THE COMPONENT METHOD (GRADE 12 STEM).pptx

THE COMPONENT METHOD (GRADE 12 STEM).pptx

1. COMPONENT METHOD

2. The component method is generally used when more than two vectors are to be added. The steps involved in adding vectors using component method are as follows: 1. Resolve the given vectors into its horizontal and vertical components. The components may be positive or negative depending on which quadratic the vector is found.

3. Signs of X and Y in the different quadrants quadrant x y 1 + + 2 - + 3 - - 4 + -

4. The component method is generally used when more than two vectors are to be added. The steps involved in adding vectors using component method are as follows. 2. Get the algebraic sum of all the horizontal components. Get also the algebraic sum of the vertical components. These sums represent the horizontal component and the vertical component of the resultant respectively.

5. The component method is generally used when more than two vectors are to be added. The steps involved in adding vectors using component method are as follows. 3.Since the vertical and horizontal components are perpendicular, the magnitude of the resultant may be calculated from the Pythagorean Theorem. R = √ ( ∑x) 2 +(∑y) 2

6. The component method is generally used when more than two vectors are to be added. The steps involved in adding vectors using component method are as follows. 4. From the signs of sum of horizontal components and the vertical components, determine the quadrant where the resultant is. This will indicate the direction of the resultant vector.

7. The component method is generally used when more than two vectors are to be added. The steps involved in adding vectors using component method are as follows. 5. Solve for the angle the resultant makes with the horizontal.

8. SIGNS OF X AND Y IN THE DIFFERENT QUADRANTS QUADRANT X Y 1 + + 2 - + 3 - - 4 + -

9. SAMPLE PROBLEM A jogger runs 4.00 m 40 o N of E, 2.00 m east, 5.20m 30.0 o S of W, 6.50 m S, and then collapses. Find his resultant displacement from where he starred. Solution: Let us tabulate the horizontal and v ertical components of each vector. VECTORS HORIZONTAL COMPONENT VERTICAL COMPONENT A = 4.00 m 40.0 O N of E +4.00 m cos 40.0 o = + 3.06 m + 4.00 m sin 40.0 o = 2.57m B = 2.00 m E + 2.00 m 0.00 C = 5.20 m 30.0 o S of W -5.20 m cos 30.0 o = -4.50 m -5.20 m sin 30.0 o = -2.60 m D = 6.50 m S 0.00 -6.50 m ∑ = +0.560 m ∑ = -6.53m

10. Solving the magnitude of the resultant R, R = √(∑x) 2 + (∑y) 2 R = √(0.56m) 2 + (-6.53m) 2 = 6.55m Θ = arctan ∑y ∑x = arctan - 6.53 0.56 = 85.1 o

11. Since ∑x is positive and ∑y is negative, the resultant must be in the fourth quadrant , hence the direction must be 85.1 o S of E. Thus R is 6.55 m 85.1 o S of E

12. Practice Exercise Find the resultant of the following forces by component method. F 1 = 12N,south, F 2 = 24N, 30 o north of west and F 3 = 15 N, 75 o south of west, and F 4 = 32N, 50 o south of east