VECTORS IN 2 DIMENSIONS

Transcription

1 Free PowerPoint Templates VECTORS IN 2 DIMENSIONS Sutherland High School Grade

2 SCALAR A physical quantity that has a magnitude and unit only. Example: Mass Time Distance Speed Volume Temperature etc. VECTOR A physical quantity that has a magnitude, unit and direction. Example: Force Weight Displacement Velocity Acceleration Momentum etc.

3 Vectors are represented by arrows. Length = magnitude Arrowhead = direction.

4 Vectors exerted in one dimension are in a straight line and are parallel to either the horizontal or the vertical axes. (So they move either up or down.) Vectors that moves in 2 dimensions form an angle with the axes and can be described in terms of it s x and y coordinates.

5 In the diagram on the right, vector F acts at an angle to the horizontal axes. F can be described in terms of its components. Components are two vectors at right angles to each other that have the same effect as the original vector. F has an x component acting in the x direction called F x. F has a y component acting in the y direction called F y.

6 CALCULATING VECTOR COMPONENTS sin θ = y r F r y cos θ = x r Horizontal component F x = F cos θ Vertical component F y = F sin θ F x x F y tan θ = y x

7 Charl pulls a grass roller over a horizontal lawn with a force of 700N. The handle of the roller makes an angle of 30 with the horizontal plane. 1. Calculate the x component, F x. 2. Calculate the y component, F y.

8 EXERCISE 1 CLASS: 1.1 HOME:

9 A slope is a plane that makes an angle with the horizontal. An object is pulled down a slope because of gravity. More specifically, the x component of gravity. Also called the parallel component. An object is able to be held stationary on a slope because of gravity. More specifically, the y component of gravity.. Also called the perpendicular component. Perpendicular component (y) F g = F g cos θ Parallel component (x) F g = F g sin θ

10 A car with a mass of 1500kg is parked on a slope of Calculate the component of the weight of the car that is parallel to the slope. F gx 2. Calculate the component of the weight of the car that is perpendicular to the slope. F gy

11 EXERCISE 1 CLASS: 2.1 HOME:

12 A force is a push or a pull action. It is a vector. Symbol: F Measured in newton (N) Represented by an arrow.

13 CONTACT Objects are in contact with each other. Example: Applied forces. Friction. Normal force. Tension. Air friction. Compression NON-CONTACT Acts over a distance. Example: Magnetic Electrostatic Gravitational (W = F g = mg)

14 1. A person or object applies a force on another person or object. The applied force can be in the same line as the direction of the movement or at an angle to the direction of movement. Symbol: F applied or F

15 2. When an object moves, or tries to move on a surface, the contact surface exerts a frictional force on the object. Friction always tries to minimise the motion. Acts in the opposite direction. Is parallel to the surface on which the object makes contact. Symbol: F f or f

16 3. This is the force exerted by the surface of an object placed on that surface. Always perpendicular (90) to the surface even if the surface is at an angle. N It is a supporting force that is equal and opposite to the force of the object acting on the contact surface. W Symbol: F N or N

17 3. The object must be in contact with the surface to experience a normal force. Objects that fall through the air do not experience a normal force.

18 5. Air particles offer resistance to objects moving through the air. Air friction always acts in the opposite direction to movement. Symbol: F air or F f.

19 6. Force exerted on a compressed spring. A force equal in magnitude is exerted on any object touching the spring when the compression force is released. 4 Symbol: F spring.

20 There are 2 diagrams that we use to represent forces acting on object. FORCE DIAGRAMS Shows an object with all forces acting on it. S Object represented by a block. Arrows represent magnitudes and directions of forces. Arrows must touch the block. Arrows must be drawn at the position where the force is exerted.

21 There are 2 diagrams that we use to represent forces acting on object. FREE BODY DIAGRAMS Object is represented by a dot. (can be big) Forces represented by arrow with magnitude and direction. Arrows always points away from dots. Arrows must touch the dot. Forces at an angle is represented by the force itself OR by its components but NEVER both. S

22 Tokela pushes a crate with a mass of 20kg horizontally from rest over a rough surface with a force of 100N to the right. The frictional force between the crate and the surface is 20N. S

23 A wooden block is pressed against a wall. S

24 An object hangs vertically at rest from a cable. S

25 A crate of mass 20kg is pulled by a force of 100N at an angle of 30 to the horizontal. There is a frictional force of 20N between the crate S and the surface.

26 HOMEWORK EXERCISE 2 Pg

27 GRADE 10 REVISION: NET OR RESULTANT VECTOR A SINGLE VECTOR THAT HAS THE SAME EFFECT AS A COMBINATION OF VECTORS. EXAMPLE 1 Ibrahim pulls a crate with a force of 20N to the right. Rafat sees that his friend is struggling and so helps by pulling with a force of 50N to the right. What is the net or resultant force?

28 EXAMPLE 2 Nazly pushes a trolley in the supermarket with a force of 100N to the right. Her friend Jody, pushes against the trolley in the opposite direction with a force of 60N. What is the net or resultant force on the trolley? Take right as +. This is actually Newton s 2 nd Law of Motion!!!

29 Friction is a contact force. This occurs when 2 objects are in close contact and attempt to move across each other. A surface might seem smooth, but microscopically it has uneven particles. The surfaces of solids are generally rough. These forces act parallel to the plane of the motion, but are always in the opposite direction to the motion.

30 There are 2 types of frictional forces. Only for 2 objects at rest relative to one another. Only for 2 objects in motion relative to one another.

31 Frikkie pushes a crate across a rough surface, as indicated in the diagram. At first the force he applies is not big enough to make the crate move eventually it moves. MAGNITUDE OF APPLIED FORCE (N) CRATE at rest at rest at point of starting to move accelerates right accelerates right MAGNITUDE OF FRICTION FORCE TYPE OF FRICTION FORCE static static static kinetic kinetic

32 CONCLUSION? An object will not move when the applied force is less than the static frictional force. An object will not move if the applied force is equal to the maximum static frictional force. An object will begin to move when the applied force is greater than the maximum static frictional force. The friction is still present, only it is now kinetic friction because the object is moving. The magnitude of kinetic friction will always be less than the magnitude of static friction.

33 The frictional force of one contact surface on another when there is no relative motion between the objects. Static friction. (N) f s(max) = μ s F N Normal force (N). Independent of the size of the contact surface. Dependant on the mass and weight of the object. Dependant on the nature of the surfaces in contact with each other. Coefficient of static friction. Acts in the opposite direction to the attempted No unit. movement. Measure of how rough a surface is. Is directly proportional to the normal force. Usually less than 1. Constant.

34 The frictional force of one contact surface on another when one or both objects are moving. Kinetic friction. (N) f k = μ k F N Independent of the size of the contact surface. Dependant on the mass and weight of the object. Dependant on the nature of the surfaces in contact with each other. Acts in the opposite direction to the attempted movement. Is directly proportional to the normal force. Is normally smaller than the static frictional force. Normal force (N). Coefficient of kinetic friction. No unit. Measure of how rough a surface is. Usually less than 1. Constant. μ s > μ k

35 μ s = tanθ The angle of the slope to the horizontal where the object is at the point of starting to slide.

36 Coeffients of frictions. CONTACT SURFACE μ S μ K Cast iron on cast iron Glass on glass Leather on oak wood Wood on wood 0.25 to Ice on ice

37 WHAT FACTORS INFLUENCE THE MAGNITIDE OF THE FRICTIONAL FORCE? 1. The normal force. Remember, the normal force is the force that the surface exerts on the object and is equal in magnitude to the force that the object exerts on the surface (which is normally the weight). So heavier objects more weight greater normal force greater frictional force.

38 WHAT FACTORS INFLUENCE THE MAGNITIDE OF THE FRICTIONAL FORCE? 2. The surface type. Smooth surface less friction. Rough surface more friction. E.g. Ice rink slightly melted ice is easy to glide over but a rubber mat makes gliding impossible.

39 HOW DO WE REDUCE FRICTION? Lubricate the surfaces with oil, grease or finely powdered graphite. Wet the surfaces with water.

40 The normal force is different in various situations. F N = F G

41 The normal force is different in various situations. F y θ F x F N = F G + F y F N = F G F y

42 The normal force is different in various situations. F y F x θ F N = F G + F y

43 The normal force is different in various situations. F N = F G F N = F G cosθ θ θ F g

44 HOMEWORK EXERCISE 3 Pg

45 EQUILIBRIUM An object is in equilibrium if: 1. It is at rest. (static equilibrium) OR 2. It is moving at a constant velocity. (dynamic equilibrium). The object is in equilibrium if the net force is 0. This means that the sum of all the forces acting on the object is o.

46 examples Book is in equilibrium.

47 examples The plane is flying at a constant height and constant velocity. The plane is in equilibrium.

48 examples Garry is in equilibrium.

49 The resultant vector The net force acting on an object is the vector sum of all the forces acting on the object. It is one force that has the same effect as all the forces acting Type equation here. simultaneously on the object. F res = F net = F

50 GRADE 10 REVISION: NET OR RESULTANT VECTOR A SINGLE VECTOR THAT HAS THE SAME EFFECT AS A COMBINATION OF VECTORS. EXAMPLE 1 Ibrahim pulls a crate with a force of 20N to the right. Rafat sees that his friend is struggling and so helps by pulling with a force of 50N to the right. What is the net or resultant force?

51 EXAMPLE 2 Nazly pushes a trolley in the supermarket with a force of 100N to the right. Her friend Jody, pushes against the trolley in the opposite direction with a force of 60N. What is the net or resultant force on the trolley? Take right as +. This is actually Newton s 2 nd Law of Motion!!!

52 Determining the resultant vector There are 2 main methods that is used to determine the resultant vector. Scale diagrams Head to tail Tail to - tail Calculations using Trigonometry

53 Scale Diagrams 1. Head-to-tail method You need a sharp pencil, ruler and protractor for this method. Two men are pulling at ropes tied around a tree. The forces exerted by the men are 140N east and 100N at 120 to the 140N force, respectively. Use the head-to-tail method to calculate the resultant force exerted on the tree.

54 Scale Diagrams 2. Tail-to-tail method You need a sharp pencil, ruler and protractor for this method. Two men are pulling at ropes tied around a tree. The forces exerted by the men are 140N east and 100N at 120 to the 140N force, respectively. Use the tail-to-tail method to calculate the resultant force exerted on the tree.

55 Scale Diagrams 3. Calculation You need a calculator, trigonometry and your brain. Result is more accurate than the scale diagram Two men are pulling at ropes tied around a tree. The forces exerted by the men are 140N east and 100N at 120 to the 140N force, respectively. Use a calculation to calculate the resultant force exerted on the tree.

56 Scale Diagrams 3. Calculation FREE BODY DIAGRAM RESULTANT FORCE IN X AND Y DIRECTION. PYTHAGORAS.

57 HOMEWORK EXERCISE 4 Pg

58 Free PowerPoint Templates