Physics 1408-002 Principles of Physics Sung-Won Lee [email protected] Lecture 5 – Chapter 4 – January 22, 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 3 1.! Vectors and Scalars 2.! Addition of Vectors – Graphical Methods 3.! Subtraction of Vectors, and Multiplication of a Vector by a Scalar 4.! Adding Vectors by Components 5.! Projectile Motion Kinematics in 2, 3-Dimensions ; Vectors We can also write the velocity in terms of its components: The magnitude of velocity is the particle’s speed: The direction is determined by the components: May be + or – But speed is always positive 3-6 Vector Kinematics Generalizing the one-dimensional equations for constant acceleration: 3-6 Vector KinematicsIt can be understood by analyzing the horizontal and vertical motions separately. 3-7 Projectile Motion Projectile move along parabolic trajectories. The launch angle ! is the angle of the initial velocity vi above the horizontal (i.e. x-axis). The components of vi are then 3-7 Projectile Motion Projectile motion is made up of 2-independent motions: 3-7 Projectile Motion A projectile follows a parabolic trajectory because it falls a distance !*gt2 below a straight-line trajectory The maximum range occurs at ! = 45o Range and Maximum Height of a Projectile •! When analyzing projectile motion, two characteristics are of special interest •! The range, R, is the horizontal distance of the projectile •! The maximum height the projectile reaches is h Height of a Projectile, Equation •! The maximum height of the projectile can be found in terms of the initial velocity vector: •! This equation is valid only for symmetric motionRange of a Projectile, equation •! The range of a projectile can be expressed in terms of the initial velocity vector: •! This is valid only for symmetric trajectory 3-8 Solving Problems Involving Projectile Motion A movie stunt driver on a motorcycle speeds horizontally off a 50.0-m-high cliff. How fast must the motorcycle leave the cliff top to land on level ground below, 90.0 m from the base of the cliff where the cameras are? Ignore air resistance. 3-8 Solving Problems Involving Projectile Motion 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 Questions: •! What is a force? •! What is the connection between force and motion? Our Definitions of Force: •! A force is a simply push or pull on an object. •! A force is a vector. It has both a magnitude and a direction. •! A force requires an agent. Something does the pushing and pulling. •! A force is either a contact force, which acts through physical contact between the agent and object (e.g. a bat hitting a ball), or a long-range force, which acts without physical contact (e.g. gravity) •! Force can be thought of as an interaction between two objects: the agent and object push on each other. Forces The magnitude of a force can be measured using a spring scale.Force is a vector, having both magnitude and direction. The magnitude of a force can be measured using a spring scale. Forces Examples 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) Fundamental Forces •! Gravitational force –!Between two objects •! Electromagnetic forces –!Between two charges •! Strong force (Nuclear force) –!Between subatomic particles •! Weak forces –!Arise in certain radioactive decay processes 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? Two Forces Applied to a Box So, when two forces are applied to a box, the box will respond by moving in a direction given by the net force. 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)Newton’s First Law: An object at rest remains at rest, and a moving object continues moving in a straight line with constant velocity, if and only if the net force acting on the object is zero. 0!!=netFis “mechanical equilibrium” There are two types: 1.!The object is at rest – Static Equilibrium 2.!The object moves with constant velocity in a straight line – Dynamic Equilibrium 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