# Newton s Laws of Motion. Chapter 4

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1 Newton s Laws of Motion Chapter 4

2 Changes in Motion Section 4.1 Force is simply a push or pull It is an interaction between two or more objects Force is a vector so it has magnitude and direction In the SI system, Force is measured in Newtons (N). In the English system, it is measured in pounds. 1 pound = Newtons The total force (or net force) exerted on an object is the vector sum of all forces acting on it

3 Aristotle & Galileo Aristotle was a great philosopher but not such a good scientist. Aristotle s theory of motion is wrong. Took 2000 years before Galileo got motion right.

4 Motion according to Aristotle (I) Every object has a natural state. In natural motion, Earth elements (stone, apple, you, etc.) are drawn to the Earth. Heavier objects are more strongly attracted so they fall faster (stone falls faster than a feather). Aristotle Important: These are Aristotle s ideas, but he s wrong! Reality

5 Motion according to Aristotle (II) Pushing or pulling an object causes unnatural motion (or violent motion). If cause is removed (stop pushing) then object returns to natural state and stops moving. Pushed brick slides but then comes to a stop BRICK BRICK

6 Galileo s Inclines (I) Downhill: Speed increases Uphill: Speed decreases Flat surface: Speed increases, decreases, or constant? Questions existence of natural Earth state of not moving.

7 Inertia section 4.2 An object s tendency to persist in its original state of motion This concept was first discovered by Galileo in the 1630 s. Objects will keep doing whatever they re already doing unless something causes it to change.

8 Isaac Newton , Lincolnshire, England Professor and Scholar at the University of Cambridge One of the most influential scientists of all time Uncovered universal laws of motion and gravity among many other discoveries. Most famous work: Principia

9 Newton s First Law of Motion also referred to as the law of inertia An object at rest remains at rest & an object in motion remains in motion*, unless an outside, unbalanced force acts on the object. *Moving in a straight line with constant speed.

10 Newton s First Law of Motion An object in motion can still maintain its state with a force acting on it. It s only when the forces acting on it are unbalanced that an object can change its motion!

11 Newton s First Law of Motion The Gare Montparnasse in France crashed through this wall in 1895, why? Trains are difficult to stop because they are so massive There is a direct relationship between mass and inertia.

12 Mass Mass is a measure of the quantity of matter in an object Mass also measures how difficult it is to change the velocity of an object Or, how much an object resists changes in its motion

13 Example: Riding the subway When a moving train stops, you continue moving forward. When the stopped train starts moving again, you remain stationary and are thrown backwards

14 Question When the rocket engines on a spacecraft are suddenly turned off, while traveling in empty space far away from distant stars and planets, the starship will.. A) go faster and faster B) slow down and then stop C)stop immediately D)move with constant speed E) move perpendicular to velocity

15 Inertia demonstrations Coin/notecard Tablecloth Hanging mass Hoop and battery Mallet and mass Rolling carts

16 Discussion topics of inertia Inertia videos Getting ketchup out When are you taller? AM or PM? Collisions: Front and rear Seatbelts work off inertia If you drop something on a moving vehicle, where does it land? How do you find your mass in space?

17 Conceptual Checkpoint The metal head of a hammer is loose. To tighten it, you drop the hammer down onto a table. Should you (a) drop the hammer with the handle end down, (b) drop the hammer with the head end down, or (c) do you get the same result either way?

18 Conceptual Checkpoint Tighten the Hammer Head

19 Net Force ( F) When several forces act on an object, the forces add together. Sum of forces called net force or total force 3 Newtons 5 Newtons BRICK same as 8 Newtons The Newton is metric unit of force (about 1/5 pound).

20 Check Yourself?

21 Equilibrium Rule If an object is at rest then the net force must be zero. Similarly if in uniform motion. 3 Newtons 3 Newtons BRICK same as Zero Newtons (No Force) When this happens we say that forces balance.

22 What is... Mass Weight, w

23 Weight vs Mass Mass is the amount of matter in an object Weight is a measure of the pull of gravity on an object. Weight (Newtons) = mass (kg) x acceleration due to gravity (m/s 2 ) Formula for weight: W = m g Q: How much does one kilogram weigh? A: 9.8 N

24 Question Is it better to have 1 N of gold on the moon or on the Earth?

25 Example An astronaut with a mass of 75 kg travels to Mars. A) What is his mass on Mars? B) What is his weight on Mars where the acceleration due to gravity is 3.8 m/sec 2? C) What is the acceleration due to gravity on top of a mountain if he weighs 683 N?

26 Free Body Diagrams A free body diagram is a diagram showing an object in free space along with all external forces acting on it

27 Free Body Diagrams The usual steps in constructing a freebody diagram are: Sketch the forces Isolate the object of interest Choose a convenient coordinate system Resolve the forces into components You can then apply Newton s 2 nd law for each coordinate direction

28 Constructing and Using a Free-Body Diagram

29 Figure 5-5bc Constructing and Using a Free-Body Diagram

30 Constructing and Using a Free-Body Diagram

31 A Book Supported in a Person s Hand

32 Example Find the magnitude and direction of the net force. 23N 45 N

33 Example Find the magnitude and direction of the net force. 15 N 13 N 24 N

34 Example Four forces act on an object. 210 N acts to the East. 305 N acts to the South. 413 N acts to the West. And, 139 N acts to the North. Find the magnitude and direction of the net force.

35 Example Three forces act on an object. 71 N act at 24 degrees North of East. 62 N act at 51 degrees North of West. And, 85 N act at 60 degrees South of West. Find the magnitude and direction of the net force.

36 Example The following object is in equilibrium. How big does the missing force have to be to keep it in equilibrium? F=? 16 N 16 N 11 N

37 Example Find the size and direction of the missing force in order for this object to be in equilibrium. 3.3 N F =? 6.3 N

38 Example Find the size and direction of the missing force in order for this object to be in equilibrium. 33 N at 60 degrees N of E F =? 63 N at 15 degrees S of E

39 Example This 1kg mass is suspended by two cables at 50 degrees. Find the size and direction of the tension force in each cable in order for this object to be in equilibrium. T=? T=? kg

40 Newton s 2 nd Law Section 4.3 When a net force acts on an object of mass m, the acceleration of the object will be given by: ΣF = ma Or in terms of components: F x ma x F y ma y

41 Newton s 2 nd Law If the net force is zero, the acceleration is zero, and the velocity of an object stays constant, which is Newton s 1 st law Force is measured in newtons (N), and from the second law, 1 N 1kg m/s 2

42 Newton s Second Law of Motion F net = ma 4.45 N = 1 lb

43 Example What is the net force required to accelerate a 1.5 kg box at 2.0 m/sec 2?

44 Example What is the net force exerted on a 1500 kg car if it is accelerated from 5 m/sec to 10 m/sec in 3 sec?

45 Example A 0.34 kg softball is accelerated from rest to 22 m/s over a length of 0.88 meters. Find the net force that was applied to the ball that produced this acceleration.

46 Example The following forces act on the 4.6 kg object. A) Find the net force acting on it. B) Find the magnitude of its acceleration. 15 N 13 N 24 N 4 N

47 Example Find the acceleration of the apparatus below. Assume there is no friction. 3.3 kg 0.75 kg

48 Example A 2,360 kg pickup truck slows down to a complete stop with a frictional force of 14,500 N directed opposite its motion. If its initial velocity was m/s, how far did it travel while slowing down? How much time did this take?

49 Newton s 3 rd Law

50 Newton s 3 rd Law For every force that acts on an object, there is a reaction force equal in magnitude and opposite in direction. For every action there is an equal and opposite reaction. An isolated force does not exist in nature, so forces always occur in pairs

51 Newton s 3 rd Law Action reaction forces act on two different objects: hence they do not cancel Action reaction forces generally produce different accelerations, since the masses of the objects are likely to be different

52 Examples of Action-Reaction Force Pairs

53 Apparent Weight When you are in an elevator accelerating upward a scale would read a greater weight When you are in an elevator accelerating downward a scale would read a lesser weight Thus, your apparent weight in an accelerator is different from your true weight

54 Apparent Weight

55 Apparent Weight If you are accelerating upward, your apparent weight is W a m( g a) If you are accelerating downward, your apparent weight is W a m( g a)

56 Normal Forces When an object rests on a surface, the surface provides a force on the object in a direction perpendicular to the surface This called the normal force, N In most cases, the normal force is equal to the weight of the object; however it can be greater or less than the weight of the object

57 Support (Normal) Force Solid surfaces exert a force, called a support force, on objects pressed against them. 100 Newton Gold Brick Downward force (weight) balanced by upward force (support). 100 Newton Support force (Normal Force) * The term normal means perpendicular. So the normal force is always perpendicular to the surfaces

58 The Normal Force May Equal the Weight

59 Normal Forces When a box is pulled by a force F at an angle θ across a smooth floor, the magnitude of the normal force is N W F sin

60 The Normal Force May Differ from the Weight in certain circumstances

61 Normal Forces For an inclined plane, the normal forces are still at right angles to the surface, but not in the vertical direction It is convenient to choose the x axis parallel to the incline surface and y axis perpendicular Then normal force is: N W cos

62 Components of the Weight on an Inclined Surface

63 Example A child of mass 45 kg rides on a sled down an ice-covered hill (frictionless) inclined at an angle of 22 degrees with respect to the horizontal. A) What is the acceleration of the child? B) What is the normal force exerted on the child by the sled?

64 Driving down the road you hit the brakes suddenly. As a result, your body moves toward the front of the car. Explain, using Newton s laws.

65 A drag-racing car accelerates forward because of the force exerted on it by the road. Why, then, does it need an engine? Explain.

66 An astronaut on a space walk discovers that his jet pack no longer works, leaving him stranded 50 m from the spacecraft. If the jet pack is removable, explain how the astronaut can still use it to return to the ship.

67 Is it possible for an object to be in motion and yet have zero net force acting on it? Explain.

69 You jump out of an airplane and open your parachute after a brief period of free fall. To decelerate your fall, must the force exerted on you by the parachute be less than, equal to, or greater than your weight? Explain.

70 Is it possible for an object at rest to have only a single force acting on it? If your answer is yes, provide an example. If your answer is no, explain why not.

71 Since all objects are weightless for an astronaut in orbit, is it possible for astronauts to tell whether an object is heavy or light? Explain.

72 Everyday Forces Section 4.4 Two types of Friction Static Kinetic

73 Friction Friction is the force that opposes motion when two surfaces are in contact Opposes motion means that the force of friction is always in the opposite direction of the motion There are two different types of friction: static and kinetic (sliding)

74 Static Friction Static means stationary or not moving When a force is first applied to an object, static friction opposes the start of motion A force greater than that of static friction must be applied for the object to start moving

75 Kinetic Friction Kinetic means related to motion Kinetic friction opposes motion once an object is moving Kinetic friction in general is less than static friction This means you have to push harder to start an object moving than to keep an object moving

76 What Affects Friction? Speed of pull? (assuming v>0) Area in contact? Weight of object? Materials in contact?

77 F f = F N s > k is the coefficient of friction

78 What if...? F A < F f F A = F f F A > F f F f is NOT an applied force!!

79

80 Question It's more difficult to start moving a heavy carton from rest than it is to keep pushing it with constant velocity, because A) the normal force (N) is greater when the carton is at rest. B) s < k C) initially, the normal force (N) is not perpendicular to the applied force. D) k < s

81 Example A 13.4 kg crate is pushed across a floor. The respective coefficients of friction are µ s = 0.85 and µ k = Find the pushing force necessary to get it moving from rest. And, find the force necessary to keep it moving at a constant velocity kg

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