1. AP Physics Michaelsen 8/2012
Vectors
AP Physics
Michaelsen
8/2012

2. The desert ant Cataglyphis fortis lives in the plains of the Sahara desert.
When one of the ants forages for food, it travels from its home nest along a haphazard search path like the one shown here. The ant may travel more than 500 m along such a complicated path over flat, featureless sand that contains no landmarks. Yet, when the ant decides to return home, it turns and then runs directly home.

4. Adding Vectors Geometrically: Parallelogram method Draw head-to-tail
(2 or more vectors)
Parallelogram method
Tail to tail, then
Complete parallelogram
(2 vectors only)

5. Adding Vectors Ex: 3m E + 4m N = _________________
Draw both ways and get R.

6. Vector Subtraction A – B = A + (-B)
To subtract vectors, just add the opposite vector (180° from original direction).
Ex: 3m E - 4m N = ___________________

7. Vector Addition/Subtraction
For any review, look at last year’s notes and worksheets.

8. Vector Resolution
A vector can be resolved into its perpendicular components.
Ex: m at 35° S of E.
CP2
SP 3-2
SP 3-3

9. Checkpoint 2
In the figure, which of the indicated methods for combining the x and y components of vector are proper to determine that vector?

10. Vector Notation Up ‘til now: 5m at 130° (magnitude angle)
X = -2.5 m y = +4.3 m (components)
Btw, we can use negative angles ° ….

11. Coordinate Axes Pg 44 Right-handed coordinate system
May be rotated, but still has same arrangement
X-Y plane = paper
Z = out of paper
Every point in 3 dimensional space can be uniquely defined by its ordered triple (x,y,z).

12. Coordinate Axes
To determine handedness you lay your hand flat on the x-axis with your fingers pointing in the positive x direction.
Now curve your fingers in the direction of the positive y-axis. The direction your thumb is pointing will be the positive z direction.

13. Coordinate Axes
Fingers +X Curl Fingers +Y Thumb = +Z

14. Coordinate Axes CADD, and sometimes math X-Y plane = floor
Z = vertical

15. 3-D Displacement
Try this: an object starts at the origin and moves to the point (3,2,4). What is the magnitude of its displacement?
 m

16. 3-D Displacement Sample Problem 3-3
For two decades, spelunking teams sought a connection between the Flint Ridge cave system and Mammoth Cave, which are in Kentucky. When the connection was finally discovered, the combined system was declared the world's longest cave (more than 200 km long). The team that found the connection had to crawl, climb, and squirm through countless passages, traveling a net 2.6 km westward, 3.9 km southward, and 25 m upward. What was their displacement from start to finish?

17. Unit Vector Notation Unit vector = 1 “unit” that points in a direction
No unit
It just points !
Designated as

18. Unit Vector Notation
a = ax ay az
direction
magnitude

19. Unit Vector Notation

20. Unit Vector Notation
Spelunker problem:

21. Unit Vector Notation
Previously, we added vectors with components (x,y).
Now, use UVN

22. Unit Vector Notation
SP 3-4

23. Sample Problem 3-4 Figure 3-16a shows the following three vectors:
What is their vector sum?

24. Sample Problem 3-5
According to experiments, the desert ant shown in the chapter opening photograph keeps track of its movements along a mental coordinate system. When it wants to return to its home nest, it effectively sums its displacements along the axes of the system to calculate a vector that points directly home. As an example of the calculation, let's consider an ant making five runs of 6.0 cm each on an xy coordinate system, in the directions shown in Figure 3-17a, starting from home. At the end of the fifth run, what are the magnitude and angle of the ant's net displacement vector , and what are those of the homeward vector that extends from the ant's final position back to home?

25. Sample Problem 3-5

26. Sample Problem 3-6
Here is a problem involving vector addition that cannot be solved directly on a vector-capable calculator, using the vector notation of the calculator. Three vectors satisfy the relation
A has a magnitude of 22.0 units and is directed at an angle of –47.0° (clockwise) from the positive direction of an x axis.
C has a magnitude of 17.0 units and is directed counterclockwise from the positive direction of the x axis by angle f. B is in the positive direction of the x axis. What is the magnitude of B?