Acceleration in 2D.notebook
February 15, 2023
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http://www.travelpod.com/travel-blog-entries/ruairioc/magicaltrip2008/1214071320/
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Acceleration in 2D.notebook
February 15, 2023
Two Dimensional Vectors in General
All vectors can be added to produce a total or resultant vector.
ex. Displacement:
Velocity
Force
To add 2D vectors, simple arithmetic will not suffice.
One of the following techniques are required.
1) Scale diagrams: (use rulers and protractors; Gr 11, not very accurate)
2) Pythagorean Theorem: (for perpendicular vectors only)
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Acceleration in 2D.notebook
February 15, 2023
3) Components: (best method, especially for multiple vectors)
Any vector can be described in terms of x and y components.
cosα
Steps for using components:
1) Sketch the vector addition.
2) Establish the positive direction for x and y
3) Sum the x and y components separately
4) Use pythagorean theorem and tangent to add the x and y components.
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Acceleration in 2D.notebook
February 15, 2023
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Acceleration in 2D.notebook
February 15, 2023
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Acceleration in 2D.notebook
February 15, 2023
4) Cosine law (gets complicated with more than two vectors; see p 758)
C
N
D
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Acceleration in 2D.notebook
February 15, 2023
Acceleration in 2 Dimensions
v1
v2
To subtract vectors, add the negative.
i.e. v2 - v1 becomes v2 + (- v1)
+v1
-v1
v2
Δv
Then solve the
triangle and calculate
acceleration.
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Acceleration in 2D.notebook
February 15, 2023
Ex. A boat takes 8.5 s to change
o
velocity from 15 m/s [25 N of E] to
o
12 m/s [10 W of N]. Calculate the
+y
average acceleration.
+x
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Acceleration in 2D.notebook
February 15, 2023
HOMEWORK
Read 28-29
Answer p 29: 25 - 28
o
Note: answer for #28 is 8.8
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