1.
1 N
2.
7 N
3.
9 N
4.
4 N

example
•
As the angle between two concurrent
forces decreases, the magnitude of the
force required to produce equilibrium
1.
decreases
2.
increases
3.
remains the same

10/9 do now
•
Write all you know all about vector
–
Definition:
–
Examples (3):
–
Representation:
–
Ways to add vectors
•
Head to tail: (sketch)
•
Parallelogram method: (sketch)

objectives
•
Homework questions?
•
How to add vectors mathematically?
•
Homework: castle learning
•
No post session today
•
Homework quiz is on Friday

Apply the Pythagorean theorem and tangent
function to calculate the magnitude and direction
of a resultant vector
•
The procedure is restricted to the
addition of two vectors that make
right angles
to each other
.
Add vectors mathematically

Using tangent function to
determine a Vector's Direction
θ
opp.
Hyp.
adj
.
opp.
adj
.
tanθ =
opp.
adj
.
θ = tan
-1
(
)

example
•
Example: Eric leaves the base camp and hikes 11 km,
north and then hikes 11 km east. Determine Eric's
resulting displacement.

•
Note: The measure of an angle as determined through use
of SOH CAH TOA is not
always the direction of the vector.
R
2
= (5.0km)
2
+ (10km)
2
R = 11 km
•
Or at 26
degrees south
of west

example
•
An archaeologist climbs the Great Pyramid in Giza,
Egypt. If the pyramid’s height is 136 m and its width is
2.30 x 10
2
m, what is the magnitude and the direction of
the archaeologist’s displacement while climbing from the
bottom of the pyramid to the top?

Equilibrant
•
The
equilibrant
vectors of A and B is the
opposite of the resultant
of vectors A
and B.
•
Example:
A
B
A
B
R
Equilibrant
A
B
R
Equilibrant
Head to tail
Parallelogram

Vector Components
•
In situations in which vectors are directed at angles to the
customary coordinate axes, a useful mathematical trick
will be employed to
transform
the vector into two parts
with each part being directed along the coordinate axes.

•
Any vector directed in two dimensions can be thought of as
having an influence in two different directions.
•
Each part of a two-dimensional vector is known as a
component
.
•
The components of a vector depict the influence of that
vector in a given direction.
•
The combined influence of the two components is
equivalent to the influence of the single two-dimensional
vector.
•
The single two-dimensional vector could be replaced by the
two components.

•
Vectors can be broken into
COMPONENTS
•
X-Y system of components
•
A
X
= A cos θ
•
A
Y
= A sin θ
–
Example
•
v
i
= 5.0 m/s at 30°
–
v
ix
= 5.0 m/s (cos 30°) = 4.33 m/s
–
v
iy
= 5.0 m/s (sin 30°) = 2.5 m/s
•
Any vector can be broken into
unlimited
sets of components

EXAMPLE
•
Calculate the x and y components of the following
vectors.
•
a. A = 7 meters at 14°
•
b. B = 15 meters per second at 115°
•
c. C = 17.5 meters per second2 at 276°

Adding with Components
•
Vectors can be added together by
adding their
COMPONENTS
•
Results are used to find
–
RESULTANT MAGNITUDE
–
RESULTANT DIRECTION
Adding Vectors Algebraically

Example
Add vectors D and F by following the steps below.

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