Conservation of Energy - Maple Help

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Conservation of Energy

 Main Concept The Law of Conservation of Energy states that the total energy in a closed system remains constant over time. Energy cannot be created or destroyed, but it can change from one form to another. In other words, at any point in time, the sum of all these different forms of energies in a closed system remains the same. An object's kinetic energy, or energy of motion, is given by the expression: where $m$ is the mass measured in kilograms, and $v$ is the object's velocity measured in meters per second. Kinetic energy(${E}_{k}$) is measured in joules.     The gravitational potential energy of an object is given by the expression: ${E}_{g}=\mathrm{mgh}$ where $m$ is the mass in kilograms, $g$ is the acceleration due to gravity ($9.8\frac{m}{{s}^{2}}$) and $h$ is change in height of the object measured in meters. The result is gravitational potential energy ($E$${}_{g}$), measured in joules.   The sum of these two forms of energy, kinetic and gravitational potential, yields the total mechanical energy in the system represented by the expression below:    + ${E}_{g}$

The scenario below illustrates that a falling object (initially at rest), only has potential energy.

However, once it reaches a height of 0 within the reference frame, the system only has kinetic energy. As the object descends, the potential energy decreases while the kinetic energy increases. The change in potential energy is completely balanced by the change in kinetic energy.

$\mathrm{Mass}:$      Height:
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