Transcript Quick Review

Quick Review
Equations of Kinematics
v  vo  at
x
1
2
vo  v  t
v  v  2ax
2
2
o
x  vot  at
1
2
2
Quick Review
Free Fall
• Drop a stone from top of 50 m building
• How long to hit the ground?
• Uniform acceleration g = -9.8 /s2
• Distance y = -50 m
• y = vot + ½ gt2
• -50 m = 0 + ½ (-9.8 m/s2)t2
2  -50 m
2
•t =
t = 3.19 s
-9.8 m/s2
Quick Review
An arrow is launched vertically upward. It moves straight up to a
maximum height, then falls to the ground. The trajectory of the arrow is
noted. At which point of the trajectory is the arrow’s acceleration the
greatest? The least? Ignore air resistance; the only force acting is gravity.
0%
he
sa
m
e
E
0%
lt
0%
Al
0%
D
0%
C
0%
B
A
B
C
D
E
All the same
A
A.
B.
C.
D.
E.
F.
2 Falling Balls
Time spent in air depends on vertical motion!
• Which will hit the ground first?
https://www.youtube.com/watch?v=zMF4CD7i3hg
around 1 minute in
Train Demo
A flatbed railroad car is moving along a track at constant velocity.
A passenger at the center of the car throws a ball straight up.
Neglecting air resistance, where will the ball land?
A) Forward of the center of the car
correct
B) At the center of the car
C) Backward of the center of the car
https://www.youtube.com/watch?v=nAifrGXkE2k
vtrain car
Ball and car start with same x position and x velocity,
Since ax = 0 they always have same x position.
vtrain car
Projectile Motion & Frames of Reference
Time spent in air depends on vertical motion!
Projectile Motion
Horizontal
Vertical
Boring = Nothing going on
Field Goal Example
A field goal kicker can kick the ball at 26 m/s horizontally and 15 m/s vertically.
If the crossbar of the goal post is 3m off the ground, from how far away can he
kick a field goal?
y
x
3m
D
y-direction
x-direction
voy = 15 m/s
vox = 26 m/s
y = yo + voyt + ½ at 2
D = xo + vox t + ½ at 2
3 m = 0 m + (15 m/s) t – ½ (9.8 m/s2) t 2
= 0 m + (26 m/s)(2.8 s) + 0 m/s2 (2.8 s )2
t = 2.8 s or t = 0.22 s.
= 72.8 m
A destroyer simultaneously fires two shells with the same
initial speed at two different enemy ships. The shells
follow the trajectories shown. Which ship gets hit first.
Destroyer
Enemy 1
A) Enemy 1
correct
B) Enemy 2
C) They are both hit at the same time
Enemy 2
1.7 The Components of a Vector

The vector components of A are two perpendicu lar


vectors A x and A y that are parallel to the x and y axes,
 

and add together vectoriall y so that A  A x  A y .
SOH CAH TOA
sin   opposite / hypotenuse  y r
y  r sin 
cos   adjacent / hypotenuse  x r
x  r cos 
Kinematics
• Descriptions of motion
• Relationships between position & time
• Equations only; no causes
Laws of Motion
Causes and Rules for Motion
Laws of Motion
 Aristotle
 Galileo
 Newton
Aristotle
 Celestial & terrestrial motion different
 Falling & horizontal motion different
 Objects had “natural” motion
 Celestial: circles
 Terrestrial: at rest
Aristotle
 Horizontal motion
 Speed result of balance between
 Propulsion
 Resistance
 Movement requires a Mover (all motion)
Aristotle
 Falling motion
 Arranged by weight (as shown)
 Elements




Fire
Air
Water
Earth
Galileo
 Starts ball rolling (literally)
to modern view of motion
 Was a premier
experimentalist
 1st experimental physicist
 Used models that
simplified problem
Galileo
 Horizontal motion
 Inclined plane to study motion
 Smaller angle of plane --> further ball rolls
 Angle zero --> ball rolls forever?
 Rolling ball rolls unless something affects rolling
 Inertia
 Moving object keeps moving unless disturbed
 “natural state” is no change in motion
Galileo
 Falling motion
 Used inclined plane to slow down falling
 During equal time periods falling body increases speed by
m/s
equal amounts
s
 Acceleration
 Falling bodies accelerate

Galileo
 Falling motion
 Couldn’t create vacuum
 Increased density of medium
 Compared rates of fall of heavy/light object
 Greater density --> different rates
 Medium w/o resistance (vacuum)
 All bodies fall with same acceleration
Galileo
 Same laws falling & horizontal motion
 Unification
 Acceleration key to falling motion
 Same rate for all bodies w/o resistance
 Inertia
 Motion doesn’t change w/o influence
 No natural motion
 Superposition
Newton’s Laws of Motion
 A body at rest tends to remain at rest, and a body in
motion tends to remain in motion at a constant
velocity, unless acted on by an outside force
 Defines inertia: resistance to change
 What happens when net force is zero
 Mass is measure of inertia (kilogram)
Newton’s Laws of Motion
 The time rate of change of momentum of a body is
proportional to the outside force acting on the body,
and is in the direction of the outside force
 Defines Force
F = ma
 F is resultant force F = 0 equilibrium
 a  F a  1/m
 Unit is Newton (N)
Newton’s Laws of Motion
 For every action there is an equal and opposite
reaction
 Forces always exist in pairs
 Single force can’t exist
 Action-reaction pairs work on different objects
 Momentum conserved