1 / 31

Chapter 4 Vectors

Chapter 4 Vectors. The Cardinal Directions. Vectors. An arrow-tipped line segment used to represent different quantities. Length represents magnitude. Arrow head represents direction. Vector Addition in 1 - Dimension.

price-bates
Download Presentation

Chapter 4 Vectors

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Chapter 4 Vectors The Cardinal Directions

  2. Vectors • An arrow-tipped line segment used to represent different quantities. • Length represents magnitude. • Arrow head represents direction.

  3. Vector Addition in 1 - Dimension • When vectors point in the same direction we add them just as we would add any two numbers.

  4. Vector Addition in 1 - Dimension • When vectors point in opposite directions we subtract them just as we would with any two numbers.

  5. Vector Addition in 2-Dimensions • Vectors in 2-dim are added by placing the tail of one to the head of another.

  6. Remember This?

  7. Addition of Several Vectors • The order of addition is not important. • R is called the resultant.

  8. Independence of Vector Quantities • Perpendicular vectors can be treated independently of each other.

  9. Analytical Method of Vector Addition • The sum of any two vectors can be determined using trigonometry.

  10. Adding Perpendicular Vectors

  11. Angle θ is = • 25 deg • 14 deg • 35 deg • 45 deg

  12. Angle θ is = • 25 deg b) 14 deg c) 35 deg d) 45 deg

  13. Vector Components • We can take two vectors and replace them with a single vector that has the same effect. This is vector addition. • We can start with a single vector and think of it as a resultant of two perpendicular vectors called components. • This process is called vector resolution.

  14. Example

  15. Example 2

  16. Problem Solving Strategy • In resolving vectors choose the most convenient axis according to the specifics of the problem. • Choose the axis that simplifies the solution. • Axis may be up-down, left-right, east-west or north-south. • Be sure to specify the positive direction for each.

  17. Adding Vectors at Any Angle • Vector resolution is the method used. • Resolve all vectors into x and y components. • Add all x’s and all y’s together. • Use xtot and ytot to create a right triangle. • Use Pythagorean formula to calculate resultant and trig to find angle.

  18. R is = ? • 15 N • 12 N • 20 N • 11N

  19. R is = ? • 15 N • 12 N • 20 N • 11N

  20. Θ is = ? • 53 deg • 35 deg • 25 deg • 45 deg

  21. Θ is = ? • 53 deg • 35 deg • 25 deg • 45 deg

  22. Applications of Vectors Vectors can be used to represent: • displacement • velocity • acceleration • force

  23. Equilibrium • When the net force is zero, the object is in equilibrium. • When the vector sum of the forces is not zero, a force can be applied that will produce equilibrium. This force is called the equilibrant. • It is equal in magnitude but opposite in direction to the resultant.

  24. 3 Forces in Equilibrium: • produce a net force. • produce a triangle for a vector diagram. • are called an equilibrant. • produce an acceleration.

  25. 3 Forces in Equilibrium: • produce a net force. • produce a triangle for a vector diagram. • are called an equilibrant. • produce an acceleration.

  26. Gravitational Force and Inclined Planes • Gravitational force always points towards center of Earth. • This is weight. • Choose one axis parallel to the plane and the other perpendicular to it.

  27. Formulas • R2 = A2 + B2 – 2AB cos Θ • Ax = A cos Θ • AY = A sin Θ • A = Ax + AY

More Related