Energy

The capacity to do work

Work

$$\begin{align*} W &= Fs \\ \text{work done} &= \text{force} \cdot \text{displacement in the direction of force} \end{align*}$$

Unit of $W$ = $\mathrm{J}$

The work done is the same as the amount of energy converted
1J of work is done when a force of 1N moves an object 1m

Principle of conservation of energy

Energy cannot be created nor destroyed, only converted from one form to another

Types of energy

• Gravitational potential energy
• Elastic potential energy
• Kinetic energy
• Chemical energy
• Internal energy
• Nuclear energy

Gravitational potential energy

Energy possessed due to a body's relative position to the Earth

$$\begin{align*} E_p &= m g h \\ \text{GPE} &= \text{mass} \cdot \text{gravitational acceleration} \cdot \text{height} \end{align*}$$

Derivation

Elastic potential energy

Energy possessed due to the relative position of molecules within a body

$$\begin{align*} E_p &= \frac{1}{2} F x \\ &= \frac{1}{2} k x^2 \\ \text{EPE} &= \frac{1}{2} \cdot \text{force} \cdot \text{extension} \\ &= \frac{1}{2} \cdot \text{spring constant} \cdot \text{extension}^2 \end{align*}$$

Derivation

Kinetic energy

Energy possessed due to the motion of a body

$$\begin{align*} E_k &= \frac{1}{2} m v^2 \\ \text{KE} &= \frac{1}{2} \cdot \text{mass} \cdot \text{velocity}^2 \end{align*}$$

Derivation