1. 1 Physics Chapter 5 Objectives: 1) Be able to add two or more vectors graphically (tip-to- tail). 2) Apply the trigonometry of right triangles in order to resolve a vector into its components. 3) Be able to add two or more vectors mathematically. 4) Define FRICTION. 5) Compare and contrast static friction and kinetic friction. 6) Use the coefficient of friction and known forces in order to calculate frictional forces.

2. 2 Chapter 5: Forces in Two Dimensions I) Vectors A) Vectors in Multiple Dimension: 1) Vectors acting HORIZONTALLY:

3. 3 2) Vectors acting VERTICALLY: 3) Vectors acting 2 – DIMENSIONALLY:

4. 4 4) Solving Vectors Graphically (the “Tip – to – Tail” method) a) A person walks: 7.0 m due North; turns East for 5.0 m; turns South for an additional 9.0 m. “It doesn’t matter which order you add these vectors.”

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6. 6 B) Components of Vectors: 1) The trigonometry of a RIGHT TRIANGLE:

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8. 8 2) Resolving a Vector into its COMPONENTS:

9. 9 C) Algebraic Addition of Vectors: 1) Sample Problem: What is the total displacement of a person who walks 0.40 km in a direction 60 degrees West of North, then goes 0.50 km due West? a) STEP 1: Resolve each vector into its X and Y components.

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11. 11 b) STEP 2: Add up all the X components and then the Y components.

12. 12 c) STEP 3: Form a right triangle out of the sum’s of the X and Y components.

13. 13 d) STEP 4: Use trig. to find the triangle’s hypotenuse (the RESULTANT’S magnitude) and the hypotenuse’s angle (the RESULTANT’S direction).

14. 14 II) Friction * _ _ _ _ _ _ _ _ : a force that opposes motion. A) Static and Kinetic Friction:

15. 15 1) _ _ _ _ _ _ Friction: ______, the force needed to overcome the inertia of an object at rest. 2) _ _ _ _ _ _ _ Friction: _____, the frictional force acting between an object in motion and the surface it moves over.

16. 16 3) Friction depends on: a) b) 4) Determining Friction:

17. 17 a) Coefficient of Friction: ______, the ratio of the force due to friction and the NORMAL FORCE acting on an object.

18. 18 b) The Formula’s: * values of _____ and _____ for various materials are given in Table 5-1 on page 129.

19. 19 c) Sample Problem 18 on p. 128: “You need to move a 105 kg sofa to a different location. It takes a force of 102 N to start it moving across the carpet. What is the coefficient of static friction between the sofa and the carpet?”

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21. 21 d) Sample Problem 23 on p. 130: “You help you friend move a 41.0 kg bookcase. If you push with a force of 65 N and the bookcase accelerates at 0.12 m/s 2, what is the coefficient of kinetic friction between the bookcase and floor?”

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