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Motion

Learn about scalar and vector quantities, distance and displacement, speed and velocity, and how to graph motion using position, velocity, and acceleration.

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Motion

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  1. Motion Physics: Unit 2

  2. Describing Movement ‘delta’ means ‘change in’ What is a ? And what is a ? vector scalar SCALAR VECTOR Represented by the symbol ‘’ and given by the equation Definitions A quantity specifies direction as well as magnitude (size). A quantity specifies the magnitude but not the direction. Distance is a measure of length of a path taken by an object. Displacement is a measure of the change in position of an object. Are distance and displacement scalar or vector quantities?

  3. Describing Movement Total Distance = Halfway to maths + Back to Locker + All the way to maths = 25 m + 25 m + 50 m = 100 m Applying these concepts to problems eg1. Rowan walks from his locker up to his Maths classroom located 50 metres away in a northerly direction, but realises halfway there that he has forgotten his calculator. He walks back to his locker, collects the calculator and goes to class. a) What is the distance travelled by Rowan after this journey? b) What is the displacement of Rowan after this journey? 50 metres North Distance is a measure of length of a path taken by an object. Displacement is a measure of the change in position of an object.

  4. Describing Movement SCALAR VECTOR Are speed and velocity scalars or vectors? Definitions Speed is ‘how fast an object moves’, or the rate at which an object covers a distance. Velocity is a measure of ‘the rate at which an object changes its position’. Understanding Velocity…… A person moves rapidly - one step forward and one step back - always returning to the original starting position. Because the person always returns to the original position, the motion would never result in a change in position. This would result in a zero velocity, since velocity is defined as the rate at which the position changes. If a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position.

  5. Describing Movement VECTOR Definitions Acceleration is the rate of change of velocity. Scalar or Vector?

  6. Describing Movement Useful Equations Average Speed = , etc.. Average Velocity = Converting km/hr to m/s = Converting m/s to km/hr = Acceleration = or

  7. Describing Movement What distance has Aimee travelled? Total Distance = 1.5 km + 2 km = 3.5 km What was the displacement of Aimee? Find the length of the yellow line using Pythagoras. S S Town Lake 1.5 km (Vector - Give direction) 2 km Start Direction given by . Solve using trigonometry. eg2. After school Aimee walks 1.5 km NORTH into town, then turns right and walks a further 2 km to the lake. The journey took her a total of 30 minutes. a) Sketch Aimee’s journey. Aimee’s displacement was 2.5 km 53.1 T

  8. Describing Movement Total Distance travelled = 3.5 km c) Aimee’s displacement was 2.5 km, 53.1 T Town Lake 1.5 km 2 km Start eg2. (continued) d) What is the average speed for the trip? Express your answer in ms-1 Average Speed = = = In m/s e) What is the average velocity for the trip? Express your answer in ms-1 Average Velocity = at 53.1 ˚T In m/s

  9. Now Do Chapter 5 – Questions 1, 2, 3, 4, 6, 7, 8, 9, 10

  10. Instantaneous Velocity and Speed – using graphs Instantaneous Velocity is the velocity at a particular instant of time. If we plot a graph of an objects Displacement (Position) versus Time, we can find an objects Instantaneous Velocity by calculating the gradient of the graph at a particular point or interval. Similarly, Instantaneous Speedis the speed at a particular instant of time. If we plot a graph of an objects Distance versus Time, we can find an objects Instantaneous Speed by calculating the gradient of the graph at a particular point or interval.

  11. Graphing Motion Position v Time Graph What are they it? What can we use them for? Plot of an objects position (y-axis) versus time (x-axis) Shows the journey of an object over a given period of time Velocity is the rate of change of position, so velocity can be found by calculating the gradient of the graph at a particular instant or over a period of time. ( recall: m = )

  12. Graphing Motion • Plot of an objects velocity (y-axis) versus time (x-axis) • Shows the velocity of an object over a given period of time • Displacement during a time interval is found by calculating the area under the graph • Instantaneous position can only be found if the initial starting position is known • Acceleration is the rate of change of velocity, so acceleration can be found by calculating the gradient of the graph at a particular instant or over a period of time. • ( recall: m = ) Velocity v Time Graph What are they it? What can we use them for?

  13. Graphing Motion • Plot of an objects acceleration (y-axis) versus time (x-axis) • Shows the acceleration of an object over a given period of time • Velocity is found by calculating the area under the graph • If the initial velocity is known, we can use the graph to find the velocity at an instant in time. Acceleration v Time Graph What are they it? What can we use them for?

  14. Graphing Motion Example 1: Position/Velocity/Acceleration v Time Graph

  15. Graphing Motion Example 2: Position/Velocity/Acceleration v Time Graph

  16. Example 2 (cont’d) : Position/Velocity/Acceleration v Time Graph

  17. eg1. During a 100m race between two runners, timekeepers were instructed to record the position of each runner at 3 second intervals. The results can be shown in the table below. a) The runners ran east, a total distance of 100 m. Plot the data on a Position v Time graph Graphing Motion – Position vs Time

  18. Instantaneous Velocity and Speed – using graphs eg1 (cont’d) b) What can be said about the overall velocity of each of the runners? c) Who wins the race? d) Calculate the velocity of each of the runners for 3 – 6 second interval. e) Calculate the average velocity of each of the runners for the entire race.

  19. Instantaneous Velocity and Speed – using graphs eg1 (cont’d) b) What can be said about the overall velocity of each of the runners? Beryl – Velocity changes throughout the race, slowing down for the last half. Sam – Velocity is constant throughout the race. We can see this by looking at the gradient of the lines. c) Who wins the race? They come a draw. This can be seen as the graph for each runner ends at 15s for both runners. d) Calculate the velocity of each of the runners for 3 – 6 second interval. Beryl Sam

  20. eg1 (cont’d) e) Calculate the average velocity of each of the runners for the entire race. Beryl Sam Instantaneous Velocity and Speed – using graphs

  21. What is the acceleration of the hovercraft at 200 sec? • What is the acceleration of the hovercraft at 400 sec? • What is the acceleration of the hovercraft at 800 sec? • What is the total distance travelled by the hovercraft?

  22. What is the acceleration of the hovercraft at 200 sec? • Given by the rate of change of the graph (ie. the gradient) • Choose any two points from the first section of graph. • What is the acceleration of the hovercraft at 400 sec? • Given by the rate of change of the graph (ie. the gradient) • Choose any two points from the middle section of graph. • What is the acceleration of the hovercraft at 800 sec? • Given by the rate of change of the graph (ie. the gradient) • Choose any two points from the third section of graph. • What is the total distance travelled? • Distance = Area under velocity-time graph • = Triangle + Rectangle + Triangle

  23. Now Do Simulation Activity

  24. Now Do Chapter 5 – Questions 11, 12, 14, 13

  25. Motion Equations – constant acceleration without graphs For straight line motion with constant acceleration, a number of formulae can be used to represent the motion and calculate unknown quantities. The terms which we use in the equations are given by: u = initial velocity (m/s) v = final velocity (m/s) a = acceleration (m/s2) t = time interval (t) x = displacement (m)

  26. Motion Equations – constant acceleration without graphs The equations which we use to calculate unknown values are given by:

  27. Motion Equations – constant acceleration without graphs eg1. A coin is dropped into awishing well and takes 2.0 s to reach the water. The coin accelerates at a constant 10 m/s2. Find: a) The coins velocity as it hits the water b) How far does the coin fall before hitting the water?

  28. Motion Equations – constant acceleration without graphs eg2. A parked car with the handbrake left off rolls down a hill in a straight line with a constant acceleration of 2.0 m/s2. It stops after colliding with a brick wall at a speed of 12 m/s. a) For how long was the car rolling? b) How far did the car roll before colliding with the wall?

  29. Now Do Chapter 5 – Questions 21, 22, 23, 24

  30. Force • A force is a push or pull applied by one object on another. • Forces can include: • - Actions imposed by people eg. Pushing a door open • - Gravity • - Friction eg. Resistance caused by rough surfaces • - Air Resistance • Force is a vector quantity as it has both a magnitude and direction. • Force is measured in Newtons (N).

  31. Force We can draw diagrams representing forces acting on an object. We represent each force with an arrow. The arrow shows the direction of the force, the length of the arrow indicates its size. An apple falls from a tree. What forces are acting on the falling apple? Air Resistance (upward) Weight (downward due to gravitational pull)

  32. Newtons First Law An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. Newtons Laws A book sitting on a bench A book sliding right across a bench

  33. Newtons Second Law The acceleration of an object is dependent upon two variables – the net force acting upon the object and the mass of the object. This can be calculated using….. Net Force = Mass (kg) x Acceleration (m/s2) The direction of the net force is in the same direction as the acceleration. If we are referring to the acceleration due to gravity, then we use a (or g) = 10 m/s2 This gravitational pull is unique to Earth. Other planets have different gravitational field strength. Newtons Laws

  34. Newtons Second Law eg1. Calculate the Force of a 100 g apple falling from a tree. eg2. Calculate the acceleration that results when a 12 N force is applied to a 3 kg object. Newtons Laws

  35. Newtons Second Law Weight is a force which can be calculated using this formula. eg3. Calculate the weight of a 70kg person. We use acceleration due to gravity = 10 m/s2 Newtons Laws

  36. Newtons Laws • Newtons Third Law • For every action there is an equal and opposite reaction. • If two objects interact with each other, they exert forces upon each other. • Forces always come in pairs - equal and opposite action-reaction force pairs.  • The size of the forces on the first object equals the size of the force on the second object. • The direction of the force on the first object is opposite to the direction of the force on the second object. • These two forces are called action and reactionforce.

  37. Newtons Laws Newtons Third Law For every action there is an equal and opposite reaction. When you sit in your chair, your body exerts a downward force on the chair and the chair exerts an upward force on your body. There are two forces resulting from this interaction - a force on the chair and a force on your body– the action-reaction forces. We call the reaction forces the ‘Normal’ reaction force.

  38. Forces in Action Apple in a tree vs Apple falling from a tree Forces are balanced, the apple stays in the tree Forces are not balanced, the Net force is downward, the Apple falls from the tree

  39. Now Do Chapter 6 – Questions 1, 2, 3, 5, 7

  40. Using what we know about Forces and Newtons Laws, we can start to draw diagrams to indicate the forces acting on objects. First lets recall Newtons First Law…. An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. This means that if an object is stationary or moving with a constant velocity (ie. Acceleration = 0 m/s2), then forces acting on the object are balanced and we say that the Net Force, The Net Force

  41. Recall: Newtons First Law An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. The Net Force A book sitting on a bench A book sliding right across a bench

  42. Using this we can start to draw diagrams to indicate the forces acting on objects and calculate Forces acting on them. eg1. What is the Net force acting on this purple box? eg2. What is the Net Force acting on the red box? eg3. If the Net Force = 0, calculate the missing force on the system. The Net Force 100 N WEST 20 N WEST vs 220 220 – 170 = 50 Missing Force = 50 N WEST

  43. eg4. Calculate the Net Force on the system of Forces shown in the diagram. Right Angled triangle: NET FORCE If not right angled consider separately: The Net Force

  44. Eg4 continued... Calculate the Net Force on the system of Forces shown in the diagram. Otherwise consider separately: NET FORCE = 282.84 N EAST The Net Force

  45. eg5. a) Calculate the Net Force on the system of forces shown in the diagram. b) If the Net Force of the system = 0, what additional force needs to be applied? The Net Force 200 N 100 N WEST

  46. eg6. If the Net Force = 200 N EAST, find the missing force in the system below. The Net Force Two triangles Net = 73.2 N EAST But if Net Force = 200 N EAST, Missing force is: Another Force of 200 – 73.2 = 126.8 N EAST is required

  47. Now Do Chapter 6 – Questions 9, 10, 11

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