To determine the change in internal energy of the ball and the surrounding air during its fall, we need to consider the energy transformations that occur as the ball descends from the height of 443 meters to the ground. The key concepts involved here are gravitational potential energy, kinetic energy, and the work done against air resistance, which ultimately contributes to the change in internal energy.
Understanding Energy Transformations
When the baseball is dropped, it initially possesses gravitational potential energy due to its height. As it falls, this potential energy is converted into kinetic energy until it reaches terminal velocity, where the forces of gravity and air resistance balance out.
Calculating Gravitational Potential Energy
The gravitational potential energy (PE) at the height of 443 meters can be calculated using the formula:
Where:
- m = mass of the ball = 0.143 kg
- g = acceleration due to gravity ≈ 9.81 m/s²
- h = height = 443 m
Plugging in the values:
PE = 0.143 kg × 9.81 m/s² × 443 m ≈ 623.57 J
Kinetic Energy at Terminal Velocity
Once the ball reaches terminal velocity, it has a constant speed of 42 m/s. The kinetic energy (KE) at this speed can be calculated using the formula:
Substituting the values:
KE = 0.5 × 0.143 kg × (42 m/s)² ≈ 126.12 J
Work Done Against Air Resistance
As the ball falls, it encounters air resistance, which does work on the ball. The work done against air resistance can be understood as the difference between the gravitational potential energy and the kinetic energy at terminal velocity:
Calculating the work done:
Work = 623.57 J - 126.12 J ≈ 497.45 J
Change in Internal Energy
The work done against air resistance is converted into internal energy, which includes the energy absorbed by the air and the ball due to friction and deformation. Thus, the change in internal energy (ΔU) of the ball and the surrounding air during the fall can be expressed as:
Therefore, the change in internal energy is approximately:
ΔU ≈ 497.45 J
Summary
In summary, as the baseball falls from the height of 443 meters, it converts its gravitational potential energy into kinetic energy until it reaches terminal velocity. The work done against air resistance, which is about 497.45 joules, represents the change in internal energy of both the ball and the surrounding air during its descent. This energy transformation illustrates the interplay between gravitational forces and air resistance in real-world scenarios.
