Newton’s Laws Of Motion

1. Newton’s Laws Of Motion

2. Objectives • Be able to state, in words, Newton’s three laws of motion • Understand the difference between mass and weight • Be able to define the term forceBe able to state what is meant by the term free-body diagram(FBD). • Be able to construct FBD’s and use them to aid in solving problems • Be able to apply Newton’s Laws of Motion in a systematic way to solve problems. • Be able to state what is meant by the term Normal Force, and incorporate this definition in solving problems. By the end of this lesson you should

3. A Shift In Focus • Up to this point in the term, we have analyzed motion (DESCRIBED) without worrying about what was causing the motion to occur. We said that such a study of motion was referred to as kinematics. • We now concern ourselves with why the object is accelerating (or not). In other words, we look for the cause of the motion. This type of a study of motion where the cause of motion is considered is called dynamics.

4. Introduction • Central to this discussion are a set of laws called Newton’s Laws of Motion. This set of laws is considered to be of fundamental importance to the study of classical mechanics. Once introduced, you should be able to state these laws and apply them correctly even if stirred from a deep, restful sleep at 2 o’clock in the morning!

5. Introduction • In the slides that follow, there are words that are highlighted in the statements of Newton’s 3 Laws of Motion. This highlighting is to indicate that these words are critical to the statement of the law, and you should keep them in mind when applying these laws so that difficulties can be avoided. • We begin with Newton’s first law of motion.THE LAW OF INERTIA

6. Newton’s First Law Of Motion • An object in motion with a constant velocity will remain in motion with that constant velocity until the object is acted upon by a net,external force. • This law is also called the Law of Inertia. • Inertia: The property of an object to resist a change in velocity. Mass is a quantification of the inertia of a body.

7. Inertia: Newton’s First Law By the end of this section you will understand the following statement and its implications in physics:An object in motion with constant velocity will continue with the same constant velocity unless acted upon by an unbalanced outside force; and, An object at rest will continue at rest unless acted upon by an unbalanced outside force. http://www.dynamicscience.com.au/tester/solutions/flight/winterolympics/curln.html

8. Balanced Forces cause what? • The statement of this law raises a question: What do you think will happen to the motion of the object if there is an unbalanced outside force?

9. Balanced Forces Cause What? Balanced forces cause an inertial state of motion called “CONSTANT VELOCITY” UNBALANCED FORCES CAUSE WHAT? AN ACCELERATION!

10. FBD….Free Body Diagrams • The forces acting on the object of interest must be identified. • Then a special diagram called a free body diagram can be constructed. All static and dynamics problems begin in this fashion.

11. Our Problem Solving Model The first three steps in constructing a model are:  1. Identify the object or system. 2. Identify the forces acting on the object or system. 3. Draw a force (or free-body) diagram assuming the object or system as a point particle.

12. Approaching FBD‘s • One cardinal rule is that once you identify the object, it cannot be changed unless you start all over with step one again and go through all of the steps with the new object.

13. On the sketch, circle the object or system with a dotted line. In order to make a conscious decision to choose the object or system, and to avoid changing it midway through the activity, you will need to draw a rough sketch of the important parts in the situation being investigated. This is the real- world representation. (At first, the sketch will be provided for you, but later in the laboratory and in word problems you will need to complete the sketches on your own.)

14. Draw all of the forces on the tree in picture below. Use an arrow () to represent each force and to indicate the direction of each force. Identify each force by what is causing it. Write the statement, “force caused by _frictional force, etc…________,” next to each arrow. Put the tail of the arrow at the place on the object where the force is being applied.

15. Identifying the Forces Acting on the Object The basic definition of a force is a push or a pull. While this definition is correct, it does little in helping to identify the necessary forces.

16. What are the forces? The forces that need to be identified are those forces acting on the object or system. Each of these forces has to be caused by an object outside of the dotted line circle. It is important to identify the agents outside the object or system that are exerting forces on the system.

17. Remember your units! The metric unit for force is the Newton (N). The English unit is the pound (lb). Since the world is converting to metrics at a slow but sure rate, we will only deal with Newtons. This is part of the Standard International System of Units. (SI)

18. Weight and Mass are not the same!!! Mass is an inherent quantity that all objects have. It is measured in kilograms (kg). In this lecture we only need to deal with the weight vector. • Weight (W) in N = mg = 9.8 m • Units m/s2 (kg) = N • The direction of the gravitational force is always toward the center of the Earth.

19. Forces on the object caused by something outside the object are the only forces that are used. • Forces at a distance vs. Forces from contact • Weight --- DISTANCE • Normal--- CONTACT • Friction--- CONTACT • Tension--- CONTACT • Thrust --- CONTACT • Drag --- CONTACT

20. Types of Forces There are two categories of forces to consider: • contact forces • forces at a distance.

21. Forces at a Distance • They arise when the object is in the “field” caused by another object, but not in contact with the object. • Examples of “fields” are electrical, magnetic, and gravitational fields. Since we are only dealing with mechanics in this module, the only force at a distance we will deal with is the gravitational force. Gravitational force is often called weight.

22. Put the tail of the arrow at the center of the object. Label this force with the symbol W and the statement "force caused by Earth."

23. FBD Representations On the sketch, represent the force by an arrow. The tail of the arrow will be at the place of contact and the tip will point in the direction of the force. Label each force with an appropriate symbol and “force caused by ________.”

24. Contact Forces The contact forces acting on the system of interest are identified by going around the dotted circle that defines that object or system. There is the likelihood of a force at any point where something outside the dotted circle is touching something inside the circle.

25. Contact Forces • There are three contact forces that deserve special attention. • These contact forces are tension, normalforce, and friction.

26. TensionTension forces are caused by ropes or cables. Tension can only be a pull. Therefore, the direction is always known. Tension is given the symbol “T.”

27. Normal ForceAny time an object exerts a force on a surface, the surface also exerts a force on the object. One common example is when the object rests on something that supports or helps to support the object. This supporting force is called the normal force. The direction of the normal force is always perpendicular to the surface that is causing the force. Normal force is given the symbol N.

28. The last “special” contact force to be discussed is surface friction. Friction is designated by the lower case letter f. Surface friction occurs whenever two surfaces rub together. It also can occur when two surfaces are touching but not moving with respect to each other.

29. This relationship between magnitude and the direction of the force is true for any two surfaces of the same material when rubbed together.

30. Types of Friction • There are two types of friction. When one surface slides on a second surface, it is called kinetic friction. When one surface tries to slide on a second surface but does not move, it is called static friction.

31. Static Friction When an object is at rest with respect to a surface, the frictional force can be greater than when the objects move across each other. In our model, imagine that the “bumps” (or “grooves”) are deeply interlaced. • If a small force is applied to the object, the static friction fs will equal the applied force and cause the object to remain in equilibrium (a = 0).

32. Kinetic Friction • In our model, when the object moves, the grooves of the object bounce along the grooves of the surface, and never go as deep as they do in the static case. Thus, the kinetic friction force fk has a smaller magnitude than the static friction force.

33. Graph of Frictional Force vs. Applied Force

34. General Rules of Friction in the Model 1.The frictional force has a direction opposite to the force that is causing, or trying to cause, the object to slide. Friction is parallel to the surface; therefore, it opposes the sliding motion. 2.The force trying to cause the object to slide (F) must be greater than fsmax for sliding to occur. When F is smaller than f­smax, the object will not slide. 3.Once the object starts to slide, the static friction (fs) becomes kinetic friction (fk). Kinetic friction is always smaller than maximum static friction. 4.Both static friction (fs) and kinetic friction (fk) are proportional to the normal force. 5.The area of contact between the surfaces does not influence the magnitude of the frictional force. The speed of the object (assuming a low speed) does not influence the magnitude of the kinetic friction.

35. This is the big idea • Isolate the system • Figure out the forces • Label each force • Ask yourself this question……… “Are the forces balanced?”

36. A soccer player starts running to the right. On the sketch of the player, show the point of application and direction of the forces (W, N, fs) on the player.

37. A car is at rest on a horizontal road. What is the value of the frictional force? Explain your answer. • For the car in question, show the forces on the car and the points of application.

38. A woman pushes a book (the object) across a table to the left. On the sketch below, show the point of application and the direction of the four forces • (W, N, fk, F). • (F is the force of the woman on the book.)

39. Make a real world to FBD representation • Recall we are modeling the forces on an object. • We need to examine if the forces are balanced or if there is a net force to determine the type of motion present.

41. Section Summary • What is inertia? • What is a net force? • What is equilibrium? • What is moving equilibrium?

42. Newton’s Second Law Of Motion • The acceleration of an object is directly proportional to the unbalanced,externalforce acting on the object and inversely proportional to the mass of the object. The acceleration of the object is in the same direction as the unbalanced, external force. • Forces produce accelerations; accelerations do not produce forces!

43. Newton’s Second Law Of Motion • In the expression on the previous slide, m represents the mass of the object experiencing the acceleration and F represents force. • Force: A push or a pull; any influence that causes an object to change its velocity. The unit of force is the unit of mass times the unit of acceleration and is measured in Newtons. 1 Newton is the force required to give a 1.0 kg object an acceleration of 1.0 m/s2. • Newton’s Second Law is also referred to as the Law of Acceleration.

44. Newton’s Third Law Of Motion • If an object A exerts a force on object B, then object B exerts a force on A which is equal in magnitude and opposite in direction. • It is important to remember that the forces in the “action-reaction” pair mentioned act on different objects. • Newton’s Third Law is also called the Law of Interaction.

45. Newton’s Third Law Of Motion • Newton’s third law tells us that forces always come in pairs and that the forces in each pair are of equal magnitude, are opposite in direction, and act on different objects. You can never have a single force without a counterpart somewhere in the universe.

46. Forces come in two types. • Contact forces • Field forces • How about forces in Pairs!

47. Newton’s Third Law There is one more important piece to the dynamic and static model. It is called Newton’s Third Law. Forces come in pairs. Understand Newton’s Third law, we can ignore internal forces, and then only search for external forces acting on the object.

48. Push Me and I Push Back!!!

49. Push me and I push back! • For example, with the palm of your hand, push on a book, desk or table. You are exerting a force on the object you are pushing. At the same time, you can feel a force on your hand. There seems to be two forces: the one your hand exerted on the object, and another force on your hand. • What is the relationship between these forces?

50. The man weighs 700 N. The force exerted by the table on the man is: • a)Larger than 700 N • b)Equal to 700 N • c)Smaller than 700 N • d)There is no force.