GenPhy1W2L1 Scalar and Vector PDF

12th grade Scalar and Vector Week 2 Lesson 1  Vector Table of contents Resolution using 01 Scalar and 03 Pythagorean. Vector. Theorem and Tangent...

12th grade Scalar and Vector Week 2 Lesson 1  Vector Table of contents Resolution using 01 Scalar and 03 Pythagorean. Vector. Theorem and Tangent Function Vector Resolution 02 04 Vector using. Representation. Component and Addition Method Quote for Today! 01. Scalar and Vector Fundamental Derived 02. Vector Representation How to read and draw Vectors? Vectors are illustrated using a straight arrow. The tail is the origin while the head is the terminal. Vector arrows should be placed on the cartesian plane to illustrate the direction which can be in cardinal or polar form. Cardinal Directions are North, West, South and East. Polar Directions are in terms of angles.  = 20 units, 30o North of east = 20 units, 60o East of North (NE) = 20 units, -3300 = 10 units, 60o North of east 30 o = 10 units, 30o East of North (NE) 30o = 10 units, -3000 Let’s say that each square is equal to 1 units, How can we read Vector ? Vector Addition Adding vectors can be resolved geometrically because of their directions. The sum of the vectors is commonly known as Resultant Vector. It can be expressed as: = + + …. + The Resultant vector can be determined by Graphical Solution and Analytical Solution Graphical Solution Parallelogram Polygon Method Method Known as Tail-Head Known as Tail-Tail Method. Method. Connect the tail of Both tails of the two the first vector at the vectors are connected at origin of the cartesian the origin of the cartesian plane and the succeding plane. At each head of the tails of vectors are vectors, draw line parallel connected at the head of to the other the last vector drawn. Polygon Method Sample Problem: Find the Resultant of the two forces acting on an object by using polygon method: = 10.0 N, 20o west of south and = 16.0 N, east. (1 cm = 2N) Given: = 10.0 N, 20o west of south = 16.0 N, east. Find: Resultant vector using polygon method Polygon Method Solution: Using a scale 2 N = 1 cm, scaled magnitude should be drawn on cartesian plane 1. Prepare graphing paper, marker or pencil and protractor. Draw cartesian plain. 2. Draw the first vector. Using a protractor, locate the 20 o west of south. Put a mark for the arrow representation of vector 3. Draw the 5 cm length as the scaled magnitude of vector from the origin of the cartesian plane. 4. Label as vector 5. Connect vector from the head of the vector following the same procedures of the previous vector. Polygon Method Solution: Using a scale 1 N = 1 cm, scaled magnitude should be drawn on cartesian plane 6. Draw the Resultant vector from the origin of the first vector to the head of the last vector. 7. The Resultant vector if in the fourth quadrant. Measure the angle within the quadrant. 8. Measure the length of the Resultant vector. 9. Write the Resultant vector.  7.8 cm = 7.8 cm = 15.6 N 5 cm = 15.6 N, 530 east of south = 15.6 N, 370 south of east = 15.6 N, 3230 200 = 15.6 N, -370 8 cm Parallelogram Method Sample Problem: Find the Resultant of the two forces acting on an object by using polygon method: = 10.0 N, 20o west of south and = 16.0 N, east. (1 cm = 2N) Given: = 10.0 N, 20o west of south = 16.0 N, east. Find: Resultant vector using parallelogram method Parallelogram Method 1. Construct the two vectors in the same origin of a cartesian plane using protractor and ruler 2. At the head of each vector, draw a line parallel to each other. 3. Draw the resultant vector from the origin to the point where parallel lines intersect and measure the length and the angle. 4. Write the Resultant vector.  7.8 cm = 7.8 cm = 15.6 N = 15.6 N, 530 east of south = 15.6 N, 370 south of east = 15.6 N, 3230 200 = 15.6 N, -370 Clarissa walks 9.0 m to the east and then runs 12 m in a direction of 750 south of east. Find the resultant vector using polygon and parallelogram method. 3m = 1 cm Analytical Solution Component Triangle Method Method Is used when the vectors Is done by taking each part are connected tail to head, of a vector along the axes and with the resultant of a cartesian plane. vector will form triangle. Solving for components is If the triangle formed is a done by using sine and right triangle, use cosine function; Pythagorean Theorem and Finding the magnitude and the Tangent function; the angle of the resultant If the traingle formed is an vector is done using the acute or an obtuse Pythagorean theorem and triangle, use law of sine the Tangent Function, and cosine. respectively  Pythagorean Theorem To determine Direction Tangent Functions To find Magnitude Triangle Method Sample Problem: Find the Resultant of the two forces acting on an object by using Triangle method: = 10.0 N, 20o west of south and = 16.0 N, east. (1 cm = 2N) Given: = 10.0 N, 20o west of south = 16.0 N, east. 200 Find: Resultant vector using triangle method Triangle Method The angle between and is 700. (Acute angle) Use the cosine law to determine magnitude of. = = == = 15.7 N To locate the direction, compute first the angle between and using the sine law. ( ) ( ) 0 0 = −1 𝐵𝑠𝑖𝑛 70 − 1 (16.0 𝑁 ) 𝑠𝑖𝑛70 0 0 𝜃= 𝑠𝑖𝑛 𝑅 𝜃=𝑠𝑖𝑛 15.7 𝑁 𝜃=73.3 −20 = 15.7 N, 53.30 east of south = 15.7 N, 36.70 south of east Component Method Sample Problem: Find the Resultant of the two forces acting on an object by using Component method: = 10.0 N, 20o west of south and = 16.0 N, east. (1 cm = 2N) Given: = 10.0 N, 20o west of south = 16.0 N, east. 200 Find: Resultant vector using component method Component Method Compute the components of each vector. Component Component = A sin θ = 16.0 N = (10.0 N) sin 200 = 3.42 N (since direction is west of south) = -3.42 N = A cos θ =0 = (10.0 N) cos 200 = 9.40 N (since direction is west of south) = -9.40 N Component Method Solve for the Resultant component. Solve for the Resultant magnitude angle θ. Component = tan θ = = Ax + Bx = tan θ = = (-3.42 N) + (16.0 N) = Θ = tan-1 -0.747 N = 12.58 N = Θ = -36.750 or 36.80 south of east = 15.7 N = Ay + By = (-9.40 N) + (0) = -9.40 N = 15.7 N, 36.8 south of east = 15.7 N, 53.2 east of south = 15.7 N, -36.80 = 15.7 N, 323.20 Clarissa walks 9.0 m to the east and then runs 12 m in a direction of 750 south of east. Find the resultant vector using triangle and component method. Asynchronous Task Answer the following in your notebook. 1. A dog, in following a lizard, goes 5 m east, turns 4 m north, and then goes 10 m west. Find the magnitude and the direction of the dog’s resultant displacement using the graphical method. 2. Using a convenient scale, find the resultant of these vectors graphically: 16 m at 1400 with the positive x-axis and 10 m at 300 with the positive x-axis. 3. Using the component method, find the resultant of these vectors: 8 N along the positive x-axis and 6 N making an angle 450 with the x-axis. 4. An object is moved 8.0 cm towards the positive x-axis and then 6.0 cm at the angle of 60 x-axis. Find the resultant displacement. 5. A 100-N force is making an angle of 600 with the horizontal. Find the vertical and horizontal components of the force. Performance Task  Resultant-Equilibrant Objective: Determine the resultant of concurrent vector forces Materials: 2 spring balances 1 100-g mass 2 iron stand 2 strong string Protractor Ruler Pencil and pen Graphing paper Lab Activity Sheet 3-5 pcs Short Bond Paper