Question

1. what is the law of conservation of energy? 12. what is mechanical energy? 13. how is mechanical energy calculated?

Explanation:

1. The law of conservation of energy states that energy cannot be created or destroyed in an isolated system, only transferred or transformed from one form to another.
2. Mechanical energy is the sum of kinetic energy (energy of motion) and potential energy (stored energy due to position or configuration) in a system.
3. Mechanical energy ($E_m$) is calculated as the sum of kinetic energy ($K = \frac{1}{2}mv^2$, where $m$ is mass and $v$ is velocity) and potential energy (gravitational potential energy $U = mgh$, where $m$ is mass, $g$ is the acceleration - due - to - gravity, and $h$ is height; elastic potential energy $U=\frac{1}{2}kx^2$, where $k$ is the spring constant and $x$ is the displacement from the equilibrium position). In general, $E_m=K + U$.

Answer:

1. Energy cannot be created or destroyed in an isolated system, only transferred or transformed.
2. The sum of kinetic and potential energy in a system.
3. $E_m = K+U$, with $K=\frac{1}{2}mv^2$ and $U$ depending on the type (e.g., $mgh$ for gravitational or $\frac{1}{2}kx^2$ for elastic).