1. Vectors To describe two dimensional forces and motion

2. GRAPHICAL TECHNIQUE You need graph paper, protractor, and a ruler Define the scale for your graph Draw all lines to scale (including angle and length) Move vectors to line up head to tail

3. ANALYTICAL TECHNIQUE Use of trigonometric functions break everything into triangles always have two components make columns of each component (X,Y) be sure to keep any sign for direction sin  = opposite hypotenuse cos  adjacent hypotenuse tan  opposite adjacent

4. VECTORS

5. Vector Practice Problem A plane is flying with North at 200 kph. A wind of 40 kph is blowing due East. What is the resultant velocity of the plane? Find the magnitude of resultant first. c 2 = a 2 + b 2 c 2 = (200) 2 + (40) 2 c = 204 kph Now, find the angle for direction. Tan  = wind/plane Tan  = 40/200  = 11.3 o Answer: 204 kph at 11.3 o east of north

6. Static –Force to prevent an object from moving –Coefficient of static friction:  s Kinetic –Force to oppose motion once an object is moving –Coefficient of kinetic friction:  k f =  F N f: friction  : coefficient F N : normal force  s >  k

7. W = m g f =  F N F = ma  F=ma

8. CH 5 HOMEWORK 80. Ex=3.54, Ey=3.54; Fx=-3.54, Fy=-3.54; Ax=-3, Ay=0 81. Picture  83. 40 m, 45 o east of south 86. 79 N, 54 o NE 88. 6.5 m/s, 32 o from vertical 90. 0.255 97. 435 N, right 98. 150 N, 110 N 104. 490 N, 150 N, 49 N kinetic, 200N

9. FRICTION LAB Materials: –spring scale –1 kg mass –6 V battery –sand paper –notebook paper –wood block

10. OBJECTIVE Each group must find the coefficient of friction for each surface (sand paper, notebook paper, table) for each object (6 V battery and wood block) Is friction really dependent upon the surface and object used?

11. PROCEDURES Using each object in turn, find its weight using the spring scale Drag each object across each surface and determine the force (in Newtons) to do so Record the data in the table Determine the coefficient of friction from the friction equation Do your numbers make sense?

12. FRICTION LAB CHART

13. Vectors and Forces Materials –Textbook –Ruler –Protractor –Wood block –Spring scale –Penny Objective –To review vectors and forces from chapters 4 & 5

14. Vectors and Forces Procedure #1 Determine the mass of the wood block. m = _____ g = _____ kg Convert mass from g to kg. Calculate its weight (use equation). W = _____ N Draw and label the force vectors on the wood block when hanging from the spring scale

15. Vectors and Forces Procedure #2 Lay your textbook flat on the desk. Place the wood block on top. Draw and label the force vectors on it. Attach the spring scale to it. Determine the force needed to just start it moving. Draw and label the force vectors on it. Determine the coefficient of static friction between the book and wood. Show me equation and work.

16. Vectors and Forces Procedure #3 Remove the wood block and place a penny on top of the book. Raise the lid of the book. Record the angle when the penny begins to slide off. Draw and label the force vectors on the penny just before it slides.

17. Vectors and Forces Procedure #4 Remove the penny and place the wood block back on book. Attach the spring scale again. Pull the wood block along the book at a constant velocity (a=0m/s 2 ). Record the amount of force needed to do this. Determine the coefficient of kinetic friction. Show me equation and work. How does it compare to the static coefficient? Explain your results.

18. Test equations – Ch.4&5 v f = v i + a t x = v i t + 1/2 a t 2 v f 2 - v i 2 = 2 a x x = (v f + v i ) t/2 v f = v i - g t y = v i t - 1/2 g t 2 v f 2 - v i 2 = - 2 g y g = 9.8m/s 2 sin  = opposite hypotenuse cos  adjacent hypotenuse tan  opposite adjacent f =  F N W = mg F = ma