How Does Air Resistance Affect Our Weight in Free Fall from High Altitude?

When discussing the physics of falling from a high altitude, the term 'free fall' is crucial. Free fall, as defined in physics, means that gravity is the only force acting on the object, including the human body. In practical scenarios, however, this scenario rarely occurs in our atmosphere due to the presence of air resistance. In this article, we will explore how air resistance affects our weight when falling freely towards Earth's surface from a high altitude.

The Physics of Free Fall

Free fall, or gravity free-fall, occurs when a body moves under the influence of gravity alone, without any other forces interfering. In the absence of air resistance, a body in free fall accelerates at a constant rate towards the surface of the Earth, known as the acceleration due to gravity (g), which is approximately 9.81 meters per second squared (m/s2).

Importance of an Ideal Vacuum

The concept of free fall is often demonstrated in a vacuum chamber. In a vacuum, air resistance is minimized, allowing objects to fall under the influence of gravity alone. This condition is essential for accurate experiments and theoretical modeling, as it eliminates other external factors that can interfere with the gravitational pull. The use of a vacuum is fundamental to the understanding of the true dynamics of free fall (see vacuum environment).

The Role of Air Resistance

However, in real-world situations, the atmosphere significantly affects the motion of a falling body. Air resistance, or drag, acts in the opposite direction to the motion of the object. This force opposes the free fall of the object and gradually reduces its acceleration, eventually balancing it to a terminal velocity. The equation for air resistance is given by:

Drag Force ? × ρ × v2 × C × A

Where:

ρ is the density of the air v is the velocity of the object relative to the air C is the drag coefficient (which depends on the shape and orientation of the object) A is the cross-sectional area of the object perpendicular to the motion

The presence of air resistance means that the acceleration of the falling object is not constant but varies depending on its velocity. As the object falls, the air resistance increases, and the acceleration decreases until it reaches a point where the forces are in equilibrium, and the object falls at a constant velocity (terminal velocity).

Comparison in Vacuum vs Air

To understand the impact of air resistance, let's consider a thought experiment: two objects of the same mass but different shapes (one spherical and one flat) are dropped from the same height in both a vacuum and the Earth's atmosphere. In the vacuum:

The objects will accelerate at the same rate and hit the ground at the same time, regardless of their shape. Each object's weight will be their mass multiplied by the acceleration due to gravity (W mg), and it will remain constant.

In the presence of air:

The spherical object will experience less air resistance because its shape presents a smaller cross-sectional area to the air. Consequently, it will reach terminal velocity faster and maintain it. The flat object will experience more air resistance due to its larger cross-sectional area, slowing it down and reaching terminal velocity at a higher speed.

These differences in terminal velocity and the rate of weight loss due to air resistance can be observed in various everyday scenarios, such as the behavior of parachutists and skydivers.

Terminal Velocity and Weight Loss

As an object accelerates in free fall, it gains speed until the air resistance force equals the gravitational force. At this point, the forces are in equilibrium, and the object falls at a constant velocity known as terminal velocity. The terminal velocity is dependent on the object's mass, shape, and the density of the air.

For a falling human body, the terminal velocity is around 53 meters per second (or about 190 km/h) in typical atmospheric conditions. If the person were to fall in a vacuum, the body would continue to accelerate towards the Earth's surface until it hit the ground, and the gravitational force would not cause a loss in weight.

So, what about the perception of weight loss? The sensation of weight loss or heaviness during free fall in the atmosphere is largely due to the high acceleration (g-force). The human body experiences a force equivalent to up to 6 g during a typical skydive, which can be intense and momentarily feel like losing significant weight. However, this is purely an illusion and does not translate to any actual change in one's mass or weight.

Practical Applications and Considerations

The impact of air resistance on falling objects has significant applications in various fields, including aviation, sports, and physics experiments. Understanding the role of air resistance is essential for designing safe and effective equipment and predicting the behavior of objects during free fall. For instance, skydivers and aircraft designers must take air resistance into account to ensure safety and efficiency.

Air resistance is also a critical factor in the design of parachutes. Parachutes are designed to produce high drag forces to slow the descent of a skydiver, enabling a safe landing. The choice of material, shape, and size of the parachute all play crucial roles in determining the terminal velocity and the landing impact.

Conclusion

In conclusion, while the term 'free fall' in physics implies the absence of external forces other than gravity, the conditions required to achieve this state in the natural world typically involve a vacuum. Air resistance plays a significant role in the real-world scenario of falling from a high altitude, affecting not only the speed of descent but also the sensation of weight during and after the fall. Understanding these factors is vital for accurate modeling and practical applications in various fields.