WORK, ENERGY, POWER
energy-stored ability to do work

energy source	type of energy
Sun (now)	sunlight
	heat
	wind power - mechanical energy
	ocean thermal - heat
	water power - grav. PE
	wave power - mechanical energy
	food plants - biomass
	wood - biomass
	biogas (methane) - biomass
	sugarcane (alcohol) - biomass
	organic wastes - biomass
Sun (106s years back)	coal, oil, gas - chemical
Earth	geothermal - heat
	tidal energy - grav. PE
	nuclear - fission + fusion

renewable resources: wind power, wave power, geothermal
non-renewable resources: coal, oil, gas, nuclear

kinetic energy: due to movement (energy obj. has from movement) (translational + rotational)
potential energy: due to obj. position, shape/state (gravitaional PE, elastic PE, chemical PE, nuclear PE, electric PE)
internal energy: KE + PE of molecules of obj (molecules: attractive F when far, repulsive F when near)
heat/thermal energy: transferred due to temp diff
radiant energy: usually in form of waves (sound, light , IR)

Law of conservation of energy = energy can not be created or destroyed, it can only be change from one form to a another or transferred from one body to another and the total amt remains constant

work done by a const. F = mag. of F × component of displacement in dirⁿ of F
W (J) = Fs cosθ [s = displacement, θ = angle bet dirⁿ of F & displacement]

Work done by gas expanding/contracting (const external pressure)
W = Fs
ΔV = As => s = ΔV/A
W = FΔV = pΔV
    A
[p: cont pressure of gas > const F]

Work done by a variable force

-for expanding/contracting gas: W = ∫ p dV

Work done by stretching a spring
obey Hooke's law: spring constant, k(F/m²) [k=F/e]
W = ½Fe = ½ke²


Deriving KE from work done
W = Fs [F = ma] > W = mas [v² = u² + 2as > as = ½ v²] > W = ½ mv²
W = ΔKE of mass = ½ m(v²-u²)

Potential energy
Gravitaional PE; GPE = mgh
-due to mass interaction
W = Fs [F = mg, s = h (no. acc > const v)] > W = mgh (only for near Earth's surface, higher up > 'g' diff)
Electric/electrostatic PE; EPE = QΔV [Q = charge of obj, ΔV = diff in electic potential bet 2 pts]
-due to charge interaction
Strain (elastic) PE; SPE = ½ ke²
-due to short range attractive F & v.short range repulsive F
-bet molecules: distortion of attraction & repulsion bet molecules

Relationship bet force & PE
for a force filed;
F = -du
     dx
[u = potential energy]

F = -ve of potential gradient
u = -∫F dx

if field uniform > F = const.
magnetic + electric field; sides: not uniform, middle: ~ uniform

gravitational field (big Earth, small room > lines to centre of Earth ~ //), u = mgy
F = -du = -d (mgy) = -mg
     dx    dy
-ve sign: shows grav. F acts downwards while PE ^ w/ y

elastic PE: not uniform force
u = ½ kx²
F = -du = -d (½kx²) = -kx
     dx    dy
-ve sign: shows elastic. F acts in opp dirⁿ to displacement

efficiency of machine = (useful energy output/ energy input) x 100%
-in practice energy output < energy input (friction > heat, wasted energy)

Internal energy: in any subs, molecule: KE(moving) + PE (attraction + repulsion bet molecules)
internal energy = microscopic(KE+PE) of molecules in obj (excludes macroscopic KE/PE that causes large scale motion)

Power = rate at which energy is transferred (rate of doing work)
P (W) = W/t or E/t [av P = W/t (F not const > W no const.)]
instantaneous power:
 P = dW = dE
     dt   dt

δW = Fδx > δW/δt = Fδx/δt
δt →0
dw = Fdx
dt    dt
P = Fv

Electrical power & energy
P = IV > E = VIt
domestic unit of energy : kilowatt-hour (kWh)
1kWh = energy used by device at a rate of 1000 watts in 1 hour
1kWh = 1000W × 3600s = 3.6 × 10⁶ J


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