GENERAL PHYSICS: UNDERSTAND VECTORS FOR STEM 12

Gen Physics for STEM 12

1. UNDERSTANDING VECTORS

2. Objectives: By the end of this lesson, you will be able to: Differentiate a Vector from a Scalar quantity Demonstrate how to add vectors graphically and by component method. Show patience in finding the resultant vector.

3. Identifying Scalars and Vectors Physical quantities can be specified completely by giving a single number and the appropriate unit. 1. a TV program lasts 40 min 2. the distance between two posts is 50 m

4. A physical quantity that can be specified completely in this manner is called a scalar quantity . A scalar is a quantity that is completely specified by its magnitude and has no direction. Example mass, volume, distance, temperature, energy, and time.

5. A vector is a quantity that includes both a magnitude and a direction. Example velocity, acceleration, and force.

6. Vectors are arrows that represent two pieces of information: a magnitude value (the length of the arrow) and a directional value (the way the arrow is pointed).

7. In terms of movement, the information contained in the vector is the distance traveled and the direction traveled. Vectors give us a graphical method to calculate the sum of several simultaneous movements.

8. We draw a vector from the initial point or origin (called the “tail” of a vector) to the end or terminal point (called the “head” of a vector), marked by an arrowhead. Magnitude is the length of a vector and is always a positive scalar quantity.

9. To sum it up, a vector quantity has a direction and a magnitude, while a scalar has only a magnitude. You can tell if a quantity is a vector by whether it has a direction associated with it.

10. Adding Vectors Using Pythagorean theorem Consider the following examples below. Example 1: Blog walks 35 m East, rests for 20 s and then walks 25 m East. What is Blog’s overall displacement? Solve graphically by drawing a scale diagram. 1 cm = 10 m Place vectors head to tail and measure the resultant vector. Solve algebraically by adding the two vectors acting in the same direction. R= 35 m East + 25 m East = 60 m East

11. Example 2: Blog walks 35 m [E], rests for 20 s and then walks 25 m [W]. What is Blog’s overall displacement? Using algebraic solution, we can still add the two vectors acting in opposite direction. We can only do this because the vectors are parallel. We must make one vector negative to indicate opposite direction.

12. R= 35 m East + 25 m West = 35 m East + – 25 m East = 10 m East

13. If the vectors are acting at a certain angle, the resultant vector is determine by: Graphical method a. Parallelogram b. Polygon 2. Analytical or Mathematical method a. Trigonometry b. Component

14. Example 3: Eric leaves the base camp and hikes 11 km, north and then hikes 11 km east. Determine Eric's resulting displacement.

15. Example: A student drives his car 6.0 km, North before making a right-hand turn and driving 6.0 km to the East. Finally, the student makes a left-hand turn and travels another 2.0 km to the north. What is the magnitude of the overall displacement of the student?

16. But if the three vectors are added in the order 6.0 km, N + 2.0 km, N + 6.0 km, E,

17. Vector Addition: Component Method When vectors to be added are not perpendicular, the method of addition by components described below can be used. To add two or more vectors A, B, C, … by the component method, follow this procedure:

18. Sample problem: An ant crawls on a tabletop. It moves 2 cm East, turns 3 cm 40O North of East and finally moves 2.5 cm North. What is the ant’s total displacement?