09/25/12

Bellwork
What is position, displacement, speed, velocity,
and acceleration?
NOTES
•
Unit Vectors
•
Position, Displacement, Velocity, and
Acceleration Vectors
3

4 Unit Vectors
Unit vectors are dimensionless vectors of unit length.
3

4 Unit Vectors
Multiplying unit vectors by scalars: the multiplier changes
the length, and the sign indicates the direction.
Unit Vectors
Relative Motion

1D ( Page 71 )
The speed of the passenger with respect to the
ground depends on the relative directions of the
passenger’s and train’s speeds:
Relative Motion
–
2D ( Page 72 )
Passenger relative to ground = passenger

train + train

ground
Relative Motion
–
2D ( Page 72 )
PhET
Simulation
–
Lab Groups
•
Goto
PhET
website
•
Search for “Motion in 2D”
•
Make sure “Show Both” is selected at top
•
Which is the Green Vector ; which is the Blue
Vector?
•
If the
Labtop
Screen represents an
x

y
axis,
visualize the two components of each
Bellwork
–
09/27/12
•
you walk “in town” and you walk 0.45 m to the
West and turn to walk 0.35 m to the North
•
Picture this in an
x

y
coordinate
system
•
Write the displacement vector in
unit vector
notation
N / +y
E / +x
W /

x
S /

y
Bellwork
–
09/27/12
N / +y
E / +x
W /

x
S /

y
NOTES
–
09/27/12
•
Unit Vectors
•
Position, Displacement, Velocity, and
Acceleration Vectors
•
WE ARE TALKING ABOUT 2

DIMENSIONS
–
Vertical AND Horizontal
•
LET’S DO IT!!!
Relative Motion
–
2D ( Page 72 )
1D Unit Vector Notation?
The speed of the passenger with respect to the
ground depends on the relative directions of the
passenger’s and train’s speeds:
Motion only in one direction,
but the 2
nd
( or even 3
rd
)
dimension doesn’t disappear
(right?)
Bellwork Question
•
you walk “in town” and you walk 0.45 m to the
West and turn to walk 0.35 m to the North
•
Picture this in an
x

y
coordinate
system
•
What is the distance traveled?
N / +y
E / +x
W /

x
S /

y
Bellwork Question
•
you walk “in town” and you walk 0.45 m to the
West and turn to walk 0.35 m to the North
•
Picture this in an x

y coordinate
system
•
What is the distance traveled?
In Green
•
0.80 m
N / +y
E / +x
W /

x
S /

y
3

5 Position, Displacement, Velocity, and
Acceleration Vectors
Position vector points from the origin to the location in question.
The displacement vector points from the original
position to the final position.
f
r
r
Bellwork Question
•
you walk “in town” and you walk 0.45 m to the
West and turn to walk 0.35 m to the North
•
Picture this in an
x

y
coordinate
system
•
Initial Position?
•
Final Position?
N / +y
E / +x
W /

x
S /

y
3

5 Position, Displacement, Velocity, and
Acceleration Vectors
Average velocity vector:
(3

3)
So
is in the same
direction as .
av
v
r
Bellwork Question
N / +y
E / +x
W /

x
S /

y
3

5 Position, Displacement, Velocity, and
Acceleration Vectors
Instantaneous velocity vector is tangent to the path:
3

5 Position, Displacement, Velocity, and
Acceleration Vectors
Average acceleration vector is in the direction of the change in instantaneous velocity:
Acceleration Vectors
•
So when considering an acceleration vector, are we
using
two average or instantaneous velocities
?
Acceleration Vectors
•
So when considering an acceleration vector, are we
using
two average or
instantaneous
velocities
?
3

5 Position, Displacement, Velocity, and
Acceleration Vectors
Velocity vector is always in the direction of motion; acceleration vector can point
anywhere:
2D Motion PhET Simulation
•
Lab Groups
–
Going to devise more variety of
groups ( partners, groups of 3, etc. )
•
Remember the acceleration vector would go
crazy, eventually point in opposite direction
when you would reverse the direction of the
“object” ( or dot on the screen )
•
Check it out again!!
Homework
•
Pg. 78 ( in text )

#36
2D Motion
–
Mini

Lab Activity
•
Everybody answers questions (
NAME!!
)
•
Separate sheet of paper
–
will use for
QUIZ
also
•
Preliminary Question: If you slide a coin off the
edge of the lab

station counter

top, is there any
interdependence between the vertical and
horizontal motion
?
2D Motion
–
Mini

Lab Activity
•
Preliminary Question: If you slide a coin off the
edge of the lab

station counter

top, is there any
interdependence between the vertical and
horizontal motion
?
–
They are independent of each other, or one is not
dependent on the other ( two ways to state it )
2D Motion
–
Mini

Lab Activity
•
Procedure
–
Go to lab station with two discs
–
Hanging masses ( up front )
–
Must be the same mass!!
–
One person slides 1
st
disc off edge of counter
–
Second person drops 2
nd
disc off edge exact moment
1
st
disc leaves the edge
–
Must measure/estimate counter height and distance
sliding discs lands away from counter
–
Other group members observe (
see / listen
) when
each disc lands
2D Motion
–
Mini

Lab Activity
•
Questions:
•
1]
Did the discs land at the same time ( after
leaving the edge of the lab counter )?
•
2]
Sketch a graph of the “sliding” disc’s motion
–
Formulate an equation (
y
as a function of
x
) for this
motion with the edge of the floor being the coordinate
system origin
–
Make +
x
point away from counter
Lab Counter

Top
Origin
+
x
+
y
Challenge Question

NOTES
•
PROBLEM
: You drop a paper

wad off a bridge ( releasing it
from rest ). The wind is blowing CONSTANTLY ( in the +
x
direction ) at 1.0 m/s. The paper

wad lands on the ground
with a vertical velocity of
–
3.0 m/s ( air resistance is very
much there so not just gravity affecting it ) after 2.0 sec.
•
Q1
: What is the velocity vector when it lands?
•
Q2
: What is the acceleration vector?
+
x
+
y
wind
Challenge Question

NOTES
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