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- 1. Stage 2 Physics Section 1Motion in Two Dimensions
- 2. What is motion?What types of motion are there?What causes motion?How to we describe motion in Physics?
- 3. What is a vector?Vector quantities have magnitude (size) anddirection.Scalar quantities have magnitude only.Length represents the vectors magnitude.
- 4. Scalar VectorDistance DisplacementSpeed VelocityMass Acceleration ForceTime weight
- 5. Velocity vector of an angry bird
- 6. Resultant of Two VectorsThe resultant is the sum or the combined addition of two vectorquantitiesVectors in the same direction: 6N 4N = 10 N Vectors in opposite directions: 6m 10 m =
- 7. Vectors• Vectors can be oriented to the gravitational field (up, down or some angle to the horizontal) or compass points (NESW). 5 ms-1 5 ms-1 30o above the horizontal
- 8. Velocity Vectors• Velocity can be resolved into its horizontal and vertical components at any instant. v vV vH
- 9. SOHCAHTOA Hypotenuse Opposite Adjacent
- 10. v vV = v sinvH = v cos
- 11. Example 1Resolve the following velocity vector into its horizontal and vertical components 30o
- 12. Example 1Resolve the following velocity vector into its horizontal and vertical components 30o
- 13. This problem can be solved in two ways(and you need to be able to do both)1. Scale Diagram2. Trigonometry
- 14. 1. Scale diagramBy drawing a vector diagram (using aprotractor and a ruler) to scale we cansimply measure the size of thecomponents ideally the vector should be10 cm or larger (for accuracy)
- 15. 2. Trigonometry vvertical = v sin = 40 sin 30o = 20 m s-1 vhorizontal = v cos30o = 40 cos 30o = 34.6 m s-1
- 16. Example 2Determine the velocity vector with initialhorizontal velocity component of 50 ms –1and vertical 20 ms-1.
- 17. v=? vv= 20 m s-1 vh= 50 m s- 1
- 18. 1. Scale diagram Again we could accurately draw the figure and measure the resultant length and angle to find the direction of v.(Note: You need to have a clear Perspex ruler and a protractor for EVERY test and exam)
- 19. 2. Pythagoras & Trigonometry By Pythagoras theory:v2 = vV2 + vH2 v = v V 2 + vH 2 = 202 + 502 = 2900 = 53.9 m s-1 v=? vv= 20 m s-1 vh= 50 m s- 1
- 20. tan vV/vHtan = 20/50 = 21.8oie. v = 53.9 m s-1 at 21.8o above the horizontal
- 21. Summary – Vectors in 2D• Given any vector quantity in 2D it can be resolved into horizontal and vertical components eg displacement, force, fields etc• Given the horizontal & vertical components you can determine magnitude and direction of the vector (formula)
- 22. Motion in a UniformGravitational Field
- 23. In the absence of gravity objects move with constant velocity in a straight line. An object will remain at rest, or continue to move at a constant velocity, unless a net force acts on it.Note: The following is all in the absence of air resistance.
- 24. When an object falls under theinfluence of gravity, the verticalforce causes a constantacceleration
- 25. vH The resultant motion is a combination of both horizontal and vH verticalvV vV components
- 26. Horizontal Projection While the vertical component undergoes constantIf an object is acceleration.projectedhorizontally, thehorizontal componentmoves with constantvelocity.
- 27. Three equations of motionNote that all the equations have “a” in them –they only apply under CONSTANT acceleration
- 28. Constant vertical acceleration Vertical formulae 2 v 2 v0 2as 1 2Horizontal velocity is constant s vt at 2Horizontal formula v vo at s vH t
- 29. Three equations of motion
- 30. Learning Symbols in PhysicsQuantity Quantity Symbol Units Unit symbol
- 31. ExampleA stone is dropped down a well and takes 3seconds to hit the ground.a) How fast does it hit the bottom?b) How deep is the well?
- 32. A stone is dropped down a well attakes 3 seconds to hit the ground.a) How fast does it hit the bottom?
- 33. b) How deep is the well?
- 34. An arrow is fired upwards at 50ms-1.a) How high does the arrow fly?
- 35. An arrow is fired upwards at 50ms-1.b) How long does the arrow take to hit theground?
- 36. Projectile Motion ProblemsExcept for time, everything can be separated into horizontal and vertical components and treated separately. sV = height V0 s H = range t = time of flight
- 37. Projectile Motion ProblemsHorizontal projection: down is +veUni-level projection: Up is considered positive, and down is negative.(Acceleration due to gravity aV = -9.8ms-2) sV = height V0 s H = range t = time of flight
- 38. Projectile Motion ProblemsAt the top of the parabolic path, vV= 0 ms-1 1 vV 0ms 2 aV 9.8ms sV height V0 sH range t = time of flight
- 39. Projectile Motion ProblemsRemember the time of flight is the time it takes to go up+ down. 1 vV 0ms 2 aV 9.8ms sV height V0 sH range t = time of flight
- 40. Example 1
- 41. Bi-level projection• An object is projected at a height
- 42. Maximum RangeTo get the maximum range sH max in a vacuum(no air resistance) the launch angle must be 45o sH max
- 43. For a projectile launched at ground level find by sample calculation the launch angle that results in a maximum range
- 44. Pairs of launch angles that yield the same range add up to 90o α + θ = ranges Projectile 90o for various angles of launch 500 450 400 350 300height 250 200 150 100 50 0 0 200 400 600 800 1000 1200 range
- 45. α + θ = 90oFind the launch angle that yields the same range as 32oθ = 32 α=? α + θ = 90o
- 46. The Effect of Air ResistanceAir resistance acts in the opposite direction to motion. vertical horizontal
- 47. The Effect of Air Resistance vertical horizontalThis decreases the• height• rangeSlight decrease in time of flight of the projectile
- 48. The magnitude of Fair resistance Fair resistance
- 49. Speed
- 50. ShapeAerodynamicteardrop
- 51. SizeMore surface area = more air resistance
- 52. TextureSmoothRough
- 53. Air densityLow air density = less air resistanceHigh air density = high air resistance
- 54. Projectiles in SportConsider the effect of launch height on range
- 55. As the object has further to fall tflight isincreased.As the object is in the air for longer ittravels farther.
- 56. 45o 41o For objects at h=0 the optimal angle is 45oFor heights › 0θ max height is less than 45o

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