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Vector Scalar
A physical
quantity that has
magnitude, unit
and direction
A physical
quantity that has
only magnitude
and unit
Eg. Force, Velocity,
Displacement,
Acceleration
Eg. Speed,
Distance, Mass,
Volume
 Equal Vectors:
Two vectors are equal if the have the
same MAGNITUDE and DIRECTION
 Negative Vector:
A vector that points in the opposite
direction as the positive reference
direction
 Addition of Vectors
MAGNITUDE and DIRECTION is taken
into account
𝑭 𝟏
𝑭 𝟐
𝑭 𝟑
𝑭 𝑻𝒐𝒕 = + +𝑭 𝟏 𝑭 𝟐 −𝑭 𝟑
 Resultant Vector
A single vector that has the same
effect as all the other vectors together
𝑭 𝟏 𝑭 𝟐
𝑭 𝑹
𝑭 𝑹 = 𝑭 𝟏 + 𝑭 𝟐
Draw the following vectors. Use a scale
of 1 cm:1 N
a) 5 N 30°
b) 4 N 20° S van W
c) 5 N 200°
30°
20° 200°
𝑭 𝟏
𝑭 𝟐
𝑭 𝑹
Johnny walks 50 m in the direction
50º. He then turns and walks
another 10 m in the direction 120º.
Determine his displacement by
means of a scale drawing
 Choose a scale
 Choose method to be used
 Draw vectors to scale
 Draw resultant
 Measure the resultant and determine its
direction using a protractor
 Convert the measured value of the
resultant to the real value using the scale
𝑭 𝟏
𝑭 𝟐
𝑭 𝑹
Johnny walks 50 m in the direction
50º. He then turns and walks
another 10 m in the direction 120º.
Determine his displacement by
means of a scale drawing
Determine the magnitude an
direction of the resultant force in the
diagram
20°
5 N
4 N
𝑭 𝟏
𝑭 𝟐
𝑭 𝑹 𝒔 𝟐
= 𝒙 𝟐
+ 𝒚 𝟐
Pythagoras:
𝑭 𝑹
𝟐
= 𝑭 𝟏
𝟐
+ 𝑭 𝟐
𝟐
s
a
t
θ
𝒄𝒐𝒔𝜽 =
𝒂
𝒔
𝒔𝒊𝒏𝜽 =
𝒕
𝒔
𝒕𝒂𝒏𝜽 =
𝒕
𝒂
Calculate the magnitude and
direction of the resultant force in the
diagram
5 N
4 N
θ
𝑹 𝒚
𝑹 𝒙
𝑹
𝒔𝒊𝒏𝜽 =
𝑹 𝒚
𝑹
∴ 𝑹 𝒚 = 𝑹 𝒔𝒊𝒏𝜽
𝒄𝒐𝒔𝜽 =
𝑹 𝒙
𝑹
∴ 𝑹 𝒙 = 𝑹 𝒄𝒐𝒔𝜽
Resolve the following force into its
perpendicular components
8 N
30°
 Resolve each vector into its
perpendicular components
 Add all the x-components
Add all the y-components
𝑭 𝑵𝑬𝑻 𝒙 = 𝑭 𝒙
𝑭 𝑵𝑬𝑻 𝒚 = 𝑭 𝒚
 Calculate the magnitude of the
resultant using pythagoras
 Calculate the direction of the
resultant using trigonometric
relationships
𝑭 𝑹
𝟐
= 𝑭 𝑵𝑬𝑻 𝒙
𝟐
+ 𝑭 𝑵𝑬𝑻 𝒚
𝟐
Calculate the resultant of the forces
in the following diagram
50°
30°
5 N
8 N
4 N

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Vektore 11 e

  • 1.
  • 2. Vector Scalar A physical quantity that has magnitude, unit and direction A physical quantity that has only magnitude and unit Eg. Force, Velocity, Displacement, Acceleration Eg. Speed, Distance, Mass, Volume
  • 3.  Equal Vectors: Two vectors are equal if the have the same MAGNITUDE and DIRECTION  Negative Vector: A vector that points in the opposite direction as the positive reference direction
  • 4.  Addition of Vectors MAGNITUDE and DIRECTION is taken into account 𝑭 𝟏 𝑭 𝟐 𝑭 𝟑 𝑭 𝑻𝒐𝒕 = + +𝑭 𝟏 𝑭 𝟐 −𝑭 𝟑
  • 5.  Resultant Vector A single vector that has the same effect as all the other vectors together 𝑭 𝟏 𝑭 𝟐 𝑭 𝑹 𝑭 𝑹 = 𝑭 𝟏 + 𝑭 𝟐
  • 6.
  • 7. Draw the following vectors. Use a scale of 1 cm:1 N a) 5 N 30° b) 4 N 20° S van W c) 5 N 200°
  • 10. Johnny walks 50 m in the direction 50º. He then turns and walks another 10 m in the direction 120º. Determine his displacement by means of a scale drawing
  • 11.  Choose a scale  Choose method to be used  Draw vectors to scale  Draw resultant  Measure the resultant and determine its direction using a protractor  Convert the measured value of the resultant to the real value using the scale
  • 13. Johnny walks 50 m in the direction 50º. He then turns and walks another 10 m in the direction 120º. Determine his displacement by means of a scale drawing
  • 14. Determine the magnitude an direction of the resultant force in the diagram 20° 5 N 4 N
  • 15. 𝑭 𝟏 𝑭 𝟐 𝑭 𝑹 𝒔 𝟐 = 𝒙 𝟐 + 𝒚 𝟐 Pythagoras: 𝑭 𝑹 𝟐 = 𝑭 𝟏 𝟐 + 𝑭 𝟐 𝟐
  • 17. Calculate the magnitude and direction of the resultant force in the diagram 5 N 4 N
  • 18. θ 𝑹 𝒚 𝑹 𝒙 𝑹 𝒔𝒊𝒏𝜽 = 𝑹 𝒚 𝑹 ∴ 𝑹 𝒚 = 𝑹 𝒔𝒊𝒏𝜽 𝒄𝒐𝒔𝜽 = 𝑹 𝒙 𝑹 ∴ 𝑹 𝒙 = 𝑹 𝒄𝒐𝒔𝜽
  • 19.
  • 20. Resolve the following force into its perpendicular components 8 N 30°
  • 21.  Resolve each vector into its perpendicular components  Add all the x-components Add all the y-components 𝑭 𝑵𝑬𝑻 𝒙 = 𝑭 𝒙 𝑭 𝑵𝑬𝑻 𝒚 = 𝑭 𝒚
  • 22.  Calculate the magnitude of the resultant using pythagoras  Calculate the direction of the resultant using trigonometric relationships 𝑭 𝑹 𝟐 = 𝑭 𝑵𝑬𝑻 𝒙 𝟐 + 𝑭 𝑵𝑬𝑻 𝒚 𝟐
  • 23. Calculate the resultant of the forces in the following diagram 50° 30° 5 N 8 N 4 N