Space, Time and Motion - Work, Energy and Power

Work done $W$ is defined as the product of the force $F$ and the displacement $s$ in the direction of the force: $W = Fs \cos \theta$, where $\theta$ is the angle between the force and the displacement vector.

Work is a scalar quantity measured in Joules ($J$). On a force-displacement graph, the work done is represented by the area under the curve.

Kinetic Energy $E_k$ is the energy an object possesses due to its motion, given by $E_k = \frac{1}{2}mv^2$.

Gravitational Potential Energy $\Delta E_p$ is the energy stored in an object due to its vertical position in a gravitational field, calculated as $\Delta E_p = mg\Delta h$.

Elastic Potential Energy $E_h$ is stored in a deformed elastic object (like a spring) and is given by $E_{el} = \frac{1}{2}kx^2$ provided the limit of proportionality is not exceeded.

The Principle of Conservation of Energy states that energy cannot be created or destroyed, only transformed from one form to another. In an isolated system, $E_{total} = E_k + E_p + Q = \text{constant}$, where $Q$ represents internal energy (heat).

Power $P$ is the rate at which work is done or the rate at which energy is transferred, measured in Watts ($W$). It can also be expressed as the product of force and velocity: $P = Fv$.

Efficiency $\eta$ is the ratio of useful energy (or power) output to the total energy (or power) input: $\eta = \frac{\text{useful output}}{\text{total input}}$.