vector refresher part 2
DESCRIPTION
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 PresentationTRANSCRIPT
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Vector Refresher Part 2• Vector Addition• Multiplication by
Scalar Quantities• Graphical
Representations• Analytical Methods
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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
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Graphical Methods For Vector Addition
• 2 ways to look at vector addition graphically• Parallelogram method
Connect the tails of both vectors to start.
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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.
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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
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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.
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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
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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
![Page 9: Vector Refresher Part 2](https://reader035.vdocuments.site/reader035/viewer/2022062302/5681636b550346895dd44729/html5/thumbnails/9.jpg)
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
![Page 10: Vector Refresher Part 2](https://reader035.vdocuments.site/reader035/viewer/2022062302/5681636b550346895dd44729/html5/thumbnails/10.jpg)
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.
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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
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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
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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
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ExampleDraw
Start by multiplying vector A by 1/2
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ExampleDraw
Start by multiplying vector A by 1/2
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ExampleDraw
Next, multiply vector B by -3
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ExampleDraw
Now add these vectors together
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ExampleDraw
The resultant vector is shown in green
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Analytical Method for Vector Addition
When vectors are added to each other, the components in each direction are summed.
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Analytical Method for Vector Addition
When vectors are added to each other, the components in each direction are summed.
![Page 21: Vector Refresher Part 2](https://reader035.vdocuments.site/reader035/viewer/2022062302/5681636b550346895dd44729/html5/thumbnails/21.jpg)
Analytical Method for Vector Addition
When vectors are added to each other, the components in each direction are summed.
![Page 22: Vector Refresher Part 2](https://reader035.vdocuments.site/reader035/viewer/2022062302/5681636b550346895dd44729/html5/thumbnails/22.jpg)
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:
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The first thing to do is determine F3
ExampleDetermine the resultant force caused by the following 3 force vectors.
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The first thing to do is determine F3
ExampleDetermine the resultant force caused by the following 3 force vectors.
![Page 25: Vector Refresher Part 2](https://reader035.vdocuments.site/reader035/viewer/2022062302/5681636b550346895dd44729/html5/thumbnails/25.jpg)
The first thing to do is determine F3
ExampleDetermine the resultant force caused by the following 3 force vectors.
![Page 26: Vector Refresher Part 2](https://reader035.vdocuments.site/reader035/viewer/2022062302/5681636b550346895dd44729/html5/thumbnails/26.jpg)
The first thing to do is determine F3
ExampleDetermine the resultant force caused by the following 3 force vectors.
![Page 27: Vector Refresher Part 2](https://reader035.vdocuments.site/reader035/viewer/2022062302/5681636b550346895dd44729/html5/thumbnails/27.jpg)
The first thing to do is determine F3
ExampleDetermine the resultant force caused by the following 3 force vectors.
![Page 28: Vector Refresher Part 2](https://reader035.vdocuments.site/reader035/viewer/2022062302/5681636b550346895dd44729/html5/thumbnails/28.jpg)
The first thing to do is determine F3
ExampleDetermine the resultant force caused by the following 3 force vectors.
![Page 29: Vector Refresher Part 2](https://reader035.vdocuments.site/reader035/viewer/2022062302/5681636b550346895dd44729/html5/thumbnails/29.jpg)
The first thing to do is determine F3
ExampleDetermine the resultant force caused by the following 3 force vectors.
![Page 30: Vector Refresher Part 2](https://reader035.vdocuments.site/reader035/viewer/2022062302/5681636b550346895dd44729/html5/thumbnails/30.jpg)
Now we can add the 3 vectors together to determine the resultant force
ExampleDetermine the resultant force caused by the following 3 force vectors.
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Now we can add the 3 vectors together to determine the resultant force
ExampleDetermine the resultant force caused by the following 3 force vectors.
![Page 32: Vector Refresher Part 2](https://reader035.vdocuments.site/reader035/viewer/2022062302/5681636b550346895dd44729/html5/thumbnails/32.jpg)
Now we can add the 3 vectors together to determine the resultant force
ExampleDetermine the resultant force caused by the following 3 force vectors.
![Page 33: Vector Refresher Part 2](https://reader035.vdocuments.site/reader035/viewer/2022062302/5681636b550346895dd44729/html5/thumbnails/33.jpg)
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.
![Page 34: Vector Refresher Part 2](https://reader035.vdocuments.site/reader035/viewer/2022062302/5681636b550346895dd44729/html5/thumbnails/34.jpg)
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.