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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
K
E
= Kinetic Energy
W = Workdone
Power = P (Watts)
x = cos
y = sin
1 km = 1000m
1kg = 1000g
ΔK = K
f
- K
i
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⋅dl
W = F
||
dl
W = (∫P
2
to P
1
) F⋅cosΘ⋅dl
W = F ⋅ s (Joules)
P
av
= ΔW / Δt
P = lim Δt > 0 (ΔW / Δt) = dW / dt
V
f
= V
i
2 + 2 ⋅ a ⋅ s
P = (W/t)
Constant Speed : (a = 0)
F = force
P = F ⋅ v
Friction (opposite) = cos(180o)
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
W
grav
= m⋅g⋅h
P = (W/t)
K
E
= (1/2)⋅m⋅V2
P
E
= m⋅g⋅h
 

Chapter 7: Potential Energy, Energy Conser­vation

Potential Energy = U, P
E
ΔK = -ΔU
grav
K = Kinetic Energy
R = Radius
s = y
f
- y
i
U
grav
= m ⋅ g ⋅ y
Δs = Δxî + Δyĵ
 
cm
= circular motion
 
k = constant of spring
P
E
= (1/2)⋅k⋅x2
W
grav
= w-vector ⋅ Δs-vector
Diameter = 2 ⋅ Radius
W
f
= Work Done by Friction
if elastic...
K
E
= P
E
W
grav
= F × s
W
grav
= m ⋅ g ⋅ y
i
- m ⋅ g ⋅ y
f
K
i
+ U
i
= K
f
+ U
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
U
cm
= m ⋅ g ⋅ R
Elastic Potential Energy
U
el
= (1/2)⋅K
E
⋅x2

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
F
x
= (1/2)⋅K⋅x2
 

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 = F
av
(t
f
- t
i
)
J = (P
f
- P
i
) = {F} : Change in Momentum
P = P
A
+ P
B
= |P
A
+ P
B
|
Assuming m
1
and m
2
don't change
m
1
⋅v
1
+m
2
⋅v
2
= constant
(P
1
+P
2
)
i
= (P
1
+P
2
)
f
P
1
+P
2
= constant
P
i
= P
f
V
f
= (m
1
⋅v
1
+m
2
⋅v
2
) / (m
1
++m
2
)
           
 

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  • Published: 3rd November, 2021

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