Formula/Review Sheet by Qiu PHY 2020 for Mid-Term Exam 2
v
x
t
[average speed = (distance)/(time)]
v
x x  x o 

t
t
a
v
t
Velocity is a vector! Speed is the magnitude of the velocity vector.
[instantaneous velocity = (change in distance)/(change in time)]
[average acceleration = (change in velocity)/(time)]
Acceleration is a vector!
v
a
t
[instantaneous acceleration = (change in velocity)/(change in time)]
When given a graph of distance versus time, the slope is the velocity.
When given a graph of velocity versus time, the slope is the acceleration.
Workhorse Equations (for constant acceleration)
g  9.8
(v  v o )
a
t
v 2  v o2
a
2x  x o 
v  v
x  xo   o
t
 2 
x  x o  v o t  at 2
2
m
ft
 32 2
2
s
s
Ax 2  Bx  C  0
F  ma
1
v x  v cos 
x
 B  B 2  4AC
2A
v y  v sin 
v  v 2x  v 2y
[Force = (mass)(acceleration)]
Force is a vector!
tan  
unit is N = Newton
vy
vx
Frictional Force is opposite to direction of motion.
In equilibrium, the sum of all forces acting on a body is zero.
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Formula/Review Sheet by Qiu PHY 2020 for Mid-Term Exam 2
Projectile Motion
x-direction
y-direction
ax  0
a y  g
v xo  v o cos  o
v yo  v o sin o
v x  v xo (constant!)
v y  v o sin o  gt
x  x o  ( v o cos  o ) t
y  y o  ( v o sin  o ) t  gt 2
1
2
Trajectory:
g
y  (tan  o ) x  2
x2
2 v o cos 2  o
Max. Height:
h
Range:
v o2 sin 2 o
R
g
Eo  Ef
v o2 sin 2  0
2g
Conservation of Energy
(PE) o  (KE) o  W  (PE) f  (KE) f
W  Fd
[Work = (Force) (distance)] (unit is J, Joule)
Force and distance are vectors and their dot product gives the scalar Work.
So, use only the component of the Force that is in the direction of the movement.
W  (F cos ) d
KE(linear) =
P
W
t
1
m v2
2
W  KE  (KE) f  (KE) o
[Power = (work)/(time)]
Spring (with spring constant k):
p  mv
F
p
t
PE 
F  kx
PE or U (Potential Energy) of gravity:
P  F v  (F cos ) v
(unit is W, Watt)
U  mgh
[momentum = (mass) (velocity)]
1
k x2
2
Momentum is a vector!
[Force = (change in momentum)/(change in time)] (recall Force is a vector)
“I or J” Impulse (if force applied in a short period of time):
2
IFt
Formula/Review Sheet by Qiu PHY 2020 for Mid-Term Exam 2
G = 6.67  1011 N m2 kg2
NA = 6.022  1023 particles = 1 mole
R = 8.314 J/(mole K)
 = 5.67  108 W m2 K4
1 bar = 1  105 Pa
1 Pa = 1 N/m2
1 cal = 4.186 J
Conservation of Momentum: no external forces and no internal work done, then
 po   pf .
Totally Elastic Collision: KE conserved and Momentum conserved.
1
1
1
1
m1 v12o  m 2 v 22 o  m1 v12f  m 2 v 22f
2
2
2
2




m1 v1o  m 2 v 2o  m1 v1f  m 2 v 2f
Totally Inelastic Collision (two bodies stick together): KE is NOT conserved ; Momentum is.



m1 v1o  m 2 v 2o  (m1  m 2 ) V
RECALL Linear vs. Rotational Motion! RECALL Conservation of Energy and Momentum
contains Linear and Rotational parts! RECALL Bodies in Equilibrium have net Force of zero
and net Torque of zero.
m m
2 R
Period (T) is a time: T 
Gravitational Force: F  G 1 2
v
R2
 mi x i
 mi yi
M   mi
Center of Mass:
X
Y
 mi
 mi
m
Density:  
Pressure is force per unit area.
V
1
P  gh  v 2  const .
Bernouilli:
and
A1v1  A 2 v 2
2
F f

Archimedes: FB  liquid Vdisplaced g
Pascal:
A a
Ideal Gas Law: PV  nRT
Temperature Scales:
°F = (9/5) °C + 32
°C = (5/9) [°F  32]
°K= °C + 273
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