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Vectors and Scalars

Vectors and Scalars. Learning outcomes. Understand scalar and vector quantities Determine resultant vector by graphical method Parallelogram Head to tail method. PHYSICAL QUANTITIES. BASE QUANTITIES. DERIVED QUANTITIES. PHYSICAL QUANTITIES. SCALARS. VECTORS.

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Vectors and Scalars

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  1. Vectors and Scalars

  2. Learning outcomes • Understand scalar and vector quantities • Determine resultant vector by graphical method • Parallelogram • Head to tail method

  3. PHYSICAL QUANTITIES BASE QUANTITIES DERIVED QUANTITIES

  4. PHYSICAL QUANTITIES SCALARS VECTORS

  5. What are scalars and vectors? • Scalar quantities are quantities that have magnitude only. • Two examples are shown below: • Scalar quantities are added or subtracted by using simple arithmetic. • Example: 4 kg plus 6 kg gives the answer 10 kg Measuring temperature Measuring mass

  6. Arrgh A Force What are scalars and vectors? • Vector quantities are quantities that have both magnitude and direction Magnitude = 100 N Direction = Left

  7. What are scalars and vectors? • Examples of scalar and vector quantities

  8. What are scalars and vectors? • Vectors can be represented graphically by arrows. • The length of the arrow represents the magnitude of the vector. • The direction of the arrow indicated the direction of the vector.

  9. Addition of vectors Adding Vectors in a Straight line

  10. Addition of vectors on the same plane If there are two vectors that act on the object at the same time, how do we find the resultant vector on the object?

  11. Addition of vectors on the same plane • Method 1 : Parallelogram Law of Vector Addition • If two vectors acting at a point are represented by the sides of a parallelogram drawn from that point, their resultant is represented by the diagonal which passes through that point of the parallelogram.

  12. Addition of vectors on the same plane • Method 2 : head to tail method

  13. Addition of vectors on the same plane Method 1 & 2 can be done in two ways * Scale drawing * Trigonometry computation Which method should you use? Parallelogram method allows only two vectors to be added at one time, while head to tail method allows more than 2 vectors to be added at one time. Hence, head to tail method is preferred.

  14. Scale drawing way of doing head to tail method Step 1 : Choose a scale and indicate it on a sheet of paper (the best choice of scale is one which will result in a diagram which is as large as possible, yet fits on the sheet of paper). Step 2 : Pick a starting location and draw the first vector to scale in the indicated direction. Label the magnitude and direction of the vector. Step 3 : Starting from where the head of the first vector ends, draw the second vector to scale in the indicated direction. Label the magnitude and direction of the vector. Step 4 : Repeat steps 2 and 3 for all vectors which are to be added. Step 5 : Draw the resultant from the tail of the first vector to the head of the last vector. Label this vector as "Resultant" or simply "R." Indicate direction with double arrows.

  15. Scale drawing way of doing head to tail method Step 6 : Using a ruler, measure the length of the resultant and determine its magnitude by converting to real units using the scale. Step 7 : Using a protractor, measure the direction of the resultant from any one of the vector.

  16. Trigonometry computation way of doing head to tail method Step 1 : Sketch a head to tail diagram (Not to scale) Step 2 : Using trigonometry computation to solve for magnitude of resultant and direction of resultant vector.

  17. Examples Question 1 The figure below shows two forces F1 and F2 acting on a body with an angle of 45° between them. Find the resultant of the two forces. Question 2 A motorboat heads due east at 16 m s-1 across a river that flows due north at 9.0 m s-1 . What is the resultant velocity of the boat? If the river is 136 m wide, how long does it take the motorboat to reach the other side? 40 N 50 N

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