Energy, Work, and Power
- 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 × Height = mgh
- 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
- 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 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 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%