Why Energy Conservation Principle Needs to be Modified in This Problem

In this lesson, we explore the motion of a vertically launched stone, weighing 5.29 N, that experiences constant air drag of 0.265 N. The key questions we tackle are:

1. How high does the stone rise before coming to a stop?
2. What is its speed just before returning to the ground?

Step-by-Step Solution:

Part 1: Calculating Maximum Height:
To determine the stone’s maximum height, we must account for both gravity and air resistance. Unlike purely conservative systems, here we must include the work done by air drag, as mechanical energy isn’t conserved. Using the work-energy theorem, we balance the initial kinetic energy and potential energy with the work done by the drag force to find the height.

After applying the appropriate energy equation, the result is:

• Maximum Height (h): 19.4 meters

Part 2: Finding Speed Before Impact
Next, we calculate the stone’s speed just before it hits the ground. This involves recognizing that air drag works against the stone both on the way up and down, making the total work done by air resistance -2fh. Using the revised energy equation, we calculate the final speed as the stone reaches the ground.

• Final Speed (v): 19.0 m/s

Key Concepts to Remember:

• In problems involving air resistance, mechanical energy is not conserved, and the work done by non-conservative forces must be considered.
• Air drag opposes motion, and its work depends on the distance traveled and the force applied opposite to the motion.
• Always account for both the ascent and descent when drag is involved in projectile motion problems.

This lesson provides a comprehensive understanding of how to apply energy principles in the presence of air resistance, perfect for mastering advanced projectile motion scenarios.