact. The elephant must accelerate (gain speed) for an extended period of time before there is enough upward drag to compensate for the great force of gravity downwards.