Chapter 2: Motion Along a Straight Line PDF

Chapter 2 Motion Along a Straight Line PowerPoint® Lectures for University Physics, 14th Edition, Global Edition – Hugh D. Young and Roger A. Freedman Lectures by Jason Harlow © 2016 Pearson Education, Ltd.  Learning Goals for Chapter 2 Looking forward at …...

Chapter 2 Motion Along a Straight Line PowerPoint® Lectures for University Physics, 14th Edition, Global Edition – Hugh D. Young and Roger A. Freedman Lectures by Jason Harlow © 2016 Pearson Education, Ltd.  Learning Goals for Chapter 2 Looking forward at … how the ideas of displacement and average velocity help us describe straight-line motion. the meaning of instantaneous velocity; the difference between velocity and speed. how to use average acceleration and instantaneous acceleration to describe changes in velocity. how to solve problems in which an object is falling freely under the influence of gravity alone. how to analyze straight-line motion when the acceleration is not constant. © 2016 Pearson Education, Ltd.  Introduction Kinematics is the study of motion. Velocity and acceleration are important physical quantities. A typical runner gains speed gradually during the course of a sprinting foot race and then slows down after crossing the finish line. © 2016 Pearson Education, Ltd.  Displacement, time, and average velocity A particle moving along the x-axis has a coordinate x. The change in the particle’s coordinate is The average x-velocity of the particle is © 2016 Pearson Education, Ltd.  Rules for the sign of x-velocity © 2016 Pearson Education, Ltd.  Instantaneous velocity The instantaneous velocity is the velocity at a specific instant of time or specific point along the path and is given by vx = dx/dt. The average speed is not the magnitude of the average velocity! © 2016 Pearson Education, Ltd.  2.1 © 2016 Pearson Education, Ltd.  Average acceleration Acceleration describes the rate of change of velocity with time. The average x-acceleration is © 2016 Pearson Education, Ltd.  Instantaneous acceleration The instantaneous acceleration is ax = dvx/dt. © 2016 Pearson Education, Ltd.  Exp. 2.3 © 2016 Pearson Education, Ltd.  Rules for the sign of x-acceleration © 2016 Pearson Education, Ltd.  Motion with constant acceleration © 2016 Pearson Education, Ltd.  The equations of motion with constant acceleration The four equations below apply to any straight-line motion with constant acceleration ax. © 2016 Pearson Education, Ltd.  Exp. 2.4 © 2016 Pearson Education, Ltd.  Exp. 2.5 © 2016 Pearson Education, Ltd.  Freely falling bodies Free fall is the motion of an object under the influence of only gravity. In the figure, a strobe light flashes with equal time intervals between flashes. The velocity change is the same in each time interval, so the acceleration is constant. © 2016 Pearson Education, Ltd.  A freely falling coin 2.6 If there is no air resistance, the downward acceleration of any freely falling object is g = 9.8 m/s2 = 32 ft/s2. © 2016 Pearson Education, Ltd.  Exp. 2.7 © 2016 Pearson Education, Ltd.  Chapter 3 Motion in Two or Three Dimensions PowerPoint® Lectures for University Physics, 14th Edition, Global Edition – Hugh D. Young and Roger A. Freedman Lectures by Jason Harlow © 2016 Pearson Education, Ltd.  Projectile motion A projectile is any body given an initial velocity that then follows a path determined by the effects of gravity and air resistance. Begin by neglecting resistance and the curvature and rotation of the earth. © 2016 Pearson Education, Ltd.  The x- and y-motion are separable The red ball is dropped at the same time that the yellow ball is fired horizontally. The strobe marks equal time intervals. We can analyze projectile motion as horizontal motion with constant velocity and vertical motion with constant acceleration: © 2016 Pearson Education, Ltd.  Projectile motion If air resistance is negligible, the trajectory of a projectile is a combination of horizontal motion with constant velocity and vertical motion with constant acceleration. © 2016 Pearson Education, Ltd.  Projectile motion – Initial velocity The initial velocity components of a projectile (such as a kicked soccer ball) are related to the initial speed and initial angle. © 2016 Pearson Education, Ltd.  The equations for projectile motion If we set x0 = y0 = 0, the equations describing projectile motion are shown below: © 2016 Pearson Education, Ltd.  3.7 © 2016 Pearson Education, Ltd.  Acceleration for uniform circular motion © 2016 Pearson Education, Ltd.  Acceleration for uniform circular motion For uniform circular motion, the instantaneous acceleration always points toward the center of the circle and is called the centripetal acceleration. The magnitude of the acceleration is arad = v2/R. The period T is the time for one revolution, and arad = 4π2R/T 2. © 2016 Pearson Education, Ltd.  Uniform circular motion © 2016 Pearson Education, Ltd.  Projectile motion © 2016 Pearson Education, Ltd.  Nonuniform circular motion If the speed varies, the motion is nonuniform circular motion. The radial acceleration component is still arad = v2/R, but there is also a tangential acceleration component atan that is parallel to the instantaneous velocity. © 2016 Pearson Education, Ltd.  3.12 © 2016 Pearson Education, Ltd.  Chapter 4 Newton’s Laws of Motion PowerPoint® Lectures for University Physics, 14th Edition, Global Edition – Hugh D. Young and Roger A. Freedman Lectures by Jason Harlow © 2016 Pearson Education, Ltd.  What are some properties of a force? © 2016 Pearson Education, Ltd.  There are four common types of forces: Normal The normal force is a contact force. © 2016 Pearson Education, Ltd.  There are four common types of forces: Friction Friction is a contact force. © 2016 Pearson Education, Ltd.  There are four common types of forces: Tension Tension is a contact force. © 2016 Pearson Education, Ltd.  There are four common types of forces: Weight Weight is a long-range force. © 2016 Pearson Education, Ltd.  What are the magnitudes of common forces? The SI unit of the magnitude of force is the newton, abbreviated N. Some typical force magnitudes are: Weight of a large blue whale 1.9 × 106 N Maximum pulling force of a locomotive 8.9 × 105 N Weight of a 250-lb linebacker 1.1 × 103 N Weight of a medium apple 1N Electric attraction between the proton 8.2 × 10−8 N and the electron in a hydrogen atom Gravitational attraction between the 3.6 × 10−47 N proton and the electron in a hydrogen atom © 2016 Pearson Education, Ltd.  Drawing force vectors The figure shows a spring balance being used to measure a pull that we apply to a box. We draw a vector to represent the applied force. The length of the vector shows the magnitude; the longer the vector, the greater the force magnitude. © 2016 Pearson Education, Ltd.  Newton’s first law When a body is either at rest or moving with constant velocity (in a straight line with constant speed), we say that the body is in equilibrium. For a body to be in equilibrium, it must be acted on by no forces, or by several forces such that their vector sum—that is, the net force—is zero: © 2016 Pearson Education, Ltd.  Net force causes acceleration A hockey puck accelerates in the direction of a net applied force. © 2016 Pearson Education, Ltd.  Newton’s first law When the net force is zero, the acceleration is zero, and the puck is in equilibrium. © 2016 Pearson Education, Ltd.  When is Newton’s first law valid? Suppose you are in a bus that is traveling on a straight road and speeding up. If you could stand in the aisle on roller skates, you would start moving backward relative to the bus as the bus gains speed. It looks as though Newton’s first law is not obeyed; there is no net force acting on you, yet your velocity changes. The bus is accelerating with respect to the earth and is not a suitable frame of reference for Newton’s first law. A frame of reference in which Newton’s first law is valid is called an inertial frame of reference. © 2016 Pearson Education, Ltd. © 2016 Pearson Education, Ltd.  Crash test dummies From the frame of reference of the car, it seems as though a force is pushing the crash test dummies forward as the car comes to a sudden stop. But there is really no such force: As the car stops, the dummies keep moving forward as a consequence of Newton’s first law. © 2016 Pearson Education, Ltd.  Newton’s second law of motion The acceleration of an object is directly proportional to the net force acting on it, and inversely proportional to the mass of the object. The SI unit for force is the newton (N). 1 N = 1 kg·m/s2 © 2016 Pearson Education, Ltd.  Systems of units: Table 4.2 We will use the SI system. In the British system, force is measured in pounds, distance in feet, and mass in slugs. In the cgs system, mass is in grams, distance in centimeters, and force in dynes. © 2016 Pearson Education, Ltd.  4.5 © 2016 Pearson Education, Ltd.  Mass and weight The weight of an object (on the earth) is the gravitational force that the earth exerts on it. The weight w of an object of mass m is: The value of g depends on altitude. On other planets, g will have an entirely different value than on the earth. © 2016 Pearson Education, Ltd.  Relating the mass and weight of a body © 2016 Pearson Education, Ltd.  Newton’s third law © 2016 Pearson Education, Ltd.  Newton’s third law The simple act of walking depends crucially on Newton’s third law. To start moving forward, you push backward on the ground with your foot. As a reaction, the ground pushes forward on your foot (and hence on your body as a whole) with a force of the same magnitude. This external force provided by the ground is what accelerates your body forward. © 2016 Pearson Education, Ltd.  Free-body diagrams © 2016 Pearson Education, Ltd.  5.3 © 2016 Pearson Education, Ltd.  5.6 © 2016 Pearson Education, Ltd.  5.7 © 2016 Pearson Education, Ltd.  Frictional forces There is friction between the feet of this caterpillar (the larval stage of a butterfly of the family Papilionidae) and the surfaces over which it walks. Without friction, the caterpillar could not move forward or climb over obstacles. © 2016 Pearson Education, Ltd.  Frictional forces When a body rests or slides on a surface, the friction force is parallel to the surface. © 2016 Pearson Education, Ltd.  Frictional forces Friction between two surfaces arises from interactions between molecules on the surfaces. © 2016 Pearson Education, Ltd.  Kinetic and static friction Kinetic friction acts when a body slides over a surface. The kinetic friction force is fk = µkn. Static friction acts when there is no relative motion between bodies. The static friction force can vary between zero and its maximum value: fs ≤ µsn. © 2016 Pearson Education, Ltd.  Static friction followed by kinetic friction: Slide 1 Before the box slides, static friction acts. But once it starts to slide, kinetic friction acts. © 2016 Pearson Education, Ltd.  Static friction followed by kinetic friction: Slide 2 Before the box slides, static friction acts. But once it starts to slide, kinetic friction acts. © 2016 Pearson Education, Ltd.  Static friction followed by kinetic friction: Slide 3 Before the box slides, static friction acts. But once it starts to slide, kinetic friction acts. © 2016 Pearson Education, Ltd.  Static friction followed by kinetic friction: Slide 4 Before the box slides, static friction acts. But once it starts to slide, kinetic friction acts. © 2016 Pearson Education, Ltd.  Static friction followed by kinetic friction: Slide 5 Before the box slides, static friction acts. But once it starts to slide, kinetic friction acts. © 2016 Pearson Education, Ltd.  Some approximate coefficients of friction © 2016 Pearson Education, Ltd.  5.13 © 2016 Pearson Education, Ltd. 68 Considering here kineticMechanics friction Gravitational force Frictional force for 68  Chapter 6 Work and Kinetic Energy PowerPoint® Lectures for University Physics, 14th Edition, Global Edition – Hugh D. Young and Roger A. Freedman Lectures by Jason Harlow © 2016 Pearson Education, Ltd.  Work A force on a body does work if the body undergoes a displacement. These people are doing work as they push on the car because they exert a force on the car as it moves. © 2016 Pearson Education, Ltd.  Units of work The SI unit of work is the joule (named in honor of the 19th-century English physicist James Prescott Joule). Since W = Fs, the unit of work is the unit of force multiplied by the unit of distance. In SI units: 1 joule = (1 newton) (1 meter) or 1 J = 1 N ∙ m If you lift an object with a weight of 1 N a distance of 1 m at a constant speed, you do 1 J of work on it. © 2016 Pearson Education, Ltd.  Work done by a constant force The work done by a constant force acting at an angle to the displacement is: This can be written more compactly as: © 2016 Pearson Education, Ltd.  Positive work When the force has a component in the direction of the displacement, work is positive. © 2016 Pearson Education, Ltd.  Negative work When the force has a component opposite to the direction of the displacement, work is negative. © 2016 Pearson Education, Ltd.  Zero work When the force is perpendicular to the direction of the displacement, the force does no work on the object. © 2016 Pearson Education, Ltd.  Total work The work done by the net force on a particle as it moves is called the total work Wtot. The particle speeds up if Wtot > 0, slows down if Wtot < 0, and maintains the same speed if Wtot = 0. © 2016 Pearson Education, Ltd.  Kinetic energy The energy of motion of a particle is called kinetic energy: Like work, the kinetic energy of a particle is a scalar quantity; it depends on only the particle’s mass and speed, not its direction of motion. Kinetic energy can never be negative, and it is zero only when the particle is at rest. The SI unit of kinetic energy is the joule. © 2016 Pearson Education, Ltd.  6.2 © 2016 Pearson Education, Ltd.  6.3 © 2016 Pearson Education, Ltd. 80 Mechanics Impulse https://en.wikipedia.org/wiki/Impulse_(physics) For a force to cause any action it must act over a period of time. infinitesimal change in momentum Newton’s Force  second infinitesim law: al change in time Impulse (a force applied over a Change period of time) in For a constant moment force: um- PHY1005 80  Power Power is the rate at which work is done. Average power is: Instantaneous power is: The SI unit of power is the watt (1 W = 1 J/s), but another familiar unit is the horsepower (1 hp = 746 W). © 2016 Pearson Education, Ltd.  Power: Lifting a box slowly © 2016 Pearson Education, Ltd.  Power: Lifting a box quickly © 2016 Pearson Education, Ltd.  6.9 © 2016 Pearson Education, Ltd.  Gravitational potential energy When a particle is in the gravitational field of the earth, there is a gravitational potential energy associated with the particle: As the basketball descends, gravitational potential energy is converted to kinetic energy and the basketball’s speed increases. © 2016 Pearson Education, Ltd.  7.6 © 2016 Pearson Education, Ltd.  Chapter 8 Momentum, Impulse, and Collisions PowerPoint® Lectures for University Physics, 14th Edition, Global Edition – Hugh D. Young and Roger A. Freedman Lectures by Jason Harlow © 2016 Pearson Education, Ltd.  Introduction In many situations, such as a bullet hitting a carrot, we cannot use Newton’s second law to solve problems because we know very little about the complicated forces involved. In this chapter, we shall introduce momentum and impulse, and the conservation of momentum, to solve such problems. © 2016 Pearson Education, Ltd.  Momentum and Newton’s second law The momentum of a particle is the product of its mass and its velocity: Newton’s second law can be written in terms of momentum: © 2016 Pearson Education, Ltd. 90 Mechanics Conservation of Momentum The total momentum in a system of interacting bodies is conserved, this is a consequence of Newton’s third law of motion which states: For every action, there is an equal and opposite reaction. isolated system of two bodies undergoing a coulomb attraction The total momentum in this system Momentum is remains the same at any time during conserved in all the interaction. interactions. i.e. does not PHY1005 - change. 90  8.2 © 2016 Pearson Education, Ltd.  8.5 © 2016 Pearson Education, Ltd.