Vectors and Scalars Vector and Scalar Quantities Scalar

Vectors and Scalars

Vector and Scalar Quantities Scalar quantities have magnitude only. Vector quantities have magnitude and direction. Note: By definition, all base quantities have no direction and so are scalar. Vectors Displacement Velocity Weight Scalars Distance Speed Mass Acceleration Force Time Energy

Vector Arrows A Vector is often represented using a straight arrow. The length of the arrow represents its magnitude, it’s direction represents the direction of the vector. E. g. A Force of 15 N at an angle 30° to the horizontal 15 N 30° It can have a vertical… = 15 sin 30 = … and horizontal component = 15 cos 30 =

Vector Addition Vectors can be added using a graphical method or by adding perpendicular components. Graphical method (Link)

Example R=a+b a + b =

Example R=a+b a + b =

Example a - b = R = a + (- b) -b

Vector addition using components Any vector can be resolved into two perpendicular components. Often these may be horizontal and vertical. If more than one vector are being added together, the parallel components may be added. E. g. Two forces act on a body as shown. What is the resultant force? 40 N For the 40 N force: Vertical component = 40 sin 60 = 34. 6 N Horizontal component = 40 cos 60 = 20. 0 N 60° 30° 50 N For the 50 N force: Vertical component = 50 sin 30 = (-) 25. 0 N Horizontal component = 50 cos 30 = 43. 3 N

E. g. Two forces act on a body as shown. What is the resultant force? 40 N For the 40 N force: Vertical component = 40 sin 60 = 34. 6 N Horizontal component = 40 cos 60 = 20. 0 N 60° 30° 50 N For the 50 N force: Vertical component = 50 sin 30 = 25. 0 N Horizontal component = 50 cos 30 = 43. 3 N Resultant: Vertical force = 34. 6 - 25. 0 = 19. 6 N Horizontal component = 20. 0 + 43. 3 = 63. 3 N 19. 6 N 63. 3 N Calculate resultant using pythagoras… Resultant force = √ (19. 62 + 63. 32) = 66. 2 N … Now calculate the angle from the horizontal

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