# 09/25/12 - Bellwork

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14 Νοε 2013 (πριν από 4 χρόνια και 5 μήνες)

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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

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

-
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

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
-
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