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Vector Refresher Part 2. Vector Addition Multiplication by Scalar Q uantities Graphical Representations Analytical Methods. Vector Addition. A lot of times, it’s important to know the resultant of a set of vectors - PowerPoint PPT Presentation
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Vector Refresher Part 2• Vector Addition• Multiplication by
Scalar Quantities• Graphical
Representations• Analytical Methods
Vector Addition• A lot of times, it’s 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 evaluate
• We’ll look at graphical and analytical techniques for doing this
Graphical Methods For Vector Addition
• 2 ways to look at vector addition graphically• Parallelogram method
Connect the tails of both vectors to start.
Graphical Methods For Vector Addition
• 2 ways to look at vector addition graphically• Parallelogram method
Create a parallelogram with each vector as one of the sides.
Graphical Methods For Vector Addition
• 2 ways to look at vector addition graphically• Parallelogram method
The resultant goes from the place where 2 tails meet to the place where 2 heads meet
Graphical Methods For Vector Addition
• 2 ways to look at vector addition graphically• Head-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.
Graphical Methods For Vector Addition
• 2 ways to look at vector addition graphically• Head-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
Graphical Methods For Vector Addition
• 2 ways to look at vector addition graphically• Head-to-tail method
If we had a 3rd vector, we could add it to the previous result
Graphical Methods For Vector Addition
• 2 ways to look at vector addition graphically• Head-to-tail method
If we had a 3rd vector, we could add it to the previous result
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 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
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
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
ExampleDraw
Start by multiplying vector A by 1/2
ExampleDraw
Start by multiplying vector A by 1/2
ExampleDraw
Next, multiply vector B by -3
ExampleDraw
Now add these vectors together
ExampleDraw
The resultant vector is shown in green
Analytical Method for Vector Addition
When vectors are added to each other, the components in each direction are summed.
Analytical Method for Vector Addition
When vectors are added to each other, the components in each direction are summed.
Analytical Method for Vector Addition
When vectors are added to each other, the components in each direction are summed.
Multiplying a Vector By a Scalar
When multiplying a vector by a scalar, the scalar must be applied to each component of the vectorThus, if we multiply by a scalar “k”, we get:
The first thing to do is determine F3
ExampleDetermine the resultant force caused by the following 3 force vectors.
The first thing to do is determine F3
ExampleDetermine the resultant force caused by the following 3 force vectors.
The first thing to do is determine F3
ExampleDetermine the resultant force caused by the following 3 force vectors.
The first thing to do is determine F3
ExampleDetermine the resultant force caused by the following 3 force vectors.
The first thing to do is determine F3
ExampleDetermine the resultant force caused by the following 3 force vectors.
The first thing to do is determine F3
ExampleDetermine the resultant force caused by the following 3 force vectors.
The first thing to do is determine F3
ExampleDetermine the resultant force caused by the following 3 force vectors.
Now we can add the 3 vectors together to determine the resultant force
ExampleDetermine the resultant force caused by the following 3 force vectors.
Now we can add the 3 vectors together to determine the resultant force
ExampleDetermine the resultant force caused by the following 3 force vectors.
Now we can add the 3 vectors together to determine the resultant force
ExampleDetermine the resultant force caused by the following 3 force vectors.
Don’t forget the units, they’re as important to the answer as the numbers are
ExampleDetermine the resultant force caused by the following 3 force vectors.
Don’t forget the units, they’re as important to the answer as the numbers are
ExampleDetermine the resultant force caused by the following 3 force vectors.