How does air resistance influence the final velocity of an object in free fall?

Answers:

• Air resistance, also known as drag, plays a significant role in influencing the final velocity of an object in free fall. The effects of air resistance can be understood through the following points:

  1. Gravity vs. Drag Force: When an object falls, it is acted upon by two primary forces: the gravitational force pulling it downward and the drag force exerted by air pushing against its motion. The gravitational force is constant and increases the object's speed, while the drag force increases with speed.

  2. Terminal Velocity: As the object accelerates downward due to gravity, the drag force also increases, but it does not do so indefinitely. Eventually, the drag force becomes equal to the gravitational force acting on the object. At this point, the net force acting on the object is zero, resulting in zero acceleration. The object then continues to fall at a constant speed known as terminal velocity.

  3. Factors Influencing Air Resistance: The magnitude of the drag force depends on several factors, including:

     • The object's shape: Streamlined shapes experience less drag than blunt shapes.
     • The object's surface area: A larger surface area increases drag.
     • The object's speed: The drag force increases approximately with the square of the speed (F_drag ∝ v²).
     • The density of the air: Drag forces are greater in denser mediums.

  4. Implications for Different Objects: Different objects experience air resistance differently. For instance, a skydiver with arms and legs spread out has a larger surface area and thus reaches a lower terminal velocity compared to a diver in a streamlined position. A feather, due to its high surface area relative to its mass, falls much slower than a stone due to significant air resistance.

  5. Final Velocity in Free Fall: In the absence of air resistance, the final velocity of an object in free fall can be calculated using kinematic equations depending on the time of fall or the height. However, with air resistance, the final velocity (terminal velocity) depends on the balance of drag and gravitational forces, which can be complex to calculate without specific parameters.

  In summary, air resistance acts against the motion of a falling object, influencing its acceleration and ultimately resulting in a lower final velocity compared to the motion in a vacuum, where gravity is the only force acting on the object.