Energy: The capacity to do work. | Work: Transfer of energy. | Power: Rate at which work is done or energy is transferred.

Kinetic Energy: Energy of motion, $K = \frac{1}{2}mv^2$. | Potential Energy: Stored energy due to position or condition, e.g., $U = mgh$ or $U = \frac{1}{2}kx^2$.

Conservative Forces: Work done is path-independent (e.g., gravity, spring force). | Non-Conservative Forces: Work done is path-dependent (e.g., friction, air resistance).

Friction causes a decrease in total mechanical energy, converting it into thermal energy.

The object's kinetic energy increases, and it speeds up.

The object's kinetic energy decreases, and it slows down.

Increasing the spring constant increases the potential energy stored in the spring for a given displacement.

Its kinetic energy increases as its potential energy decreases, maintaining constant total mechanical energy.

1. Equate initial potential energy to final kinetic energy: $mgh = \frac{1}{2}mv^2$. 2. Solve for v: $v = \sqrt{2gh}$.

1. Use the formula for potential energy in a spring: $U = \frac{1}{2}kx^2$, where k is the spring constant and x is the compression/extension distance.

1. Calculate the normal force (N). 2. Calculate the frictional force: $f = \mu N$. 3. Calculate work: $W = f d$.

1. Identify all forces doing work. 2. Calculate the work done by each force. 3. Calculate the net work: $W_{net} = \Delta K$. 4. Solve for the unknown (e.g., final velocity).

1. Calculate the work done or energy transferred (W or $\Delta E$). 2. Measure the time (t) over which the work is done. 3. Calculate power: $P = \frac{W}{t}$ or $P = \frac{\Delta E}{t}$.