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Chapter 2: Problem 18

Explain how the change in the force of air resistance on a falling body causes it to eventually reach a terminal speed.

Short Answer

Expert verified
Question: Explain the relationship between the force of air resistance on a falling body and terminal speed. Answer: The force of air resistance on a falling body is directly related to its terminal speed. As the object falls, the air resistance force increases in opposition to the object's motion. When the air resistance force becomes equal to the gravitational force acting on the object, it reaches a constant terminal speed where no further acceleration occurs. This balance of forces ensures that the object maintains a consistent terminal speed throughout its descent.

Step by step solution

01

Understand Air Resistance

Air resistance, also known as drag, is the force that opposes the motion of an object through the air. When an object falls, gravity pulls it toward the ground, and the air resistance force acts in the opposite direction, i.e., upwards against the object's motion. This force increases with the speed of the object.
02

Newton's Second Law of Motion

Newton's Second Law states that the net force acting on an object is equal to the product of its mass and acceleration (\(F_{net} = m * a\)). In the case of a falling object, the gravitational force acts in the downward direction (positive direction in this case) and the air resistance force acts in the opposite direction (negative direction or upwards).
03

Balance of Forces

As the object falls and speeds up, the air resistance force also increases. At some point, the object reaches a speed where the air resistance force becomes equal to the gravitational force acting on it. When these two forces are equal, the net force is zero, and the object's acceleration becomes zero, meaning it won't speed up any further.
04

Terminal Speed

The point at which the air resistance force equals gravitational force is called the terminal speed. At this point, the object reaches a constant speed and won't accelerate further. The terminal speed depends on the mass of the object, the gravitational force, and the characteristics of the medium through which it is falling (e.g., the density of air).
05

Conclusion

The change in the force of air resistance on a falling body eventually causes it to reach a terminal speed. As the object falls, both gravitational force and air resistance come into play. Once air resistance becomes equal to gravity, the net force on the object becomes zero, and the object no longer accelerates, attaining a constant terminal speed.

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