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Vector Addition
Suppose 3 forces act on an object
at the same time. Fnet is not 15 N
because these forces aren't
working together. But they're not
8N
completely opposing each either. 4N
So how do find Fnet ? The answer
is to add the vectors ... not their
magnitudes, but the vectors
themselves. There are two basic 3N
ways to add vectors w/ pictures:
· Tip to tail method
· Parallelogram method…read more

Slide 3

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Tip to Tail Method 20 N
12 N in-line examples
Place the tail of one vector 16 N
9N at the tip of the other. The
vector sum (also called the
resultant) is shown in red. It
starts where the black vector 20 N
16 N
21 N began and goes to the tip of
the blue one. In these 4N
9N cases, the vector sum
represents the net force.
12 N You can only add or
subtract magnitudes when
the vectors are in-line!…read more

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Tip to Tail ­ 2 Vectors
To add the red and blue displacement vectors first note:
· Vectors can only be added if they are of the
same quantity--in this case, displacement. 5m
· The magnitude of the resultant must be less
than 7 m (5 + 2 = 7) and greater than 3 m
(5 - 2 = 3).
2m
Place the vectors tip to tail Interpretation: Walking 5 m in
and draw a vector from the the direction of the blue vector
tail of the first to the tip of and then 2 m in the direction
the second. of the red one is equivalent to
2m walking in the direction of the
black vector. The distance
5m walked this way is the black
r e d vector's magnitude.
blu e+…read more

Slide 5

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Commutative Property
b lu e
re d+
+ r ed
blue
As with scalars quantities and ordinary numbers, the
order of addition is irrelevant with vectors. Note that
the resultant (black vector) is the same magnitude
and direction in each case.
(We'll learn how to find the resultant's magnitude soon.)…read more

Slide 6

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Tip to Tail ­ 3 Vectors
We can add 3 or more vectors
by placing them tip to tail in
any order, so long as they are
of the same type (force,
velocity, displacement, etc.).
blue + green + red…read more

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