#### Energy, Work, and Power

**ENERGY**

- Energy is the amount of work done and it is measured in Joules (J)
- An object may have energy due to its motion or its position.
- The Law of Conservation of Energy states that the total energy of an isolated system cannot change – it is conserved over time.
- An example of conservation of energy: A book on a shelf has GPE. If it falls off the shelf, it will have K.E
- Energy can be neither created nor destroyed, but can change form.
- Energy can be stored.

**Deriving Kinetic Energy**

- W = Fs and F = ma
- ∴ W = ma • s
- v
^{2}= u^{2}+ 2as ⇒ as =^{1}/_{2}(v^{2}– u^{2}) - ∴ W = m •
^{1}/_{2}(v^{2}– u^{2}); the initial velocity, u = 0 - ∴ W =
^{1}/_{2}mv^{2} - Kinetic Energy (K.E.) =
^{1}/_{2}×*Mass*×*Velocity*=^{2}^{1}/_{2}*mv*^{2}

__Gravitational Potential Energy (GPE)__

__Gravitational Potential Energy (GPE)__

- Gravitational Potential Energy arises in a system of masses where there are attractive gravitational forces between them.
- The GPE of an object is the energy it possesses by virtue of its position in a gravitational field.
*Elastic Potential Energy*arises in a system of atoms where there are either attractive or repulsive short-range inter-atomic forces between them.*Electric Potential Energy*arises in a system of charges where there are either attractive or repulsive electric forces between them.

**Deriving Gravitational Potential Energy**

- W = Fs and F = mg
- ∴ W = mg • s
- s in the direction of the force = h above ground
- ∴ W = mgh
- Gravitational Potential Energy (GPE) =
*Mass*×*Gravity*×*Height*=*mgh*

__Internal Energy__

__Internal Energy__

- Internal energy is the sum of K.E. of the molecules due to its random motion and the P.E. of the molecules due to the inter-molecular forces.
- Gases: K.E. > P.E.
- Molecules are far apart and in continuous motion; K.E.
- Weak inter-molecular forces are so very little; P.E.

- Liquids: K.E. ≈ P.E.
- Molecules are able to slide past each other; K.E.
- Inter-molecular forces is present; P.E.

- Solids: K.E. < P.E.
- Molecules can only vibrate; K.E. is very little
- Strong inter-molecular forces; P.E. is high

__Energy Resources__

__Energy Resources__

- Renewable sources are not exhaustible.
- Non-renewable sources of energy are exhaustible.

- The sun is the source of energy for all our energy resources, except geothermal, nuclear, and tidal.
- In the sun, energy is created through a process called
*nuclear fusion*; hydrogen nuclei are pushed together to form helium.

**WORK**

- Work is done whenever a force makes something move.
- The unit of work is the Joule (J).
- 1 Joule of work = The force 1 Newton moves an object by 1 meter.
- Work done by a force is the product of the force and the displacement in the direction of the force.
- W = Fs
- Work done (J) = Force (N) × Distance (m)

- Work done by an expanding gas is the product of the force and the change in the volume of the gas.
- W = p • δV
- Condition for the formula:
- The temperature of the gas is constant
- The change in the distance of the piston, δx, is very small, therefore, it is assumed that p remains constant.

**POWER**

- Power is the rate of work done (work done per unit of time).
- The unit of power is Watts (W)
- 1 W = 1 J/s
- Power =
^{Work Done (J)}/_{Time Taken (s)} - Deriving it to form P = Fv
- P =
^{W}/_{t}and W = Fs - ∴ F
^{s}/_{t}= F(^{s}/_{t}) and v =^{s}/_{t} - ∴ P = Fv

- P =

- Efficiency is how much useful work is done with the energy supplied; it is the ratio of (useful) output energy of a machine to the input energy.
- Efficiency =
^{Useful Energy Output}/_{Total Energy Input}× 100%