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Physics

Physics. PHS 5042-2 Kinematics & Momentum Displacement & Vectors. PHS 5042-2 Kinematics & Momentum Displacement & Vectors. Distance (travelled) measures the length of the trajectory of a moving object Displacement is the distance between the initial and final positions of movement.

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Physics

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  1. Physics

  2. PHS 5042-2 Kinematics & MomentumDisplacement & Vectors

  3. PHS 5042-2 Kinematics & MomentumDisplacement & Vectors Distance (travelled) measures the length of the trajectory of a moving object Displacement is the distance between the initial and final positions of movement

  4. PHS 5042-2 Kinematics & MomentumDisplacement & Vectors A scale is the mathematical ratio between a length measured on a plan (or map) and the actual measurement it represents Scales tells us the factor by which a measurement must be multiplied in order to obtain the actual measurement Scales have different forms: _graduated _ratio of distances with units (1 cm = 10 km) without units( 1: 1 000 000)

  5. PHS 5042-2 Kinematics & MomentumDisplacement & Vectors Practice Exercises: Page 2.10, Ex 2.3 (distance on map* = 4 cm) Page 2.11, Ex 2.4 (first distance* = 6.5 cm) (second distance* = 2.5 cm)

  6. PHS 5042-2 Kinematics & MomentumDisplacement & Vectors Distance _It is a scalar, that is a quantity that is fully described by a magnitude (or numerical value) alone. Examples: speed, temperature, mass and volume Displacement _It is a vector, that is a quantity that is fully described by both a magnitude and a direction. Examples: velocity, acceleration, momentum and forces

  7. PHS 5042-2 Kinematics & MomentumDisplacement & Vectors Vectors that are equal have: _Same magnitude and same direction Vectors that are not equal have: _Same magnitude, different direction _Same magnitude, opposite direction _Different magnitude, same direction _Different magnitude, different direction

  8. PHS 5042-2 Kinematics & MomentumDisplacement & Vectors Vector’s notation (magnitude + direction): _Initial position: origin point _Final position: terminal point _Using cardinal points: X u[CP] (X: magnitude) (u: unit of measurement) (CP: Cardinal Point, e.g. N, S, E, W) (CP: NE, NW, SE, SW when angle of displacement = 45°) Example: 6 km [E] Displacement of 6 km in East direction

  9. PHS 5042-2 Kinematics & MomentumDisplacement & Vectors Vector’s notation (magnitude + direction): _Initial position: origin point _Final position: terminal point _Using cardinal points: Xu[CP (origin) Angle CP (terminal)] (X: magnitude) (u: unit of measurement) Angle is measured with respect to origin cardinal point Example: 10 km [E30°N] Displacement of 10 km, 30° north of east (with respect to due East) What would the notation be with respect to due North? 10km [N60°E] 10km,60° east of north

  10. PHS 5042-2 Kinematics & MomentumDisplacement & Vectors Vector’s notation (magnitude + direction): _Initial position: origin point _Final position: terminal point _Using Cartesian axes (x vs y): X u A° (X: magnitude) (u: unit of measurement) (A: Angle with respect to positive “x” axis) Example: 5 cm, 135° Displacement of 5 cm, 135° of the “x” axis

  11. PHS 5042-2 Kinematics & MomentumDisplacement & Vectors Vectors notation: Represent: _10 u [N 15° W] _15 u [S 75° E] _25 u, 35° _5 u [W] 5 u [E 35° N]

  12. PHS 5042-2 Kinematics & MomentumDisplacement & Vectors Practice Exercises: Page 2.21, Ex 2.15 Page 2.25 – 2.26, Ex 2.17 & 2.18

  13. PHS 5042-2 Kinematics & MomentumDisplacement & Vectors Example of calculations: _A car travels ten kilometers East, and then five kilometers North. Determine: a) Distance travelled b) Displacement

  14. PHS 5042-2 Kinematics & MomentumDisplacement & Vectors Example of calculations: _A car travels ten kilometers East, and then five kilometers North. Determine: a) Distance travelled 10km + 5 km = 15 km

  15. PHS 5042-2 Kinematics & MomentumDisplacement & Vectors Example of calculations: _A car travels ten kilometers East, and then five kilometers North. Determine: b) Displacement c2 = a2 + b22 c = √(10km)2 + (5km)2 c = 11.18 km

  16. PHS 5042-2 Kinematics & MomentumDisplacement & Vectors Example of calculations: _A car travels ten kilometers East, and then five kilometers North. Determine: b) Displacement c = 11.18 km tanΦ = Opp/Adj tanΦ = 5km/10km tanΦ = 0.5 Φ= tan–(0.5) Φ = 26.6° Displacement is 11.18 km [E 26.6° N]

  17. PHS 5042-2 Kinematics & MomentumDisplacement & Vectors Calculations: _A biker rides four kilometers West, and then heads three kilometers South. Determine: a) Distance travelled b) Displacement

  18. PHS 5042-2 Kinematics & MomentumDisplacement & Vectors Vector addition is commutative. Therefore, the order in which we add vectors does not change the final result Polygon method (tip-to-tail) • Distance between A (x1,y1) and B (x2,y2) is d = √[(x2-x1)2 + (y2-y1)2] • Successive joining of vectors tip-to-tail • Magnitude and direction must remain unchanged • Resultant’s origin is the tail of first vector and its terminal is the tip of the last one

  19. PHS 5042-2 Kinematics & MomentumDisplacement & Vectors Vector addition methods: Polygon method (tip-to-tail) Practice Exercise: Page 2.36, Ex. 2.25

  20. PHS 5042-2 Kinematics & MomentumDisplacement & Vectors Vector addition is commutative. Therefore, the order in which we add vectors does not change the final result Parallelogram method (tail-to-tail) • Distance between A (x1,y1) and B (x2,y2) is d = √[(x2-x1)2 + (y2-y1)2] • Only two vectors can be added • Place vectors tail to tail (same origin) • From the tip of each vector, draw a parallel line to the other vector • The point where these lines intercept is the tip of the resultant • The origin of the resultant is the origin of both vectors (tail-to-tail)

  21. PHS 5042-2 Kinematics & MomentumDisplacement & Vectors Vector addition methods: Parallelogram method (tail-to-tail) Practice Exercise: Page 2.47, Ex. 2.35

  22. PHS 5042-2 Kinematics & MomentumDisplacement & Vectors Vector addition is commutative. Therefore, the order in which we add vectors does not change the final result Component method • Distance between A (x1,y1) and B (x2,y2) is d = √[(x2-x1)2 + (y2-y1)2] • Using Cartesian axes, determine vertical (y) and horizontal (x) components of each vector • Add parallel components algebraically to obtain components of the resultant • Calculate magnitude of resultant • Measure (calculate) direction of resultant

  23. PHS 5042-2 Kinematics & MomentumDisplacement & Vectors Vector addition is commutative. Therefore, the order in which we add vectors does not change the final result 3. Component method Example (Page 2.57) _Three vectors A, B & C are added _From graph: Ax = 7m, Bx = -2m, Cx = 1m so Rx = 6m _From graph: Ay= 3m, By= -5m, Cy= -6m so Ry= -8m _R = √(6m)2+ (-8m)2] R = 10m _Φ = tan – (6m/8m) Φ = 37° , thus Φ = (270 + 37)° Φ = 307° _R = 10 km, 307°

  24. PHS 5042-2 Kinematics & MomentumDisplacement & Vectors Vector addition methods: Component method Practice Exercise: Page 2.59, Ex. 2.39

  25. PHS 5042-2 Kinematics & MomentumDisplacement & Vectors Practice exercises: Page 2.63 – 2.67, Ex 2.40 – 2.47

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