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Skipped to slide 40 for 2008 and 2009. Introduction to Vectors. Scalars and Vectors In Physics, quantities are described as either scalar quantities or vector quantities. Introduction to Vectors. Scalar Quantities Involve only a magnitude, which includes numbers and units.
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Introduction to Vectors Scalars and Vectors • In Physics, quantities are described as either scalar quantities or vector quantities .
Introduction to Vectors Scalar Quantities • Involve only a magnitude, which includes numbers and units. • Examples include distance and speed.
Introduction to Vectors Vector Quantities • Involve a direction, in addition to numbers and units. • Can be represented graphically with arrows. • The longer the arrow, the greater the magnitude it represents.
Introduction to Vectors 15 m/s east 25 m/s west
Vector Addition in One direction • When vector quantities are in the same direction, vectors are added by placing the tail of one vector at the head of the other vector. • Be sure to maintain direction and length of vectors! • This creates one Resultant vector (R) which is drawn from the tail of the 1st vector to the head of the second vector.
Example: A child walks 2.0 m east, pauses, and then continues 3.0 m east. The resultant (R) = 5.0 m east.
If the two vectors have different directions, they are still added head to tail. Example: A child walks 2.0 m east, then turns around and walks 4.0 m west.
Component vectors are added “tip-to-tail.” The resultant vector is drawn “tail-to-tip.”
4 m east 3 m north Adding vectors graphically, using the “tip-to-tail” method.
A man walks 3 m north, and then 4 m east. Find his displacement. 4 m east 3 m north
You are allowed to move the vectors, but don’t change the direction or length. 4 m east 3 m north
Line up the tip of one vector with the tail of the other. tail tip 4 m east 3 m north
Line up the tip of one vector with the tail of the other. 4 m east 3 m north
Now, draw the resultant vector from “tail-to-tip” as shown above. 4 m east 3 m north Resultant vector
Remember to line up the component vectors from tip-to tail. 4 m east 3 m north
If you line them up incorrectly, you get the wrong resultant vector. 4 m east 3 m north
This is wrong! 4 m east How did this man go East, and then North, and end up back where he started!?!? 3 m north Now, the resultant vector will be wrong, no matter how it is drawn.
Always line up the tip of one component vector with the tail of the other. 4 m east 3 m north
Then draw your resultant vector from “tail-to-tip” as shown below. 4 m east 3 m north Resultant vector
It doesn’t matter in what order you add the component vectors. 4 m east 3 m north
You will still get the same resultant vector. Resultant vector 3 m north 4 m east
It doesn’t matter which order you place the component vectors. A B B A
The resultant vector will be the same in either case. resultant resultant
We will find the correct resultant vector. Resultant vector
We can also subtract vectors graphically. B A Find the resultant vector of vector A – vector B
A – B is the same as A + (-B) B A Find the resultant vector A + (-B)
The vector called “-B” has the same magnitude as vector B, but the opposite direction. -B B A
Now we add Vector A and Vector –B with the tip-to-tail method -B B A
Now we add Vector A and Vector –B with the tip-to-tail method A -B
And draw the resultant vector. A -B Resultant vector
IF skip 3A beginning lecture (2008 and 2009)….use the next slides from lecture one and assign 3A
Happy Wednesday!! • Please complete the maze on your desk. • Both sides!
Introduction to Vectors Scalars and Vectors • In Physics, quantities are described as either scalar quantities or vector quantities .
Introduction to Vectors Scalar Quantities • Involve only a magnitude, which includes numbers and units. • Examples include distance and speed.
Introduction to Vectors Vector Quantities • Involve a direction, in addition to numbers and units. (velocity and displacement) • Can be represented graphically with arrows. • The longer the arrow, the greater the magnitude it represents.
Vector Operations Drawing Vectors In order to draw vectors that indicate direction, you need to work within a coordinate system.
Vector Operations Coordinate Systems
Vector Operations Coordinate System When working with the Cartesian coordinates, adding vectors can be accomplished with the “tip-to-tail” method.
Example: A child walks 2.0 m east, pauses, and then continues 3.0 m east. 0 The resultant (R) = 5.0 m east.
If the two vectors have different directions, they are still added tip to tail. Example: A child walks 2.0 m east, then turns around and walks 4.0 m west. 0 The resultant is 2.0 m west.
Component vectors are added “tip-to-tail.” The resultant vector is drawn “tail-to-tip.”
4 m east 3 m north Adding vectors graphically, using the “tip-to-tail” method.