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Chapter 4 Vectors

Chapter 4 Vectors. Vector quantities have both magnitude and direction Scalar quantities only have magnitude Velocity, acceleration, displacement, and Force are vector quantities. Vector Addition. 1.5 N. 2 N. Resultant = 3.5N. The resultant is the sum of the vectors.

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Chapter 4 Vectors

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  1. Chapter 4 Vectors • Vector quantities have both magnitude and direction • Scalar quantities only have magnitude • Velocity, acceleration, displacement, and Force are vector quantities

  2. Vector Addition 1.5 N 2 N Resultant = 3.5N The resultant is the sum of the vectors

  3. Vector Addition 1.5 N 2 N Resultant = - 0.5N The resultant is the sum of the vectors

  4. Vector addition • When doing vector addition graphically, the vectors must be drawn to scale and in the correct direction. • The resultant is found by adding them “Tip to Tail” 5 m/s -7m/s Resultant = -2m/s The resultant is drawn from the initial reference point to the tip of the last vector

  5. Vector addition at Right Angles to each other • You can never add 2 vectors “Tail to Tail” 5 N 20 N One of the vectors needs to be moved to the “tip” of the other So that it is “Tip to Tail”

  6. Vector addition at Right Angles to each other R 5 N θ 20 N c2= a2+ b2 C2 = (20 N)2+ (5N)2 Resultant = 20.6 N

  7. Trig. Functions • Sin θ= Opp. Hypotenuse Cos θ = Adj Hypotenuse Tan θ = Opp Adj.

  8. Vector addition at Right Angles to each other R 5 N θ 20 N θ = 14° Tan-1θ =opp adj Tan-1θ = 5N 20N

  9. Vector addition at Right Angles to each other The final answer is 20.6 N @ 14° R 5 N θ 20 N

  10. Vectors in all quadrants A plane flies due west at 125 m/s. A wind blows due North at 15 m/s. What is the plane’s velocity? 15 m/s 125 m/s One of the vectors needs to be moved so that it is “tip to tail”

  11. Vectors in all quadrants A plane flies due west at 125 m/s. A wind blows due North at 15 m/s. What is the plane’s velocity? 15 m/s 15 m/s 125 m/s

  12. Vectors in all quadrants A plane flies due west at 125 m/s. A wind blows due North at 15 m/s. What is the plane’s velocity? 15 m/s r 15 m/s θ 125 m/s

  13. Vectors in all quadrants A plane flies due west at 125 m/s. A wind blows due North at 15 m/s. What is the plane’s velocity? 15 m/s θ 125 m/s c2= (15m/s)2 + (125m/s)2 Resultant = 125.9 m/s

  14. Vectors in all quadrants A plane flies due west at 125 m/s. A wind blows due North at 15 m/s. What is the plane’s velocity? 15 m/s θ 125 m/s Tan-1 θ = 15m/s 125 m/s θ = 6.8° N of W Or 173.2°

  15. Vectors in all quadrants A plane flies due west at 125 m/s. A wind blows due North at 15 m/s. What is the plane’s velocity? 15 m/s θ 125 m/s The final answer is 125.9 m/s @ 6.8 N of W

  16. Components of Vectors • In the previous problems, you were to find the resultant of 2 or more vectors. • In a component problem, the resultant is given along with a direction and you need to determine what 2 vectors would give that resultant. • The 2 vectors are always on the X and Y axis

  17. Components of Vectors • The following symbols are used to represent various components: • Horizontal Force Fh • Vertical Force Fv • Horizontal velocity vh • Vertical velocity vv • Any vector quantity can have 2 components

  18. Component Vectors A rope makes a 30 ° angle with the ground. If you pull with a force of 58 N, what is the vertical and horizontal components of the force? 30°

  19. Component Vectors A rope makes a 30 ° angle with the ground. If you pull with a force of 58 N, what is the vertical and horizontal components of the force? Fv 30° Fh

  20. Vertical ComponentFv Sin 30° = Fv ----- 58 N Fv= (Sin 30°)(58 N) Fv = 29 N Fv 58 N Fv 30° Fh

  21. Horizontal ComponentFh Cos 30° = Fh 58 N Fh= (Cos 30°)(58 N) Fh = 50.2 N Fv 58 N Fv 30° Fh

  22. Fh = 50.2 N Fv = 29 N Fv 58 N Fv 30° Fh

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