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Gravitational potential energy (GPE) is a concept used to describe the energy that an object possesses due to its position in a gravitational field. It is an essential idea in physics as it helps us understand how energy is stored and transformed. The formula for gravitational potential energy is given by:
\[ \text{PE} = m \cdot g \cdot h \]
where:

• \( m \) is the mass of the object (measured in kilograms)
• \( g \) is the acceleration due to gravity \((9.8 \, \text{m/s}^2)\)
• \( h \) is the height above the reference point (usually the ground) measured in meters.

The initial potential energy when the basketball is released from a height of 6.1 meters can be calculated by substituting these values into the formula. Similarly, when the basketball is caught at a height of 1.5 meters, the potential energy decreases because the height is reduced. These calculations illustrate how gravitational potential energy is directly proportional to the height at which the object is located.

Work done by gravity is a fundamental principle that describes how gravity affects the movement of an object. In simpler terms, it is the energy transferred from gravity to the object as it moves downward. This is calculated by using the work formula:
\[ W = F \cdot d \cdot \cos(\theta) \]
Since gravity acts in the direction of motion (downwards), \( \theta \) is 0 degrees, and \( \cos(0) = 1 \), simplifying the formula to:
\[ W = m \cdot g \cdot d \]This formula represents the product of the object's weight and the distance it moves in the direction of the force. In our scenario, the basketball moves from 6.1 meters to 1.5 meters. Therefore, the distance \( d \) is 4.6 meters.
The work done by gravity in this context is the gravitational force acting on the basketball causing it to move downward a certain distance. This work done is effectively the energy transfer that lowers the basketball's potential energy as it falls.

Energy conservation is a core principle of physics, emphasizing that energy cannot be created or destroyed, only transformed from one form to another. In the context of the basketball scenario, energy is transformed from gravitational potential energy to kinetic energy and vice versa.
When the basketball is initially dropped, it holds gravitational potential energy due to its position. As it falls, this energy is converted into kinetic energy (the energy of motion). By the time the basketball is caught, the potential energy is lower due to its reduced height, and kinetic energy is at a maximum.
The relationship between the work done by gravity and the change in gravitational potential energy is expressed as:

• Work done by gravity = negative change in potential energy (\( W = -\Delta \text{PE} \))

This equation demonstrates the principle of energy conservation by showing that the decrease in potential energy corresponds exactly to the work done by gravity, confirming that energy within the system remains constant overall.