Chapter Work

• An object of mass $m$ with initial potential energy $mgh$ and zero kinetic energy falls freely from height $h$.
• Zero initial kinetic energy reflects the object's starting velocity of zero.
• The object's total initial energy is $mgh$.
• As the object falls, its potential energy decreases while its kinetic energy increases.
• At any point with velocity $v$, the object's kinetic energy is $\frac{1}{2}mv^2$.
• Just before hitting the ground $(h = 0)$, the object has maximum velocity $v$, resulting in the highest kinetic energy and lowest potential energy.
• The sum of the object's potential and kinetic energy remains constant across its fall.
• This conservation of energy is expressed as $mgh + \frac{1}{2}mv^2 = \text{constant}$.
• The sum of kinetic and potential energies is the object's total mechanical energy.
• During the fall, the decrease in potential energy at any point equals the increase in kinetic energy, representing a continual conversion of gravitational potential energy to kinetic energy.

Law of Conservation of Energy