Vector Refresher Part 2 Vector Addition Vector Addition
Multiplication by Scalar Quantities Multiplication by Scalar
Quantities Graphical Representations Graphical Representations
Analytical Methods Analytical Methods
Slide 2
Vector Addition A lot of times, its important to know the
resultant of a set of vectorsA lot of times, its important to know
the resultant of a set of vectors The resultant vector can be
described as the sum of all the vector quantities you wish to
evaluateThe resultant vector can be described as the sum of all the
vector quantities you wish to evaluate Well look at graphical and
analytical techniques for doing thisWell look at graphical and
analytical techniques for doing this
Slide 3
Graphical Methods For Vector Addition 2 ways to look at vector
addition graphically2 ways to look at vector addition graphically
Parallelogram methodParallelogram method Connect the tails of both
vectors to start.
Slide 4
Graphical Methods For Vector Addition 2 ways to look at vector
addition graphically2 ways to look at vector addition graphically
Parallelogram methodParallelogram method Create a parallelogram
with each vector as one of the sides.
Slide 5
Graphical Methods For Vector Addition 2 ways to look at vector
addition graphically2 ways to look at vector addition graphically
Parallelogram methodParallelogram method The resultant goes from
the place where 2 tails meet to the place where 2 heads meet
Slide 6
Graphical Methods For Vector Addition 2 ways to look at vector
addition graphically2 ways to look at vector addition graphically
Head-to-tail methodHead-to-tail method With this method, the
vectors are added by placing the tail of a vector at the head of
another one to make a continuous path.
Slide 7
Graphical Methods For Vector Addition 2 ways to look at vector
addition graphically2 ways to look at vector addition graphically
Head-to-tail methodHead-to-tail method The addition of these
vectors results in a vector that starts at the tail of the first
vector and ends at the head of the final vector
Slide 8
Graphical Methods For Vector Addition 2 ways to look at vector
addition graphically2 ways to look at vector addition graphically
Head-to-tail methodHead-to-tail method If we had a 3 rd vector, we
could add it to the previous result
Slide 9
Graphical Methods For Vector Addition 2 ways to look at vector
addition graphically2 ways to look at vector addition graphically
Head-to-tail methodHead-to-tail method If we had a 3 rd vector, we
could add it to the previous result
Slide 10
Multiplying a Vector By a Scalar When a vector is multiplied by
a scalar, the length of the vector can be elongated or shortened.
If the scalar is a negative number, the direction is reversed.
Slide 11
Multiplying a Vector By a Scalar When a vector is multiplied by
a scalar, the length of the vector can be elongated or shortened.
If the scalar is a negative number, the direction is reversed.
Multiplying a vector by 2 yields a vector with the SAME DIRECTION
and twice the length
Slide 12
Multiplying a Vector By a Scalar When a vector is multiplied by
a scalar, the length of the vector can be elongated or shortened.
If the scalar is a negative number, the direction is reversed.
Multiplying a vector by 1/2 yields a vector with the SAME DIRECTION
and half the length
Slide 13
Multiplying a Vector By a Scalar When a vector is multiplied by
a scalar, the length of the vector can be elongated or shortened.
If the scalar is a negative number, the direction is reversed.
Multiplying a vector by -1 yields a vector with the OPPOSITE
DIRECTION and the same length
Slide 14
Example Draw Start by multiplying vector A by 1/2
Slide 15
Example Draw
Slide 16
Example Draw Next, multiply vector B by -3
Slide 17
Example Draw Now add these vectors together
Slide 18
Example Draw The resultant vector is shown in green
Slide 19
Analytical Method for Vector Addition When vectors are added to
each other, the components in each direction are summed.
Slide 20
Analytical Method for Vector Addition When vectors are added to
each other, the components in each direction are summed.
Slide 21
Analytical Method for Vector Addition When vectors are added to
each other, the components in each direction are summed.
Slide 22
Multiplying a Vector By a Scalar When multiplying a vector by a
scalar, the scalar must be applied to each component of the vector
Thus, if we multiply by a scalar k, we get:
Slide 23
The first thing to do is determine F 3 Example Determine the
resultant force caused by the following 3 force vectors.
Slide 24
The first thing to do is determine F 3 Example Determine the
resultant force caused by the following 3 force vectors.
Slide 25
The first thing to do is determine F 3 Example Determine the
resultant force caused by the following 3 force vectors.
Slide 26
The first thing to do is determine F 3 Example Determine the
resultant force caused by the following 3 force vectors.
Slide 27
The first thing to do is determine F 3 Example Determine the
resultant force caused by the following 3 force vectors.
Slide 28
The first thing to do is determine F 3 Example Determine the
resultant force caused by the following 3 force vectors.
Slide 29
The first thing to do is determine F 3 Example Determine the
resultant force caused by the following 3 force vectors.
Slide 30
Now we can add the 3 vectors together to determine the
resultant force Example Determine the resultant force caused by the
following 3 force vectors.
Slide 31
Now we can add the 3 vectors together to determine the
resultant force Example Determine the resultant force caused by the
following 3 force vectors.
Slide 32
Now we can add the 3 vectors together to determine the
resultant force Example Determine the resultant force caused by the
following 3 force vectors.
Slide 33
Dont forget the units, theyre as important to the answer as the
numbers are Example Determine the resultant force caused by the
following 3 force vectors.
Slide 34
Dont forget the units, theyre as important to the answer as the
numbers are Example Determine the resultant force caused by the
following 3 force vectors.