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Kinetic energy is the energy of motion. Whenever an object is moving, it possesses kinetic energy. The amount of kinetic energy depends on two key factors: the mass of the object and its velocity (speed with direction). The formula to calculate kinetic energy (\( KE \)) is: \( KE = \frac{1}{2} m v^2 \), where \( m \) is the mass and \( v \) is the velocity.
It's essential to understand that kinetic energy increases with the velocity squared. This means that if the speed of an object doubles, its kinetic energy quadruples. This principle helps us understand why faster moving objects have significantly more energy.
In our basketball example, the ball starts with a certain kinetic energy because it's moving at 7.20 m/s. As the ball goes through the net, its velocity decreases to 4.20 m/s, resulting in a decrease in kinetic energy. This change plays a crucial role in calculating the work done on the ball by the air resistance.

Potential energy is stored energy that an object possesses due to its position or condition. For objects near the earth, gravitational potential energy is the most relevant. This type of potential energy is determined by the height of an object above the ground, the object's mass, and the gravitational acceleration (usually \( 9.81 \, \text{m/s}^2 \) on Earth). The formula for gravitational potential energy (\( PE \)) is: \( PE = mgh \), where \( m \) is the mass, \( g \) is the gravitational acceleration, and \( h \) is the height.
When considering our basketball scenario, the ball initially has potential energy based on its height of 2.00 m above the floor. As it rises to a new height of 3.10 m, its potential energy increases. This change in height means a change in potential energy, which contributes to the calculation of work done on the ball by non-conservative forces, like air resistance.

Non-conservative forces include forces that cause energy to be dissipated from a system, such as friction or air resistance. These forces do not conserve mechanical energy, meaning they can change the total energy of a system in ways that cannot be recovered simply by retracing a path.
In our basketball problem, air resistance acts as a non-conservative force that does work on the ball as it moves through the air. Unlike conservative forces (like gravity) that only transfer energy between kinetic and potential forms, non-conservative forces reduce the system's mechanical energy, often converting it into heat or sound.
The work done by air resistance, calculated using the work-energy principle, shows how much energy was taken away from the system due to this non-conservative force. Here, the work done by air resistance is negative, indicating that the ball loses mechanical energy as it travels from its initial to final position.