1. Quick Review
Equations of Kinematics

2. Free Fall Quick Review 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
t2 = t = 3.19 s

3. 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. A B C D E
All the same
Answer: Same at all points.

4. 2 Falling Balls Time spent in air depends on vertical motion!
Which will hit the ground first?
around 1 minute in

5. 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
B) At the center of the car
C) Backward of the center of the car
correct
Do x(t) for cart and ball. Show they are the same.
vtrain car
Ball and car start with same x position and x velocity, Since ax = 0 they always have same x position. 5

6. vtrain car 6

7. Projectile Motion & Frames of Reference
Time spent in air depends on vertical motion! 7

8. Projectile Motion
Horizontal
Vertical
Boring = Nothing going on 8

9. 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
3 m D
y-direction
voy = 15 m/s
y = yo + voyt + ½ at 2
3 m = 0 m + (15 m/s) t – ½ (9.8 m/s2) t 2
t = 2.8 s or t = 0.22 s.
x-direction
vox = 26 m/s
D = xo + vox t + ½ at 2
= 0 m + (26 m/s)(2.8 s) + 0 m/s2 (2.8 s )2
= 72.8 m
74-90 mph is initial velocity
Bob Thomas, now a justice on the Illinois Supreme Court, shares the team record for the longest field goal. He nailed a 55-yarder against the L.A. Rams in feet high
yard practice 9

10. 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
Enemy 2
A) Enemy 1
B) Enemy 2
C) They are both hit at the same time
correct 10

11. 1.7 The Components of a Vector

12. SOH CAH TOA

13. Kinematics Descriptions of motion
Relationships between position & time
Equations only; no causes

14. Causes and Rules for Motion
Laws of Motion
Causes and Rules for Motion

15. Laws of Motion
Aristotle
Galileo
Newton

16. Aristotle Celestial & terrestrial motion different
Falling & horizontal motion different
Objects had “natural” motion
Celestial: circles
Terrestrial: at rest

17. Aristotle Horizontal motion Speed result of balance between
Propulsion
Resistance
Movement requires a Mover (all motion)

18. Aristotle Falling motion Arranged by weight (as shown) Elements Fire
Air
Water
Earth

19. Galileo Starts ball rolling (literally) to modern view of motion
Was a premier experimentalist
1st experimental physicist
Used models that simplified problem

20. Galileo Horizontal motion Inclined plane to study motion Inertia
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

21. Galileo Falling motion Used inclined plane to slow down falling
During equal time periods falling body increases speed by equal amounts
Acceleration
Falling bodies accelerate

22. 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

23. 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

24. 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)

25. 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)

26. 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