chapter 2 vectors, scalars and their examples.pptx

Vectors and its examples

1. VECTORS

2. SCALAR A SCALAR quantity is any quantity in physics that has MAGNITUDE ONLY Number value with units Example Magnitude Speed 35 m/s Distance 25 meters Age 16 years

3. VECTOR A VECTOR quantity is any quantity in physics that has BOTH MAGNITUDE and DIRECTION Example Magnitude and Direction Velocity 35 m/s, North Acceleration 10 m/s 2 , South Force 20 N, East An arrow above the symbol illustrates a vector quantity. It indicates MAGNITUDE and DIRECTION

4. VECTOR APPLICATION ADDITION : When two (2) vectors point in the SAME direction, simply add them together. EXAMPLE : A man walks 46.5 m east, then another 20 m east. Calculate his displacement relative to where he started. 66.5 m, E MAGNITUDE relates to the size of the arrow and DIRECTION relates to the way the arrow is drawn 46.5 m, E + 20 m, E

5. VECTOR APPLICATION SUBTRACTION : When two (2) vectors point in the OPPOSITE direction, simply subtract them. EXAMPLE : A man walks 46.5 m east, then another 20 m west. Calculate his displacement relative to where he started. 26.5 m, E 46.5 m, E - 20 m, W

6. NON-COLLINEAR VECTORS When two (2) vectors are PERPENDICULAR to each other, you must use the PYTHAGOREAN THEOREM Example : A man travels 120 km east then 160 km north. Calculate his resultant displacement. 120 km, E 160 km, N the hypotenuse corresponds to the RESULTANT HORIZONTAL COMPONENT VERTICAL COMPONENT START FINISH

7. WHAT ABOUT DIRECTION? In the example, DISPLACEMENT is asked for and since it is a VECTOR quantity, we need to report its direction. N S E W N of E E of N S of W W of S N of W W of N S of E E of S NOTE: When drawing a right triangle that conveys some type of motion, you MUST draw your components HEAD TO TIP . N of E

8. NEED A VALUE – ANGLE! Just putting N of E is not good enough (how far north of east ?). We need to find a numeric value for the direction. N of E 160 km, N 120 km, E To find the value of the angle we use a Trig function called TANGENT. θ 200 km So the COMPLETE final answer is : 200 km, 53.1 degrees North of East  

9. What are your missing components? Suppose a person walked 65 m, 25 degrees North of East. What were his horizontal and vertical components? V= 65 m 25 o V x = ? V y = ? The goal: ALWAYS MAKE A RIGHT TRIANGLE! To solve for components, we often use the trigonometric functions sine and cosine.      

10. Resolution of Vectors A B C A= 50 N, 25 N of E B= 20 N, 30 N of W C= 30 N, S Vectors Summation of x-components Summation of y-components A 50 N (cos25 ) 45 N 50 N (sin25 ) 21 N B -20 N (cos30 ) -17 N 20 N (sin30 ) 10 N C 10 N (cos90) 0 N -10 N (sin90) -10 N ∑V x =28 N ∑ V y =21 N    

11. Example A storm system moves 5000 km due east, then shifts course at 40 degrees North of East for 1500 km. Calculate the storm's resultant displacement. 5000 km, E 40 1500 km H.C. V.C. 5000 km + 1149.1 km = 6149.1 km 6149.1 km 964.2 km R θ The Final Answer: 6224.2 km @ 8.92 degrees, North of East

12. Solve for the following: summation of components along x or ΣV x summation of components along y or ΣV y net displacement or R direction or θ

13. Resolution of Vectors A B C A= 50 N, 25 N of E B= 20 N, 30 N of W C= 30 N, S Vectors Summation of x-components Summation of y-components A B C

14. Seatwork Problem: Three forces act on a point object, and you need to determine the resultant force. Force 1 (F₁) : 10 N acting at an angle of 30° above the positive x-axis. Force 2 (F₂) : 15 N acting at an angle of 120° from the positive x-axis. Force 3 (F₃) : 20 N acting at an angle of 225° from the positive x-axis.

15. Quiz No. 2 PART 1. Rewrite the following vectors in terms of its components (unit vectors). 20 N, 30 o North of East 5 km, 15 o South of West 2.3m/s 2 , 40 o East of South PART 2. Give the corresponding vector (magnitude and direction) of the following components. V x =15m, V y = 10m V x =100N, V y = 250N

16. Part 3 .Refer to the diagram below. By using component method, solve for the: 1. summation of Fx 2. summation of Fy 3. magnitude of the net force 4. direction of the net force 5. resultant vector PART 2. Give the corresponding vector (magnitude and direction) of the following components. V x =15m, V y = 10m V x =100N, V y = 250N