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Chapter 6: Work and Kinetic Energy
Chapter 7: Potential Energy, Energy Conservation
Chapter 8: Momentum, Impulse, Collision
Chapter 6: Work and Kinetic Energy
m = mass 
g = 9.8 m/s 
F = Weight (N) 
F = m ⋅ g 
s = distance 

W = Workdone 
Power = P (Watts) 
x = cos y = sin 
1 km = 1000m 
1kg = 1000g 

Friction = always negative 
g = 9.8 (decreasing) 
g = 9.8 (normal) 
a = g (gravitational acceleration) 
Θ = Angle between F and s 
 = Component of F parallel to dl 
v = velocity 


W = (∫P 2
to P 1
) F⋅cosΘ⋅dl 
W = F ⋅ s (Joules) 

P = lim Δt > 0 (ΔW / Δt) = dW / dt 

P = (W/t) 
Constant Speed : (a = 0) 
F = force P = F ⋅ v 
Friction (opposite) = cos(180^{o}) 
W x
= F (cosΘ)⋅s  W y
= F (sinΘ)⋅s 
a = (V f ^{2}  V i ^{2}) / (2⋅ s) 
F s
= (1/2)⋅m⋅V f ^{2}  (1/2)⋅m⋅V i ^{2} 

P = (W/t) 




Chapter 7: Potential Energy, Energy Conservation


K = Kinetic Energy 
R = Radius 


Δs = Δxî + Δyĵ 


k = constant of spring 

W grav
= wvector ⋅ Δsvector 
Diameter = 2 ⋅ Radius 
W f
= Work Done by Friction 


W grav
= m ⋅ g ⋅ y i
 m ⋅ g ⋅ y f


(1/2)⋅m⋅V i ^{2} + m⋅g⋅y i
= (1/2)⋅m⋅V f ^{2} + m⋅g⋅y f

if gravity does work.... E = K + U grav

W total
= K f
 K i W total
= W grav
+ W el
+ W other

W other
+ U i
 U f
= K f
 K i arrange to.... K i
+ U i
+ W other
= K f
+ U f

Work done on a spring W = (1/2)K E
⋅X f ^{2}  (1/2)K E
⋅X i ^{2} Work done by a spring W = (1/2)K E
⋅X i ^{2}  (1/2)K E
⋅X f ^{2} 

Elastic Potential Energy U el
= (1/2)⋅K E
⋅x ^{2} Work Done by Elastic Force W el
= (1/2)⋅K E
⋅x i ^{2}  (1/2)⋅K E
⋅x f ^{2} 
if elastic force does work, and mechanical energy is conserved K i
+ U el
, i
= K f
+ U el
, f

Work Done by Friction: W f
= W fric
W f
= (f k
⋅ s) W f
= μ k
⋅m⋅g⋅s 
Law of Conservation of Energy ΔK + ΔU + ΔU int
= 0 
F = F x
+ F y
+ F z
F x
(x) = m⋅g F y
(y) = m⋅g F z
(z) = m⋅g 



Chapter 8: Momentum, Impulse, Collisions
p = momentum 
J = Impulse 
m = mass 
v = velocity 
P = m ⋅ v (kg ⋅ m/s) 
F = d p
/ d t J y
= (∫t f
to t i
) ΣFy dt J y
= (F av
) y
(t f
 t i
) J y
= P fy
 P iy J y
= (m⋅V fy
)  (m⋅V iy
) 
J = ΣF (t f
 t i
) J = ΣF⋅Δt J = (∫t f
to t i
) ΣF dt J x
= (∫t f
to t i
) ΣFx dt J x
= (F av
) x
(t f
 t i
) J x
= P fx
 P ix J x
= (m⋅V fx
)  (m⋅V ix
) 
ΣF = (P f
 P i
) / (t f
 t i
) 

J = (P f
 P i
) = {F} : Change in Momentum 

Assuming m 1
and m 2
don't change 




V f
= (m 1
⋅v 1
+m 2
⋅v 2
) / (m 1
++m 2
) 

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