1. Physics I Unit 4 VECTORS & Motion in TWO Dimensions http://hyperphysics.phy- astr.gsu.edu/hbase/vect.html#vec1 Web Sites

2. Objectives: Calculate and / or measure Velocities Vectors using graphical means Calculate and / or measure Velocities Vectors using algebraic means Do Now  Page 117 #1 Homework Unit 4 Lesson 1 IN CLASS: Page 121 Example 1  Pg 121 – 125 Practice Problems: 1-9 ODD:  Pg 141 – 142 Problems: 80 – 89 all  80 – 88 EVEN 

3. Vectors and Scalars A vector has magnitude as well as direction. Some vector quantities: displacement, velocity, force, momentum A scalar has only a magnitude. Some scalar quantities: mass, time, temperature

4. Addition of Vectors – Graphical Methods For vectors in one dimension, simple addition and subtraction are all that is needed. You do need to be careful about the signs, as the figure indicates. 8 km + 6 km = 14 km East 8 km - 6 km = 2 km East

5. Addition of Vectors – Graphical Methods Even if the vectors are not at right angles, they can be added graphically by using the “ Head to Tail ” method: 1. Draw V1 & V2 to scale. 2. Place tail of V2 at tip of V1 3. Draw arrow from tail of V1 to tip of V2 This arrow is the resultant V (measure length and the angle it makes with the x-axis) Same for any number of vectors involved.

6. Addition of Vectors – Graphical Methods The parallelogram method may also be used; 1. Draw V1 & V2 to scale from common origin. 2. Construct parallelogram using V1 & V2 as 2 of the 4 sides. Resultant V = diagonal of parallelogram from common origin (measure length and the angle it makes with the x-axis)

7. Addition of Vectors – Graphical Methods If the motion is in two dimensions, the situation is somewhat more complicated. Here, the actual travel paths are at right angles to one another; we can find the displacement by using the Pythagorean Theorem.

9. Objectives: Word Problems with VECTORS Do Now Page 117 #2 Page 121 #4 Homework Pg 141 – 142 Problems: 80 – 89 all Unit 4 Lesson 2 IN CLASS: Pg 125 Section Review Problems: 11 -15 ALL http://hyperphysics.phy- astr.gsu.edu/hbase/vect.html#vec1

10. Adding Vectors by Components Any vector can be expressed as the sum of two other vectors, which are called its components. Usually the other vectors are chosen so that they are perpendicular to each other. Unit 4 Lesson 2

11. Adding Vectors by Components If the components are NOT perpendicular, they can be found using trigonometric functions. Vx = V Cosθ Vy = V Sin θ 1) __________ _________ 2)___________ _________ 3)___________ _________ + Total Vx Total Vy

12. Objectives: -Determine Equilibrium Forces -Determine the motion of an object on an inclined plane with and without friction Do Now  Page 128 #17  Next SLIDE(s) Homework  Page 133-135 Practice Problems: 33- 41 odd Unit 4 Lesson 3 Nov 2 IN CLASS: Pg 133 Example 5 Pg 134 Example 6

13. DO NOW 3 Vector Problem Graphically Analytically Unit 4 Lesson 3 Find the resultant vector (Magnitude and Direction of the THREE FORCE vectors acting on the Object at the origin

14. Solving the components X Components Vx = V Cosθ Ax = 44.0 * COS (28.0) = 38.85 Bx = 26.5 *COS (124) = - 14.82 Cx = 31.0 * COS (270.0) = 0.00 X total = 24.031 Y Components Vy = V SINθ Ay = 44.0 * SIN(28.0) = 20.66 By = 26.5 *SIN(124) = 21.97 Cy = 31.0 * SIN(270) = - 31.0 Y total = 11.63 V = √{[24.031] 2 + [11.63] 2 } V = √{[712.748]} = 26.6973 m/s = 26.7 m/s 3 Vector Problem Θ = Tan -1 {11.63/24.031} Θ = Tan -1 {0.483958} Θ = 25.8225 degrees Θ = 25.8 degrees Unit 4 Lesson 3

15. Objectives: Two Dimensions in Motion Do Now  If F ┴ = F app Cosθ  If F ⁄⁄ = F app SINθ  And  If F g = 2.55 Kg * 9.8 m/s 2 = 25 N  Θ = 15.0 °  What is the Velocity after 10 seconds of the object rolling down a 15.0 degree ramp? Homework  page 135  #’s 38 -45 ALL Unit 4 Lesson 5 NOV 5 IN CLASS: A 62 kg skier is going down a 37 degree slope. The coefficient of friction is 0.15. How fast is the skier going after 5.0 sec?

16. Grade quiz Grade quiz Now  A 62 kg skier is going down a 37 degree slope. The coefficient of friction is 0.15.  How fast is the skier going after 5.0 sec?  Vf = ______________ solution  F N = F ┴ = F g Cosθ  = mg(Cosθ)  = 62*9.8*(Cos37) = 485.2509N  If F ⁄⁄ = F g SINθ  = mg(Sinθ)  = 62*9.8*(Sin37) = 365.6628N  F net = F app - F fric  F net = F ⁄⁄ - μmg(Cosθ)  F net = 365.6628N – μ 485.2509N  F net = 365.6628N – ( 485.2509N  F net = 365.6628N – ( 0.15) 485.2509N  F net = 298.8752 N = ma  a = F net /m = 298.8752 /62 = 4.7238 m/s 2  Vf = Vi + at = (4.7238 m/s 2 )* (5.0)  Vf = 23.6190 = 2.4 X 10 1 m/s Unit 4 Lesson 5A NOV 6

17. Objectives: Multiple Vectors Do Now  Vector 1 = 42.5N @ 56.0 Degrees  Vector 2 = 75.1 N @ 245.0 deg  Vector 3 = 10.5 N @ 315.0 deg  Mass = 15.5 Kg  Find F net = ___________  Find Vel (5 sec)= _________  Find Distance (5 sec) = _________ Homework  Page 159 # 23, 25 Unit 4 Lesson 6 Nov 6 IN CLASS: Solve** V x = Vi COS  V x Total = V y = Vi SIN  V y Total = V resultant = √{[V x Total] 2 + [V y Total] 2 }

18. Objectives: Adding Vectors ALGEBRAICALLY Forces in Equilibrium Do Now 1  A vector has a Magnitude of 10.0 Newton’s, 30.0  from the horizontal.  Find the “X” component of the vector :  Find the “Y” component of the vector : Homework  Page 142  #’s 88, 90, 92, 94, 95, 96  97 HONORS Unit 4 Lesson 7 Nov 8 DO NOW 2: What is the actual magnitude and the direction of a boat if it is heading due NORTH (0 degrees) at 3.0 m/s on a river that is flowing due EAST (90 degrees) at 2.0 m/s and a wind that is blowing @ 5.0 m/s to the North East (30 degrees)?

19. DO NOW: What is the Frictional Force required to keep a 10.0 Kg block from sliding down a 25 degree incline? Unit 4 Lesson 7 Nov 9 IN CLASS 1: Romac hangs his 50.0 Kg Repair sign from two wires that make a 90.0 degree angle between themselves and a 45.00 degree angle from the horizontal. What is the tension on each wire? Equilibrium 50.0*9.801 = 490.0 N 490 / 2 = 245.0 Sin (45) = 174.94785 / Hyp Hyp = 174.94785 / Sin (45) = 45.00 90.0

20. Objectives: Exam Review Do Now Homework  Putting it all together Unit 4 Lesson # IN CLASS: