91Ó°ÊÓ

The principle of conservation of mechanical energy is a pivotal concept in physics. It states that the total mechanical energy of an object remains constant if only conservative forces act upon it. This principle makes it possible to predict how energy transforms without being created or destroyed.
In the context of our exercise, the meteor, initially at rest far away from Earth, is influenced solely by Earth's gravitational pull. The mechanical energy throughout its descent to Earth is conserved. This means:

• The sum of kinetic energy (\( \frac{1}{2} mv^2 \)) and potential energy (\( U = -\frac{GMm}{r} \)) remains constant.
• Initially, both potential and kinetic energies are negligible or zero, making the initial total energy (\( E_0 \)) practically zero.

As the meteor moves closer to Earth, potential energy decreases (becomes more negative) while kinetic energy increases, maintaining the balance of mechanical energy.

Kinetic energy represents the energy an object possesses due to its motion. It plays an essential role in determining the speed of an object as it moves under constant forces.
In this scenario, as the meteor approaches Earth, it will gain kinetic energy, which can be calculated using the formula:\[ K = \frac{1}{2} mv^2 \]Here,

• \( K \) is the kinetic energy,
• \( m \) is the mass of the meteor,
• \( v \) is the velocity of the meteor.

By using the conservation of mechanical energy, we can establish a relationship between the initial potential energy and kinetic energy at various altitudes. For example, when the meteor enters the ionosphere or stratosphere, the kinetic energy increases as gravitational potential energy decreases. This allows us to solve for the meteor's speed at these altitudes.

Gravitational attraction is the attractive force between two masses. According to Newton's law of universal gravitation, any two objects in the universe exert a gravitational pull on each other.
In our exercise, Earth's gravitational attraction is the only force acting on the meteor after disregarding other potential forces. The gravitational potential energy at a distance 'r' from Earth's center is described by:\[ U = -\frac{GMm}{r} \]In this equation:

• \( G \) is the gravitational constant,
• \( M \) is the mass of the Earth,
• \( m \) is the mass of the meteor,
• \( r \) is the distance from the center of Earth to the meteor.

The "negative" sign reflects that gravitational potential energy decreases as the object gets closer to Earth. As outlined in the exercise, the meteor's potential energy decreases while its kinetic energy increases, verifying the conservation of mechanical energy.