Physics 1408-002 Principles of Physics Sung-Won Lee [email protected] Lecture 6 – Chapter 4 – January 27, 2009 Announcement I Lecture note is on the web Handout (4(or 6) slides/page) http://highenergy.phys.ttu.edu/~slee/1408/ HW Assignment #2 is placed on MateringPHYSICS, and is due by 11:59pm on Tuesday, 1/27 *** Class attendance is strongly encouraged and will be taken randomly. Also it will be used for extra credits. Announcement II SI session by Reginald Tuvilla Monday 4:30 - 6:00pm - Holden Hall 106 Thursday 4:00 - 5:30pm - Holden Hall 106 SI sessions will be at the following times and location. Chapter 4 Dynamics: Newton’s Laws of Motion; 1.! Force 2.! Newton’s First Law of Motion 3.! Mass 4.! Newton’s Second Law of Motion 5.! Newton’s Third Law of Motion 6.! Weight – the Force of Gravity; and the Normal Force Up until now, we have only studied the Kinematics of moving objects. •! Kinematics tell us how an object moves (Ch. 2,3) •! Dynamics tell us why an object moves (Ch 4,5,6) •! Kinematics + Dynamics = Mechanics (Part I) i.e. Mechanics deals with both the “how” & “why” of motion To study dynamics, we must first introduce the concept of force. Newton’s laws are central to dynamics. 4.1 The Concept of Forces Force is a vector, having both magnitude and direction. The magnitude of a force can be measured using a spring scale. ForcesExamples of Force Vectors Pull (contact force) Gravity (long-range force) This spring is compressed, so it pushes outwards. The box is falling. . . Again, a force is either a contact force, which acts through physical contact between the agent and object, or a long-range force, which acts without physical contact Push (contact force) Two Forces Applied to a Box 1 21Nnet i NiF F F F F=! = + + """ +#! ! ! ! !When several individual forces act on the same object, they combine to form a net force given by the vector sum of the individual forces Fig. shows a box being pulled by two ropes. How will the box respond? 4.2 Newton’s First Law Newton’s 1st Law: In the absence of external forces, an object at rest remains at rest; an object in motion remains in motion. (see next page) Mass is the measure of inertia of an object. In the SI system, mass is measured in kilograms [kg]. Mass is not weight: (see later) Mass is a property of an object. Weight is the force exerted on that object by gravity. If you go to the moon, whose gravitational acceleration is about 1/6 g, you will weigh much less. Your mass, however, will be the same. 4.3 Mass Newton’s second law is the relation between acceleration and force. Acceleration is proportional to force and inversely proportional to mass. It takes a force to change either the direction or the speed of an object. More force means more acceleration; the same force exerted on a more massive object will yield less acceleration. 4.4 Newton’s Second Law 4.4 Newton’s Second Law A law of Nature An object of a given mass m subjected to forces F1, F2, F3, … will undergo an acceleration a given by: a = Fnet/m where Fnet = F1 + F2 + F3 + … The mass m must be positive so that force and acceleration are in the same direction. amFnet!!=Algebraically, !F = ma !Fx = max !Fy = may !Fz = maz4-4 Newton’s Second Law of Motion v0 = 100km/h = 27.8 m/s, v = 0, "x=55m What average net force is required to bring a 1500-kg car to rest from a speed of 100 km/h within a distance of 55 m? •! If two objects interact, the force F12 exerted by object 1 on object 2 is equal in magnitude and opposite in direction to the force F21 exerted by object 2 on object 1 •! F12 = - F21 –! Note on notation: FAB is the force exerted by A on B •! Forces always occur in pairs •! A single isolated force cannot exist •! The action force is equal in magnitude to the reaction force and opposite in direction 4.5 Newton’s Third Law of Motion 4.6 Weight – the Force of Gravity; and the Normal Force Weight is the force exerted on an object by gravity. Close to the surface of the Earth, where the gravitational force is nearly constant, the weight of an object of mass m is: where Weight – the Force of Gravity; and the Normal Force An object at rest must have no net force on it. If it is sitting on a table, the force of gravity is still there; what other force is there? The force exerted perpendicular to a surface is called the normal force and noted by the symbol FN The normal force always points in a direction normal (perpendicular) to the surface of the agent. Normal Force - Examples Free-Body Diagrams It represents the object as a particle & shows all forces acting on object. How to set up problems: 1. Identify all forces acting on the object. 2. Draw a suitable coordinate system. 3. Use the particle model – draw a dot at the origin. 4. Draw a vector for each force acting on the object. 5. Add all the forces: Draw and label the net force.Solving Problems with Newton’s Laws – Free-Body Diagrams When a rope pulls on an object, it is said to be under tension, and the force it exerts is called a tension force. 5.7 Applications of Newton’s Law •! Assumptions –! Objects can be modeled as particles –! Masses of strings or ropes are negligible –! Interested only in the external forces acting on the object –! Initially dealing with frictionless surfaces Objects in Equilibrium An object on which the net force is zero is said to be in equilibrium. There are two types: 1.!static equilibrium: The object is at rest. 2.!dynamic equilibrium: The object is moving in straight line with constant velocity. Both of these conditions are identical from a Newtonian perspective because Fnet = 0 and a = 0. Since Newton’s 2nd Law is represented by vector equations, equilibrium implies the following simultaneous equations: ( ) ( ) 0( ) ( ) 0( ) ( ) 0net x i xinet y i yinet z i ziF FF FF F= == == =!!!Equilibrium, Example 1 •! A lamp is suspended from a chain of negligible mass •! The forces acting on the lamp are –!the force of gravity (Fg) –!the tension force in the chain (T) •! Equilibrium gives Equilibrium, Example 2 !! Categorize as an equilibrium problem: No movement; i.e. a = zero !! Analyze –! Need two free-body diagrams –! Apply equilibrium equation to the light and find T3 –! Apply equilibrium equations to the knot and find T1 and T2 Objects Experiencing a Net