Transcript Slide 1

I. Distances and displacements
Distance is ____________________________________
how far an object moves
or _________________________________________________
the change in position of an object
initial
xi
position
change in position =
xf
xf - xi
final
position
= Dx
d for
Dx
Instead of _________
, we will use _____
distance. We will use SI (international system)
meter
units. The SI unit for distance is the ___________
.
changed
Any other unit for distance must first be ___________
_______________________
before using any equation in
to meters
Regents Physics.
magnitude
scalars
______________–
quantities with ______________(size)
only
Ex: distance d = 2.0 m
magnitude
vectors
____________– quantities with magnitude and direction
_________
direction
Ex: displacement d = 2.0 m, west
distance =
magnitude
scalar
Distance d is a _______________.
vector.
Displacement d is a_____________________
.
arrows
Vectors are represented by ________________:
Ex: Draw d = 2.0 m, west. Use a scale of 1 cm:1 m.
Use a scale of 1cm:1 m to draw d.
head
tail
magnitude
direction
head for_________________
•must have arrow __________
•use a ___________
ruler to draw a scale and straight line
negative
positive
•right or up is______________;
down or left is ___________
north
•right =___________;
up =_______________,
etc
east
equal
•any vector with same mag. and dir. is_______________
equal
Ex: All these vectors are _________________
because
direction
they have the same _______________
magnitude and _______________:
Use a ruler to draw the vectors to the scale: 1 cm:1 m
B = 3m, E
A = 2m, E
II. Adding vectors
“head to tail”
 add using the ________________method.
resultant displacement _____
R
 draw the _____________
as
head of B
an ________
of A to the ________
tail
arrow from the ________
Ex:
B
A
R
5 m, E
Resultant R = _________
A+B
R = _____________
5m.
Total distance traveled = _________
Resultant displacement =____________
5m, E
mag.
dir.
Ex. What is B + A = ?
B
A
R
B+A
R =__________
5m, E
resultant
The ________________
displacement R = ____________
5m
magnitude of R: _________
E
direction of R: _________
A+B
Notice that this new R is same as _________________
order
 The ______________
in which vectors are added
does not matter
__________________________
. This is true even if
more than two vectors.
you add ______________________________________
.
Ex:
If A = 3m, east
3 m, west
Then –A = ___________
-3 m (the __________
or
= __________
negative sign shows direction)
If X =
Then -X =
magnitude
Compared to X, -X has the same ________________
,
direction
but the opposite _____________________
.
III. Subtracting vectors using the head to tail method.
Given:
B = 3m
A = 2m
-B
A + (-B)
Find A – B = ____________
A + (-B):
A
R
-B
1m, W
R =_________
-1 m
= _________
1m
mag. = ______
W
dir. = ______
5m
Total distance traveled =___________
1 m, W
but resultant displacement = ______________
Ex: Using same vectors, what does B – A = ?
B=3m
A = 2m
-A
B
B + (-A)
B – A =_____________
R
-A
1 m, E = _________
+1 m
R = __________
5 m.
Total distance covered = ______________
1 m, E
Resultant displacement =______________
resultant
Notice that the ____________________
here is exactly
opposite
__________________
to the one in the previous example.
IV.
Adding non-parallel vectors.
C
Find C + D
4m
D
3m
3m
q
start
here
4m
5 m, 370 N of E
R = _________________
7m
Total distance = _______
2 + 42)
√
(3
mag. of R = ____________
5m
=___________
dir. of R:
q = tan-1 (3/4)
= 370
Ex: What is D + C?
C
4m
D 3m
q
start
here
2 + 42)
√
(3
mag. of R = ____________
5m
=___________
dir. of R:
q = tan-1 (4/3)
= 530
5 m, 530 E of N
R =__________________
R could also be written:
(Same as C + D)
R = 5 m, 370 N of E
R = _______________________________________
IV. Subtracting non-parallel vectors.
Ex. Find C – D
C
start
here
D
= C + (–D)
3m
4m
-D
3m
4m
q
3m
5m
mag. of R = ____________
dir. of R:
q = tan-1 (3/4)
= 370
0 S of E
5
m,
37
R = __________________
7 m.
Total distance =____________
Skip next slide if time is short.
Ex. Draw D- C.
= D + (–C)
C:
-C:
4m
D
3m
4m
4m
mag. of R = ________
5m
dir. of R:
q = tan-1 (4/3)
3m
= 530
0 W of N
5
m,
53
R = __________________
7 m.
Total distance =____________
q
start
here