FORCE & MOTION Instructional Module 6

Transcription

1 FORCE & MOTION Instructional Module 6 Dr. Alok K. Verma Lean Institute - ODU 1

2 Description of Module Study of different types of forces like Friction force, Weight force, Tension force and Gravity. This Module studies relationship between forces and the different types of Motion they produce, using Newton s three laws of Motion. Dr. Alok K. Verma Lean Institute - ODU 2

3 Targeted Sols : A-1, 3, 11, 15,G -3, 4, 9, AII-2,3,T-3, AII/T-3, AII/T-2 PH - 5d, 5C, 5E Learning objectives Activity Force and motion Tension Hooke's law Projectile motion Gravity Identify the forces that cause an object s motion Calculate tension on string and force acting on it. To verify Hooke's law relation ship between force and elongation How projectile angle effects range and velocity on different masses. Calculate weight on different planets Acceleration Dr. Alok K. Verma Lean Institute - ODU Calculate acceleration on connected objects 3

4 Topics Covered No Topic Time 1. Force and Motion 2. Balanced and Unbalanced forces 3. Types of Forces 4. Types of Friction. 5. Tension Force 6. Hooke s law 7. Gravity 8. Mass and Weight 9. Newton's First Law 10. Newton's Second Law 11. Newton's Third Law Dr. Alok K. Verma Lean Institute - ODU 4

5 Force &Motion Force: A push or pull that one body exerts on another. Motion: A Change of Position or Location. Dr. Alok K. Verma Lean Institute - ODU 5

6 Unit of Force Forces are measured in Newton A Newton is the force required to give a mass of 1 kilogram (1 kg) an acceleration of 1 meter per second per second (1 m/s 2 ). It is abbreviated as N. 1 N is equivalent to 1 kg-m/s 2. Dr. Alok K. Verma Lean Institute - ODU 6

7 Different Ways of Measuring Force 1. Spring Scale 2. Force Meter 3. Force Gauges a) Mechanical Gauges b) Digital Gauges 4. Dynamometer Dr. Alok K. Verma Lean Institute - ODU 7

8 Balanced Forces Balanced forces do not cause change in motion They are equal in size and opposite in direction F F F F Dr. Alok K. Verma Lean Institute - ODU 8

9 Unbalanced Forces An unbalanced force always causes a change in motion They are not equal in size and opposite in direction F F 2F 2F Dr. Alok K. Verma Lean Institute - ODU 9

10 Which one is balanced and unbalanced? 4 N, left 4 N, right 4 N, left 10 N, right Dr. Alok K. Verma Lean Institute - ODU 10

11 Answers Which one is balanced and unbalanced? 4 N, left 4 N, right Balanced 4 N, left 10 N, right Unbalanced Dr. Alok K. Verma Lean Institute - ODU 11

12 Types of Forces 1. Normal force 2. Friction Force 3. Tension force 4. Gravitational Force 5. Spring Force 6. Electromagnetic Force 7. Nuclear force Dr. Alok K. Verma Lean Institute - ODU 12

13 Normal Force It is the force exerted by one surface on another. It is perpendicular to the surface. Normal Force (F n ) Friction Force (F f ) Weight of block (W) Dr. Alok K. Verma Lean Institute - ODU 13

14 The person is walking on the floor and he slips suddenly. What is the reason? Because of lack of Friction Dr. Alok K. Verma Lean Institute - ODU 14

15 Friction Force Force that opposes motion between two surfaces. Depends on the: types of surfaces different materials Friction force (F f ) F f = m F n Normal force (F n ) Coefficient of friction Dr. Alok K. Verma Lean Institute - ODU 15

16 Four Types of Friction 1. Static Friction: Force that acts on objects that are not moving Dr. Alok K. Verma Lean Institute - ODU 16

17 Four Types of Friction 2. Sliding Friction: Force resulting when pushing or pulling an object over a surface MarineTech Dr. Alok K. Verma Lean Institute - ODU 17

18 Four Types of Friction 3. Rolling Friction: is the resistance that occurs when a round object such as a ball or tire rolls on a flat surface. Much easier to move object. Dr. Alok K. Verma Lean Institute - ODU 18

19 Four Types of Friction 4. Fluid Friction: Solid moving through a liquid or a gas Force of a fluid friction is always less than sliding friction The resistance that a body experiences in fluid is knows as Drag force. This is proportional to square of velocity of a body. Dr. Alok K. Verma Lean Institute - ODU 19

20 Coefficient of Friction Coefficient of Friction (µ) (mu): It is the ratio of the force of friction between two bodies and the force pressing them together. We use the symbol µ (Greek alphabet). Value of µ depends on the two surfaces involved and material they are made up of. Example: Teflon on steel has a low coefficient of friction. µ = 0.04 Rubber on concrete has a high coefficient of friction. µ = 1.0 Dr. Alok K. Verma Lean Institute - ODU 20

21 Calculation of Coefficient of Friction Coefficient of Friction (µ) can be calculated experimentally by the following formula: Normal Force (F n ) Friction Force (F f ) µ = Height/ Length Height Dr. Alok K. Verma Lean Institute - ODU Length Weight of block (W) 21

22 1. The direction of friction is always to the direction in which the object is moving. a. Same b. Opposite c. Unrelated 2. When an object is moving faster through a fluid what happens to the force of friction on it? a. Force of Friction increases. b. Force of Friction decreases. c. There is no force. Dr. Alok K. Verma Lean Institute - ODU 22

23 1. The direction of friction is always to the direction in which the object is moving. a. Same b. Opposite c. Unrelated 2. When an object is moving faster through a fluid what happens to the Drag force? a. Drag Force increases. b. Drag Force decreases. c. There is no force. Answers Dr. Alok K. Verma Lean Institute - ODU 23

24 Hands on Activity - 1 Measure Coefficient of Friction Dr. Alok K. Verma Lean Institute - ODU 24

25 MarineTech Objective: Measuring the coefficient of friction between different surfaces. Materials for class activity: 1. A Flat corrugated plastic board to be used as a ramp. 2. Square block with six different surfaces.(copper,brass,rubber, Wood(Rough surface),wood(smooth Surface),Cork sheet Ruler dowels. 5. Base Stand. Hands on Activity - 1 Measure Coefficient of Friction 6. Square beam with pulley. 7. Wooden clamp Dr. Alok K. Verma Lean Institute - ODU 25

26 Assembled Equipment: Dr. Alok K. Verma Lean Institute - ODU 26

27 Activity Procedure: 1. Put the square block on the top of the ramp in the center with the surface materials in contact according to the worksheet. 2. Gently release the clamp and slide down the centre post raising the ramp until the block starts to slide. 3. Lock the clamp in this position. 4. Measure the height and length of the inclined plane and enter in the work sheet. 5. Calculate the coefficient of friction between the surfaces using the formula: µ = Height/Length 6. Repeat the steps for other five surfaces on the block and record height and length on the worksheet for each surface combination. Dr. Alok K. Verma Lean Institute - ODU 27

28 S.No Slide surface material Block Surface material 1 Plastic Copper Work Sheet Length Height Average Length Average Height MarineTech Coefficient of Friction = Height/Length 2 Plastic Brass 3 Plastic Rubber 4 Plastic Wood (Rough Surface) 5 Plastic Wood (smooth) 6 Plastic Cork Dr. Alok K. Verma Lean Institute - ODU

29 Tension Force Tension is the magnitude of the pulling force exerted by a string, cable, chain, or similar object on another object The tension force is directed along the length of the wire and pulls equally on the objects on the opposite ends of the wire. Dr. Alok K. Verma Lean Institute - ODU 29

30 Hands on Activity - 2 Tension Force Objective: Calculate Tension force in the string and observe in the tension protractor. Materials for class activity: 1. Tension Protractor 2. Vertical Square stick 3. Ruler. 4. String. 5. Weight 300 grams. 6. Weight 200 grams. 7. Weight 100 grams. Dr. Alok K. Verma Lean Institute - ODU 30

31 T = Tension in the string F = Force in the horizontal arm Hands on Activity - 2 Tension Force MarineTech Free Body Diagram T T Y θ Y X F θ X W= mg W= mg Sum of all the forces in the x and y direction should be zero Dr. Alok K. Verma Lean Institute - ODU 31

32 Hands on Activity - 2 Free Body Diagram Tension Force Sum of all the forces in the y T Y direction F y = 0 T Sin(θ) W = 0 F θ W= mg T = Tension in the string F = Force in the horizontal arm X MarineTech Sum of all the forces in the x direction F x = 0 F T Cos(θ) = 0 Sum of all the forces in the x and y direction should be zero Dr. Alok K. Verma Lean Institute - ODU 32

33 Work Sheet Suspended Mass (kg) W = mg (N) F y = 0 T Sin(θ) W = 0 Tension (T) (N) F x = 0 F T Cos(θ) = 0 Force (F) (N) Dr. Alok K. Verma Lean Institute - ODU 33

34 Hands on Activity - 2 Tension Force Dr. Alok K. Verma Lean Institute - ODU 34

35 10 Minutes Dr. Alok K. Verma Lean Institute - ODU

36 Gravity Force of attraction between any two objects in the universe. Gravity Force Increases As mass increases As distance decreases between two objects g earth = 9.81m/s 2 Dr. Alok K. Verma Lean Institute - ODU 36

37 MASS & WEIGHT Mass: Mass is a measure of matter. Mass is constant. m = mass (kg) Weight: Weight is a force. Weight is not constant. The weight of an object depends on location with respect to the Earth s surface W = mg W = Weight (N) m = Mass (kg) g = Acceleration due to gravity(m/s 2 ) Dr. Alok K. Verma Lean Institute - ODU 37

38 Comparison of Weight on Earth and Mars Dr. Alok K. Verma Lean Institute - ODU 38

39 Class Exercise - 1 To find gravity force on different Planets Dr. Alok K. Verma Lean Institute - ODU 39

40 1. The amount of matter in an object is called its weight a. True b. False 2. The mass of an object is 20 kg on earth, its weight is a. 196 N b. 200 N c.76 N d. 96 N 3. An object has a weight of 30 N on earth. A second object weighs 30 N on the moon, which object has greater mass? a. The one on the earth b. They have the same mass c. The one on the moon d. Not enough information provided Dr. Alok K. Verma Lean Institute - ODU 40

41 Answers 1. The amount of matter in an object is called its weight a. True b. False 2. The mass is 20 kg on earth and its weight is a. 196N b. 200N c. 76N d. 96N 3. An object has a weight of 30N on earth. A second object weighs 30N on the moon, which object has greater mass? a. The one on the earth b. They have the same mass c. The one on the moon d. Not enough information provided Dr. Alok K. Verma Lean Institute - ODU 41 41

42 Hooke's Law MarineTech It states that the Elongation of a spring is in direct proportion with the load added to it as long as this load does not exceed the elastic limit. Elastic Limit: The maximum stress that can be applied to a Spring without producing permanent deformation Force (N) F = k x Elongation (m) Spring Stiffness (N/m) Dr. Alok K. Verma Lean Institute - ODU 42

43 Hands on Activity - 3 Hooke's Law Objective: To verify Hooke's Law (Relation between force & Elongation) MarineTech Materials for class activity: 1. 10N/m Spring 2. 20N/m Spring 3. 40N/m Spring 4. Weights (5 Hooke's law apparatus 5. 50g, 100g, 200g and 500g) Dr. Alok K. Verma Lean Institute - ODU 43

44 Activity Procedure: 1. Hang the 10 N (Red) spring from the notch on the support arm 2. Align the top surface of the washer with zero on the scale 3. Hang the specified weight from the spring 4. Measure the stretch of the spring and note the values in the work sheet 5. Repeat the steps for additional weights according to the worksheet 6. Repeat the above steps for 20 N (Blue) and 40 N (Green) spring. Dr. Alok K. Verma Lean Institute - ODU 44

45 No Spring Stiffness 10 N/m Work Sheet Weights (grams) Force(N) Elongation(cm) No Spring Stiffness 20 N/m Weights (grams) Force(N) Elongation(cm) Spring Stiffness 40 N/m No Weights (grams) Force(N) Elongation(cm) Dr. Alok K. Verma Lean Institute - ODU 45

46 Hands on Activity - 3 To Verify Hooke s Law (Relationship between Force & Elongation) Dr. Alok K. Verma Lean Institute - ODU 46

47 VELOCITY Velocity: Velocity is the rate of change of position The velocity v of an object moving through a displacement (Δ x) during a time interval (Δ t) is described by the formula: Velocity Total Displacement Travel Time Units = meters/sec Dr. Alok K. Verma Lean Institute - ODU 47

48 ACCELERATION Acceleration: Acceleration is defined as the rate of change of velocity. The acceleration is the ratio between the change in velocity and the time interval. Accelerati on Change in velocity Travel Time Units = meters/sec 2 Dr. Alok K. Verma Lean Institute - ODU 48

49 Height(H) MarineTech Projectile Motion When an object is thrown into the air, its motion is affected by gravity and wind resistance. It follows a parabolic path as shown on the right. At the maximum height, the vertical component of velocity becomes zero and changes direction. V X V Y Dr. Alok K. Verma Lean Institute - ODU Range 49

50 Slow projectile - shoot a monkey Fast projectile - shoot a monkey Fast Projectiles travel longer distances Dr. Alok K. Verma Lean Institute - ODU 50

51 Hands-on Activity - 4 Projectile Motion Objective: To observe how projectile angle affects distance and velocity of different masses. Materials for Class Activity: 1.Catapault 2. Two balls of different masses. (17 grams, 25 grams) 3. Stop Watch 4. Measuring Tape Dr. Alok K. Verma Lean Institute - ODU 51

52 Activity Procedure: 1. Arrange the equipment such that the ball will land in a safe area by calculating the maximum distance it might travel 2. Place the ball in the catapult 3. Start the gun of the catapult at 38 degrees 4. Release the ball and note down the time taken when it touches the ground by using Stop watch 5. Repeat the Step 4 for angles 62, 84 and note down the values in worksheet 1 provided Dr. Alok K. Verma Lean Institute - ODU 52

53 Free Body Diagram Assembled Equipment: V V y V x V = Velocity V x = Velocity in Horizontal direction V y = Velocity in Vertical direction Dr. Alok K. Verma Lean Institute - ODU 53

54 NO Mass = 17 grams Angle(θ ) degrees Distance (meters) D 1 D 2 T 1 T 2 Work Sheet Time of flight(sec) V x = V Cos(θ) MarineTech Mass = 25 grams NO Angle(θ) degrees Distance (meters) D 1 D 2 T 1 T 2 Time of flight(sec) V x = V Cos(θ) Dr. Alok K. Verma Lean Institute - ODU 54

55 Hands on activity - 4 Projectile Motion Dr. Alok K. Verma Lean Institute - ODU 55

56 15 Minutes Dr. Alok K. Verma Lean Institute - ODU

57 Inertia The tendency of all objects to resist any change in motion. More mass= More inertia Harder to start or stop motion of an object. Less mass = Less inertia Easier to start or stop motion an object Dr. Alok K. Verma Lean Institute - ODU 57

58 NEWTON S FIRST LAW An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force. No force FORCE Dr. Alok K. Verma Lean Institute - ODU 58

59 NEWTON S FIRST LAW These pumpkins will not move unless acted on by an unbalanced force. Unless acted upon by an unbalanced force, this golf ball would sit on the tee forever. Dr. Alok K. Verma Lean Institute - ODU 59

60 1. The inertia applies to a. Objects that are not moving b. Moving objects c. Both moving & non moving objects 2. An object wants to maintain its state of motion because it has a. Inertia b. Velocity c. Speed d. Acceleration 3. Why then, do we observe every day objects in motion slowing down and becoming motionless seemingly without an outside force? Dr. Alok K. Verma Lean Institute - ODU 60

61 1. The inertia applies to Answers a. Objects that are not moving b. Moving objects c. Both moving & non moving objects 2. An object wants to maintain its state of motion because it has a. Inertia b. Velocity c. Speed d. Acceleration 3. Why then, do we observe every day objects in motion slowing down and becoming motionless seemingly without an outside force? Ans: It s a force we sometimes cannot see Friction. Dr. Alok K. Verma Lean Institute - ODU 61

62 Newton s Second Law The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. F a m F m net F net F ma Dr. Alok K. Verma Lean Institute - ODU 62

63 1. Acceleration is produced by a. Forces b. acceleration c. Pressures d. velocities e. masses 2. Mary is accelerating her little red wagon when Tom begins to pull in the same direction effectively doubling the net force on the wagon what happens to the Wagons acceleration? a. It halves b. It doubles c. It quarters d. It stays the same Dr. Alok K. Verma Lean Institute - ODU 63

64 Answers 1. Acceleration is produced by a. Forces b. acceleration c. Pressures d. velocities e. masses 2. Mary is accelerating her little red wagon when tom begins to pull in the same direction effectively doubling the net force on the wagon what happens to the Wagons acceleration? a. It halves b. It doubles c. It quarters d. It stays the same Dr. Alok K. Verma Lean Institute - ODU 64 64

65 Class Exercise - 2 Find Force, Mass, Acceleration in the given problems Dr. Alok K. Verma Lean Institute - ODU 65

66 Hands on Activity - 5 Acceleration Objective: To study the impact of force on the acceleration of a cart under varying load conditions Case 1: Mass of cart constant, Varying force. Case 2: Force constant,mass of cart varying. Materials for class activity 1. Motion sensor 2. Wooden track 3. Wooden cart 4. Mass hanger 5. Washers (mass = 34 grams = kgs) MarineTech Dr. Alok K. Verma Lean Institute - ODU 66

67 Assembled Equipment: Dr. Alok K. Verma Lean Institute - ODU

68 MarineTech Activity procedure: Case Place one washer on the mass hanger. 2. Pull the cart back so the mass is just below the pulley. 3. Make sure that the cart is at least 15cm away from the motion sensor. 4. Tap play button to start recording data and release the cart so it moves toward the pulley. 5. Tap stop button to stop recording after it reaches at the end of the track. 6. Record the value of acceleration from Spark and note it in the last column. 7. Place a second washer on the mass hanger and repeat steps 2 to Place a third washer on the mass hanger and repeat steps 2 to 6. Dr. Alok K. Verma Lean Institute - ODU 68

69 Work sheet Case - 1 Mass of the Cart Constant, Varying Force Suspended Mass M 1 (KG) W 1 =M 1 g=n 1 (Newton) Cart on track M 2 (Kg) W 2 =M 2 g=n 2 (Newton) F=µN 2 (Newton) T=M 2 a+f Theoretical value a=w 1 -T/M 1 (m/s 2 ) Experiment values of a (m/s 2 ) Force = Mass * 9.81N Mass of the cart = 131 grams. Mass of the washer = 34 grams. Coefficient of friction = 0.2 Dr. Alok K. Verma Lean Institute - ODU 69

70 MarineTech Case Place two washers in the mass hanger. 2. Pull the cart back so the mass is just below the pulley. 3. Make sure that the cart is at least 15 cm away from the motion sensor. 4. Tap play button to start recording data and release the cart so it moves toward the pulley. 5. Tap stop button to stop recording after it reaches at the end of the track. 6. Record the value of acceleration from Spark and note it in the last column. 7. Place one washer on the top of the cart and repeat steps 2 to Place a Second washer on top of the cart and repeat steps 2 to 6. Dr. Alok K. Verma Lean Institute - ODU 70

71 Suspended Mass M 1 (KG) W 1 =M 1 g=n 1 (Newton) Work sheet - 2 Mass Cart Varying and Force Constant Cart on track M 2 (Kg) W 2 =M 2 g=n 2 (Newton) F=µN 2 (Newton) T=M 2 a+f Theoretical value a=w 1 -T/M 1 (m/s 2 ) MarineTech Experiment values of a (m/s 2 ) Force = Mass*9.81N Mass of the cart = 131 grams. Mass of the washer = 34 grams. Coefficient of friction = 0.2. Dr. Alok K. Verma Lean Institute - ODU 71

72 Hands on Activity - 5 Acceleration of Connected Objects Dr. Alok K. Verma Lean Institute - ODU 72

73 Newton s Third Law For every action there is an equal and opposite reaction Dr. Alok K. Verma Lean Institute - ODU 73

74 Action-Reaction Example F G The rocket exerts a downward force on the exhaust gases The gases exert on equal but opposite upward force on the rocket F R Dr. Alok K. Verma Lean Institute - ODU 74

75 Class Exercise - 3 Complete the table by writing the reaction for each action. Dr. Alok K. Verma Lean Institute - ODU 75

76 Class Exercise - 4 Solve the word puzzle and match the following on force and motion. Dr. Alok K. Verma Lean Institute - ODU 76