Work is when a force moves an object over a distance. It is a scalar quantity measured in Joules (J).

Energy is the capacity to do work. It comes in many forms: kinetic, potential, thermal, etc.

Kinetic Energy (K) is the energy of motion.

Gravitational Potential Energy (Ug) is the energy due to height above a reference point.

Elastic Potential Energy (Usp) is the energy stored in a spring or elastic material.

Power is the rate at which work is done or energy is transferred.

An open system allows both matter and energy to be exchanged with its surroundings.

A closed system allows energy exchange but *not* matter exchange with its surroundings.

Mechanical energy is the sum of kinetic and potential energy in a system.

A system that allows both matter and energy to be exchanged with its surroundings.

A system that allows energy exchange but not matter exchange with its surroundings.

Work is when a force moves an object over a distance; calculated as $W = Fd$.

The capacity to do work; it comes in many forms (kinetic, potential, thermal, etc.).

The sum of kinetic and potential energy in a system.

Energy of motion; calculated as $K = \frac{1}{2}mv^2$.

Energy due to height above a reference point; calculated as $U_g = mgh$.

Energy stored in a spring or elastic material; calculated as $U_{sp} = \frac{1}{2}kx^2$.

The rate at which work is done or energy is transferred; calculated as $P = \frac{W}{t}$ or $P = \frac{\Delta K}{t}$.

W = Fd, where W is work (in Joules, J), F is the force (in Newtons, N), and d is the distance (in meters, m).

K = (1/2)mv^2, where K is kinetic energy (in Joules, J), m is mass (in kilograms, kg), and v is velocity (in meters per second, m/s).

Ug = mgh, where Ug is gravitational potential energy (in Joules, J), m is mass (in kilograms, kg), g is acceleration due to gravity (9.8 m/s² on Earth), and h is height (in meters, m).

U_{sp} = (1/2)kx^2, where Usp is elastic potential energy (in Joules, J), k is the spring constant (in N/m), and x is the displacement from equilibrium (in meters, m).

P = W/t or P = \Delta K/t, where P is power (in Watts, W), W is work (in Joules, J), \Delta K is the change in kinetic energy (in Joules, J), and t is time (in seconds, s).