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Physics MidTerm 2 Cheat Sheet by

Goes over...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
KE = Kinetic Energy
W = Workdone
Power = P (Watts)
x = cos
y = sin
1 km = 1000m
1kg = 1000g
ΔK = Kf - Ki
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 = (∫P2 to P1) F⋅dl
W = F|| dl
W = (∫P2 to P1) F⋅cosΘ⋅dl
W = F ⋅ s (Joules)
Pav = ΔW / Δt
P = lim Δt > 0 (ΔW / Δt) = dW / dt
Vf = Vi2 + 2 ⋅ a ⋅ s
P = (W/t)
Constant Speed : (a = 0)
F = force
P = F ⋅ v
Friction (opposite) = cos(180o)
Wx = F (cosΘ)⋅s || Wy = F (sinΘ)⋅s
a = (Vf2 - Vi2) / (2⋅ s)
Fs = (1/2)⋅m⋅Vf2 - (1/2)⋅m⋅Vi2
Wgrav = m⋅g⋅h
P = (W/t)
KE = (1/2)⋅m⋅V2
PE = m⋅g⋅h
 

Chapter 7: Potential Energy, Energy Conser­vation

Potential Energy = U, PE
ΔK = -ΔUgrav
K = Kinetic Energy
R = Radius
s = yf - yi
Ugrav = m ⋅ g ⋅ y
Δs = Δxî + Δyĵ
cm = circular motion
 
k = constant of spring
PE = (1/2)⋅k⋅x2
Wgrav = w-vector ⋅ Δs-vector
Diameter = 2 ⋅ Radius
Wf = Work Done by Friction
if elastic...
KE = PE
Wgrav = F × s
Wgrav = m ⋅ g ⋅ yi - m ⋅ g ⋅ yf
Ki + Ui = Kf + Uf
(1/2)⋅m⋅Vi2 + m⋅g⋅yi = (1/2)⋅m⋅Vf2 + m⋅g⋅yf
if gravity does work....
E = K + Ugrav
Wtotal = Kf - K i

Wtotal = Wgrav + Wel + Wother
Wother + Ui - Uf = Kf - Ki
arrange to....
Ki + Ui + Wother = Kf + Uf
Work done on a spring
W = (1/2)KE⋅Xf2 - (1/2)KE⋅Xi2

Work done by a spring
W = (1/2)KE⋅Xi2 - (1/2)KE⋅Xf2
Ucm = m ⋅ g ⋅ R
Elastic Potential Energy
Uel = (1/2)⋅KE⋅x2

Work Done by Elastic Force
Wel = (1/2)⋅KE⋅xi2 - (1/2)⋅KE⋅xf2
if elastic force does work, and mechanical energy is conserved
Ki + Uel, i = Kf + Uel, f
Work Done by Friction:
Wf = -Wfric
Wf = -(-fk⋅ s)
Wf = μk⋅m⋅g⋅s
Law of Conser­vation of Energy
ΔK + ΔU + ΔUint = 0
F = Fx + Fy + Fz
Fx(x) = -m⋅g
Fy(y) = -m⋅g
Fz(z) = -m⋅g
Fx = (1/2)⋅K⋅x2
 

Chapter 8: Momentum, Impulse, Collisions

p = momentum
J = Impulse
m = mass
v = velocity
P = m ⋅ v (kg ⋅ m/s)
F = dp / dt

Jy = (∫tf to ti) ΣFy dt
Jy= (Fav)y (tf - ti)
Jy = Pfy - Piy
Jy = (m⋅Vfy) - (m⋅Viy)
J = ΣF (tf - ti)
J = ΣF⋅Δt
J = (∫tf to ti) ΣF dt

Jx = (∫tf to ti) ΣFx dt
Jx= (Fav)x (tf - ti)
Jx = Pfx - Pix
Jx = (m⋅Vfx) - (m⋅Vix)
ΣF = (Pf - Pi) / (tf - ti)
J = Fav(tf- ti)
J = (Pf - Pi) = {F} : Change in Momentum
P = PA + PB = |PA + PB|
Assuming m1 and m2 don't change
m1⋅v1+m2⋅v2 = constant
(P1+P2)i = (P1+P2)f
P1+P2 = constant
Pi = Pf
Vf = (m1⋅v1+m2⋅v2) / (m1++m2)
           
 

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