ECP Chapter 3 PowerPoint

1. Essential College Physics
Chapter 3: Motion in
Two Dimensions

2. Chapter 3 Objectives
• Distinguish scalars and vectors.
• Understand vectors in component form and
as a magnitude and direction.
• Add and subtract vectors both analytically
and graphically.
• Describe position, velocity, and acceleration
vectors.

3. Chapter 3 Objectives
• Understand and analyze projectile motion.
• Understand and analyze uniform circular
motion.

4. The Paperboy Problem
• A paperboy’s route happens to also take him
to school. He leaves home and walks 8
blocks east. He then walks 4 blocks north
and, finally, walks 5 blocks west to get to
school.
• Through what distance (in blocks) did he
walk?
• What is the displacement between his home
and school?

5. The Paperboy Problem Figure

6. Trigonometry Review

7. Trigonometry Review
SOHCAHTOA (41)
opposite
sin( )
hypotenuse
 
adjacent
cos( )
hypotenuse
 
opposite
tan( )
adjacent
 

8. Example 3.1 (42)

9. Scalars vs. Vectors
Scalars
• Only magnitude
• Normal variable symbols
• Examples: time, volume,
mass
• Distance and speed
Vectors
• Magnitude and direction
• Symbolized by
superscripted arrow or
bold symbols
• Examples: force,
momentum
• Displacement and velocity

10. Unit Vectors (43)
ˆi 1,0
ˆj 0,1

11. A Position Vector
ˆ ˆv 4i 3j 

12. Displacement Vector (44)

13. Position Vector (45)

14. Vector Magnitude and Direction (45)
• Magnitude
• Direction
• Vector Components
2 2
r x y 
y1
x
tan ( )
 
x r cos( )   y r sin( )  

15. Vector Magnitude and Direction (45)

16. Graphical Interpretation of Vector Arithmetic

17. Reviewing New Concepts (47)
• To add vectors, add the components
• To subtract vectors, subtract the components
• Graphically form the vector sum by
placing the tail of at the head of . The sum
is the vector drawn from the tail of to the
head of .
• Graphically subtract vectors by adding the
opposite.
• To multiply a vector by a scalar, multiply each
component of the vector by that scalar.
1 2r r
2r 1r
1r
2r

18. Vector Definition of
Average Velocity (47)
r
v
t




19. Velocity Magnitude and Direction (48)
• Magnitude
• Direction
• Velocity Components
2 2
x yv v v 
y
x
v1
vtan ( )
 
xv v cos( )   yv v sin( )  

20. Problems
• Example 3.3 (49)
• Conceptual Example 3.4 (50)

21. Vector Definition of
Average Acceleration
v
a
t




22. Projectile Motion
• Independence thought experiment
• Independence demonstration

23. Projectile Motion
Monkey and Hunter Video
http://www.youtube.com/watch?v=MkKEwrshYWs&feature=related

24. Projectile Motion Equations (52)
Horizontal
xx v t 
Vertical
21
0y 2y v t g t    
y 0yv v g t  
2 2
y 0yv v 2 g y   

25. Projectile Motion Problems
• Example 3.5 (53)
• Conceptual Example 3.6 (53)
• Example 3.7 (54)
• Example 3.9 (55)

26. Projectile Motion Lab
• The purpose is to predict the range of a
projectile
• One will be fired horizontally
• One will be fired at an angle

27. Uniform Circular Motion (56)
• Constant speed, but changing direction
• Speed equation
• Changing velocity vector means there is an
acceleration
2 R
v
T

Speed, m/s
Radius, m
Period, s

28. Centripetal Acceleration (57)

29. Centripetal Acceleration
Formulas (57)
2
r
v
a
R

2
r 2
4 R
a
T


Centripetal
acceleration, m/s2
Speed, m/s
Radius, m
Period, s

30. Example 3.10 (58)

31. Chapter 3 Problem Sets
• Honors: P. 61, Ex. 34, 46, 50, 54, 66, 70, 72,
82, 88, 94
• UConn: P. 61, Ex. 34, 46, 50, 54, 66, 70, 72, 74,
76, 82, 88, 94