The total energy of an isolated system remains constant; energy can change forms but is neither created nor destroyed.

The sum of potential (U) and kinetic (K) energies in a system: $TME = U + K$.

The net work done on an object equals its change in kinetic energy: $W_{net} = \Delta K = K_f - K_i$.

The rate at which work is done or energy is transferred: $P = \frac{W}{t}$ or $P = \frac{\Delta E}{t}$.

Watts (W), equivalent to joules per second (J/s).

Energy possessed by an object due to its motion.

Energy stored in an object due to its position or condition.

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 $P = \frac{\Delta E}{t}$.