1. Combining vectors in 2D Components, Overall Velocity or force Equilibrium, Equilibriants

2. BREAKING A VECTOR DOWN INTO ITS COMPONENTS

3. Components of a vector Portion of a vector value that affects 1 dimension Any vector moving at an angle not parallel or perpendicular to a coordinate axis can be broken down into 2 perpendicular components

4. How to find components Draw 2-d vector Create a triangle using the 2-D vector as hypotenuse Drawn legs should intersect at a right angle Use trig to calculate unknown sides or angles Indicate direction through drawing or name

5. To solve for components Need to be able to use right triangle trigonometry Trigonometry focuses on the ratio values of sides of a right triangle As angles change vary in different right triangles, so do the ratio of sides to each other

6. If you walk 32 m towards the NE, how far do you travel east?

7. Components Horizontal component Vertical Component Resultant side

8. Adding vectors not in cardinal directions Break all vectors down into components, that’s is smaller vectors in cardinal directions that add up to the original vector. Example: 4 m/s [E] Horizontal component 3 m/s [N] Vertical component 5 m/s [E 36.9 N]

9. Find the components of : 57 N [N 57W]

10. Find the components of: 87.6 m ( 300°) Remember, here the cardinal directions are 0/360, 90, 180, 270

11. Overall velocity problem If the projectile landed with a vertical velocity of 37 m/s downward and a horizontal velocity of 29 m/s to the right, what would be the overall final velocity (magnitude and direction)

12. Add the following vectors 30 m/s [ NE] + 45 m/s [S 67 W]

13. Calculate sides or angles

14. PUTTING ALL VECTOR IDEAS TOGETHER TO SOLVE A PROBLEM

15. Friday’s in class question 173 N [W 57.352 S] + 142 [E 51.22 N]

16. Answer The vectors Drawn with Components

17. Calculations for the answer The 4 component vectors: 93.3N [W], 146N [S] 88.9N [E], 111N [N] These combine to : 4.4 N [W], 35 N [S]

18. Final Recombination and answer Final triangle is drawn as: Final answer is: 35.3 N [W 82.8 S] or 35.5 N [S 7.2 W]

19. FINDING THE EQUILIBRIANT

20. Equilibrium When the sum of all forces acting on an object cancel each other out. Net force = 0

21. Equilibrant A force added to all other forces applied to an object to achieve equilibrium

22. equilibrium problems These are problems that require an object to be at equilibrium. Equilibrium = all forces applied to object balance each other out. Net force on object = 0 Equilibriant: the force applied to an object that produces equilibrium

23. ALL VECTOR VALUES CAN BE COMBINED USING THE ABOVE METHODS Displacement, Velocity, Acceleration, Force

24. SCALAR VALUES COMBINED WITH VECTORS

25. Effect of scalar values on2-D force problems Scalar values: Those that do not indicate a direction (time, mass) Scalars affect magnitude, not direction

26. APPLICATION OF VECTOR MATH TO SOLVING 2D PROBLEMS