As an object falls under the influence of gravity, its kinetic energy and potential energy are inversely related, and they transform into each other while conserving the total mechanical energy of the system, assuming no energy losses due to air resistance or friction.
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Potential Energy (PE): This is the energy stored in an object due to its position above the ground. It can be calculated using the formula: \[ PE = mgh \] where \( m \) is the mass of the object, \( g \) is the acceleration due to gravity, and \( h \) is the height above a reference point.
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Kinetic Energy (KE): This is the energy of an object due to its motion, calculated using the formula: \[ KE = \frac{1}{2}mv^2 \] where \( v \) is the velocity of the object.
As the object falls:
- At the top of its fall (maximum height), the object's potential energy is at its maximum and kinetic energy is zero because it is not moving.
- As it begins to fall, potential energy decreases while kinetic energy increases as the velocity of the object increases.
- Just before it reaches the ground (the lowest point), the potential energy is at its minimum (close to zero if we assume the ground is the reference point), and kinetic energy is at its maximum.
The principle of conservation of mechanical energy states that the total mechanical energy (sum of kinetic and potential energy) remains constant during the fall: \[ PE_{initial} + KE_{initial} = PE_{final} + KE_{final} \] This principle holds true if there are no non-conservative forces (like air resistance) doing work on the system.
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