09/25/12 - Bellwork

filercaliforniaMechanics

Nov 14, 2013 (3 years and 6 months ago)

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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