A large air-filled 0.100 -kg plastic ball is thrown up into the air with an initial speed of \(10.0 \mathrm{~m} / \mathrm{s}\). At a height of \(3.00 \mathrm{~m}\) the ball's speed is \(3.00 \mathrm{~m} / \mathrm{s}\). What fraction of its original energy has been lost to air friction?

Energy conservation is a fundamental principle of physics stating that the total energy in an isolated system remains constant over time. It's important to recognize that while energy can neither be created nor destroyed, it can change forms, such as from kinetic energy (movement energy) to potential energy (stored energy due to position) and vice versa. This concept explains why a ball thrown up in the air starts with kinetic energy and gains potential energy as it rises, only to lose that potential energy and regain kinetic energy as it falls back down.

For the case of the plastic ball, as it ascends, its initial kinetic energy is converted into potential energy. Summing the ball's kinetic and potential energy at the peak gives us the total mechanical energy, which should be equal to its initial kinetic energy. However, air friction—also known as air resistance—introduces a force that does work against the ball's motion, causing a loss in the system's total mechanical energy. This loss is observed as the difference between the initial and remaining energy at a certain height.

The work-energy principle is another core concept that provides a relationship between the work done by all the forces acting on an object and the change in its kinetic energy. The principle states that the work done by the forces on the object results in a change in the object's kinetic energy. Mathematically, this can be expressed as \( W_{total} = \Delta KE \), where \( W_{total} \) is the total work done and \( \Delta KE \) is the change in kinetic energy.

In the scenario with the plastic ball, air friction does negative work on the ball, which leads to the decrease in the ball's total mechanical energy. If we had considered the ball's motion without air friction, the ball's mechanical energy would have been conserved, and its kinetic energy at any point could be calculated from the initial conditions. However, the presence of air friction means work is done by air resistance on the ball, thus converting some of the ball's mechanical energy into thermal energy, which explains the energy lost in our calculations.

Air friction, also termed as drag in physics, is a resistive force that acts opposite to the direction of an object's motion through the air. This resistance force is significant for objects traveling at substantial speeds or with large surface areas. The amount of air friction an object experiences depends on factors such as the object’s speed, the density of the air, the cross-sectional area facing the airflow, and the shape of the object. For streamlined objects, air friction is reduced, while it's much greater for objects with flat or irregular surfaces.

In the case of our exercise, the air-filled plastic ball experiences air friction as it moves upward and downward. This friction does work on the ball, causing a loss of kinetic energy which transforms into thermal energy that disperses into the surrounding air. The work done by air friction is not recoverable as mechanical energy, leading to a permanent reduction in the ball's total mechanical energy. It's calculations like these that allow us to quantify the effects of air friction on an object's motion and energy. By understanding the energy lost, we can better predict the object's behavior under the influence of such resistive forces.