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#### 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
• v2 = u2 + 2as ⇒ as = 1/2 (v2 – u2)
• ∴ W = m • 1/2 (v2 – u2); the initial velocity, u = 0
• ∴ W = 1/2 mv2
• Kinetic Energy (K.E.) = 1/2 × Mass × Velocity2 = 1/2 mv2
###### 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 × Heightmgh
###### 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
• 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
• ∴ Fs/t = F(s/t) and v = s/t
• ∴ P = Fv
• 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%