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Vectors & Scalars Physics 11

Vectors & Scalars Physics 11. Vectors & Scalars. A vector has magnitude as well as direction. Examples: displacement, velocity, acceleration, force, momentum A scalar has only magnitude Examples: time, mass, temperature. Vector Addition – One Dimension.

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Vectors & Scalars Physics 11

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  1. Vectors & ScalarsPhysics 11

  2. Vectors & Scalars • A vector has magnitude as well as direction. • Examples: displacement, velocity, acceleration, force, momentum • A scalar has only magnitude • Examples: time, mass, temperature

  3. Vector Addition – One Dimension A person walks 8 km East and then 6 km East. Displacement = 14 km East A person walks 8 km East and then 6 km West. Displacement = 2 km

  4. Vector Addition Example 1: A person walks 10 km East and 5.0 km North Order doesn’t matter

  5. Graphical Method of Vector AdditionTail to Tip Method

  6. Graphical Method of Vector Addition“Head-to-Tail” Method

  7. Graphical Method of Vector Addition Parallelogram Method • Helpful hints about parallelograms: • All four angles add to equal 360o • Opposite angles are equal

  8. Properties of Parallel Lines

  9. Subtraction of Vectors • Negative of vector has same magnitude but points in the opposite direction. • For subtraction, we add the negative vector.

  10. Multiplication by a Scalar • A vector V can be multiplied by a scalar c • The result is a vector cV that has the same direction but a magnitude cV • If c is negative, the resultant vector points in the opposite direction.

  11. Adding Vectors by Components • Any vector can be expressed as the sum of two other vectors, which are called its components (i.e. Vx & Vy). • Components are chosen so that they are perpendicular to each other.

  12. Trigonometry Review Hypotenuse Opposite Adjacent Pythagorean Theorem: (Hypotenuse)2 = (Opposite)2 + (Adjacent)2

  13. Adding Vectors by Components If the components are perpendicular, they can be found using trigonometric functions.

  14. Adding Vectors by Components • The components are effectively one-dimensional, so they can be added arithmetically:

  15. Signs of Components

  16. Adding Vectors by Components • Adding vectors: • Draw a diagram; add the vectors graphically. • Choose x and y axes. • Resolve each vector into x and y components. • Calculate each component using sines and cosines. • Add the components in each direction. • To find the length and direction of the vector, use:

  17. Relative Velocity • Relative velocity considers how observations made in different reference frames are related to each other. Example: A person walks toward the front of a train at 5 km/h (VPT). The train is moving 80 km/h with respect to the ground (VTG). What is the person’s velocity with respect to the ground (VPG)?

  18. Relative Velocity • Boat is aimed upstream so that it will move directly across. • Boat is aimed directly across, so it will land at a point downstream. • Can expect similar problems with airplanes.

  19. Practise Problems • #1, page 70 • #9, page 71 • #12, page 71 • #40, page 73 • #41, page 74

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