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aqa Alevel physics Year 1(yr12) work, energy and power: chapter 6
Work Done and Energy
Work done is maximum when cos0 = 0 (the force and distance travelled are therefore parallel)
Work done is minimum when cos0 = 90 (the force and distance travelled are therefore perpendicular)
types of energy:
 kinetic energy
 potential energy
 thermal energy (not covered in this spec point)
for example:
a ball held at a height will have Ep, when dropped and landing on the ground (assuming there is no energy loss) all the energy will be converted into Ek.
Δ E = W > change in energy in a system = work done on a system 
Derrivations
Gravitational Potential Energy:
ΔE = W
ΔE = Fxcos0
(work done is force x distance x angle)
where F = ma (in this case a is g)
and distance is hieght travelled
ΔE = mghcos0
as cos0 where 0 is 0' cos0 = 1 so
ΔE = mgh
Kinetic Energy:
ΔE = W
ΔE = Fxcos0
(work done is force x distance x angle)
ΔE = Fs
(cos0 = 1)
ΔE = mas
as v^{2} = u^{2} + 2as
rearrange where u = 0
as = v^{2}/2
therefore
ΔE = 1/2 mv^{2} 


Definitions
Work done 
product of the force and the distance moved in this direction 
power 
rate of work done 

rate of energy transferred 
Equations
Work done 
Fxcos0 (where x is distance and 0 is theta between f and x) 
change in energy 
ΔE = W 
power 
W/t 

Fx/t 

Fv 
efficiency 
useful/total (x100) 
Conversion of energy
example of findign resistive forces going down hill
top  v=0



bottom  v=8
a ball is roll down from the top to the bottom
length of the ramp is 7m
height is 5m
as ΔE = W
energy at top (Ep no Ek) then energy at bottom (Ek no Ep)
from this we know it is all transferred (assuming no loss to heat) therefore
ΔE = mgh  1/2mv^{2}
mgh  1/2mv^{2} = Fx
(where x is length of ramp)
then just put in numbers to solve for F 

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