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Mechanics

Mechanics. L2 NCEA Achievement Standard 2.4 Text Book reference: Chapters 7-13. Scalars and Vectors. A scalar quantity is one that has a size (or magnitude ) only Eg. Mass, energy, time A vector quantity is one that has a size and a direction Eg. Force, velocity, momentum. Motion.

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Mechanics

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  1. Mechanics L2 NCEA Achievement Standard 2.4 Text Book reference: Chapters 7-13

  2. Scalars and Vectors • A scalar quantity is one that has a size (or magnitude) only • Eg. Mass, energy, time • A vector quantity is one that has a size and a direction • Eg. Force, velocity, momentum

  3. Motion

  4. Motion

  5. Velocity is calculated by Where d is displacement, t is time and D means “the change in”. Velocity may refer to either average velocity or instantaneous velocity. Constant velocity means that neither the speed nor the direction of the objects motion is changing. Motion

  6. Motion • Acceleration can be calculated by Acceleration is always in the direction of ……………

  7. 1440km hr-1 is 400ms-1 and 100km is 100,000mUsing v=d/t  t=d/v  100,000/400 and t=250s The concorde flies at an average velocity of1440 km hr-1. How long in seconds does it take to fly 100km? How far will the concorde fly in a minute? 24km Anyone not sure how to get that?

  8. 1500m -500m 10ms-1 -3.3ms-1 A car travels 500m to the right turns around and travels another 1000m to the left.The car travelled with a uniform speed and the time taken was 150s.Find: total distance travelled total displacement average speed of the car average velocity of the car

  9. Motion • Acceleration is used to describe motion where the object slows down as well as when it speeds up. • Sometimes the word deceleration is used. • Acceleration is given a negative value when the object is slowing down. • Objects are accelerating when their direction changes, even though their speed may remain constant.

  10. A=2.5ms-2Does everyone know how that was solved? A car accelerates from 10ms-1 to 20ms-1 in 4.0s Calculate its acceleration The same car can brake from 20ms-1 to rest in 5.0s Find the acceleration. a= 4.0ms-2 What is wrong with that answer? a=-4.0ms-2

  11. Task • Measure the speed and velocity of your birds. • I need to see times – distances and calculations • The birds seem to move between 3-12 cms-1 Eric the snail moves at 3.0mms-1 Nsees a bird and takesoff West at 4mms-1. What is his change in velocity?

  12. Vectors • A vector is drawn as a straight, arrowed line. • The arrow points in the direction of the vector • The length of the line represents the size of the quantity

  13. Vectors • Vectors can be multiplied or divided by a scalar • This will change the length of the vector • A negative scalar will reverse the direction • Eg Force F= So 2F= 1/2F= -3F=

  14. d1 d2 d1+ d2 Vectors • Vectors can be added together. • This is done by drawing them “head to tail”. • The result is a vector called a resultant. The resultant has the same effect as the 2 vectors combined. • The order in which they are added does not matter. • Eg d1+d2 Sp p137

  15. v1 v2 v1- v2 -v2 Vectors • Vectors can be subtracted. • This is done by adding a negative vector • Order does matter. • Eg. v1-v2

  16. DV DV=Vf-Vi try the ball thing If the velocity changes this means the object is……… If the object is accelerating there must be a …………..applied in the direction of the acceleration.

  17. Working out DV when Non Linear • Draw a vector representing each motion. • Draw the –Vi vector. • Draw a vector diagram of • DV=Vf-Vi or DV=Vf +-Vi • 4. Using trig and/or pythagarosfind the magnitude and • DIRECTION • ofDV Example on the board

  18. Distance / diplacement versus time… A=Constant velocity (slow) B=Constant velocity (faster) C=Stopped D=Constant velocity (backward) E=Constant velocity (backward past starting point) Displacement(m) C B D A Time (s) E Graphs of Motion

  19. Speed / velocity versus time A=Constant acceleration (low) B=Constant acceleration (high) C=Constant velocity D=Constant deceleration to stop E=Constant acceleration in opposite direction Velocity (ms-1) C B D A Time (s) E Graphs of Motion …area under the graph?

  20. Kinematic Equations • To solve problems involving objects moving in straight lines with constant acceleration. Terms used: • d=distance/displacement (m) • vi=initial velocity (ms-1) • vf=final velocity (ms-1) • a=acceleration (ms-2) • t=time (s)

  21. Kinematic Equations If you know 3 variables you can work out the other 2

  22. Tricks of the Trade • It is assumed you know gravity in any problem which involves rising or falling. • Look out for Vi=0 or Vf=0 in other words from rest or stops. • Make sure you get the signs correct.A rising object will have –acceleration due to gravity acting in the opposite direction to motion.

  23. A grasshopper’s legs extend by 2.0cm in 0.020s when jumping from rest. Assuming the jump is vertical: • What is the average acceleration of the grasshopper while extending it’s legs? • With what velocity does the grasshopper leave the ground? • What is the maximum height the grasshopper can jump?

  24. A flea takes 1.0 millisecond to reach take off speed of 1.2 ms-1 in a jump. • What is it’s average acceleration? • Assuming vertical take off how high does the flea reach?

  25. A jet plane lands on one end of a runway 1.0km long. It’s maximum stopping acceleration is -4.0ms-2 and it takes 20s to come to rest. Does the plane stop in time?

  26. Vectors • Vectors can be resolved into components. • This is done using SOHCAHTOA and/or a2+b2=c2 Vertical Component F 40° Horizontal component

  27. A ship sails from Lyttelton and sets a straight course of 130km in a direction N230E from the New Brighton pier.How far North of the pier is the ship? 130 cos 230 =120km How far east of the pier is the ship? 130 sin230 = 51km

  28. 200N400 FH=Fcos =200 cos 400= 153N A supermarket trolley is pushed with a force of 200N acting at an angle of 400 to the ground. Find the effective horizontal force pushing the trolley along.

  29. Vv = V sin 47.10 = 52.0 sin 47.10= 38.1ms-1 VH=Vcos 47.10 =52.0 cos 47.10= 35.4ms-1 How fast is the ball rising after being hit? How fast is the ball moving horizontally? 52.0ms-1 47.10

  30. Kiwi Bobsled When a green light shows the team accelerates at 2.0ms-2 for 5.0s and then they all jump in. Acceleration still the same. How fast is it going after 5.0s? What is the distance after 5.0s? What is the average speed @ 5.0s? What distance is covered when v=40ms-1

  31. R.McLeod the Cyclist • If he rides at 6.0ms-1 for 6.0s then 12ms-1 for 12s what is his average speed. • Clue: the answer is not 9.0ms-1 10ms-1

  32. Mr KK runs athletically up the stairs at 5.5ms-1. A bunch of chemists are lazily traveling on the esculator at 2.3ms-1. What is the relative speed of Mr KK w.r.t. : The chemists? The ground? A group of shoppers going down a similar esculator?

  33. A train goes by at 95ms-1 • A Man is walking forward at 1.2ms-1 • How fast will the man be moving to an observer on the ground? In the train?

  34. A train goes by at 95ms-1 • The Man is walking towards the back now at 1.2ms-1 • How fast will the man be moving to an observer on the ground? In the train?

  35. A train goes by at 95ms-1 • A Man is walking forward at 1.2ms-1 • How fast will a bird flying 10ms-1 in the same direction see the man moving? How fast will the man see the bird flying?

  36. A train goes by at 95ms-1 A bird is flying 10ms-1 in the same direction as the train. How fast will these people see the bird flying?

  37. A train goes by at 95ms-1 A bird is flying 10ms-1 in the opposite direction as the train. How fast will these people see the bird flying?

  38. Relative Velocity • The velocity of one object in relation to another object. • The velocity an object appears to move at may change if the object measuring is also moving. • The velocity of B relative to A can be calculated by doing this vector subtraction…. (Do Page 49 Questions 3B)

  39. Projectile Motion • Projectile motion is a parabolic shaped motion experienced by moving objects that have only the force due to gravity acting on them. • Eg. Bullets,shotputs,netballs, water jets, rugby balls

  40. Projectile Motion • When dealing with projectiles, the horizontal and vertical components are treated separately. • The horizontal motion is constant velocity (as there are no forces acting in this direction). • The vertical motion is constant acceleration of 10ms-2 due to the force of gravity. • Kinematic Equations for vertical motion Do Page 89 Questions 6B

  41. The canon ball travels 25ms-1 when fired horizontally from the top of a 45m cliff. t=0s t=1.0s t=2.0s For each position find the horizontal, vertical and resultant velocity. t=3.0s

  42. t=1.0s t=2.0s t=0s t=3.0s

  43. What is a projectile path? A projectile path is the movement of an object under the action of gravity only. Type 1 Questions Explain the motion of the golf ball inthe vertical direction. Give a reason for your explanation

  44. acting vertically downwards (constantly decelerating upwards). The ball is moving with a constant acceleration The golf ball’s acceleration is due to gravity. The golf ball’s weight is the unbalanced force acting on it. Type 1 Questions

  45. Back to Golf-Still Type 1 Draw clearly on the diagram a velocity vector to represent the size and direction of the initial velocity (U) of the golf ball.

  46. Golf Analysis What is the size and direction of the ballsspeed ? Quote the answer to the correct number ofsignificant figures. U

  47. Golf Analysis u2 = 202 + 322 u = 37.735925 = 38 ms1tan = 20/32 = 320. What is the time taken for the ball to reach the topof its flight? vf = vi + at  0 = 20 – 10t  t = 2.0 s

  48. Golf Analysis Calculate the maximum vertical height (H) reached by the golf ball at the top of its flight.Acceleration due to gravity is 10 m s-2. vf 2 = vi 2 + 2ad  02 = 202 + 2 x(- 10)H  H = 20 m

  49. Golf Analysis Explain the motion of the golf ball inthe horizontal direction, Give a reason for your explanation. Motion is constant velocity (speed and direction) as there is no unbalanced force acting on the golf ball in the horizontal direction. What is the velocity of the ball at the top of its flight? 32ms-1 horizontal

  50. Golf Analysis Calculate the horizontal distance (R) travelled by the golf ball. v = d / t  32 = R/2t where t = 2t  R = 2 x 32 x 2 = 128m What is the velocity of the ball when it lands? 38ms-1 @320 to the ground What is a force? (type 1)

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