Physics 1408-002 Principles of Physics Sung-Won Lee [email protected] Lecture 2 – Chapter 2 – January 13, 2009 Announcement I Lecture note is on the web Handout (4 slides/page) http://highenergy.phys.ttu.edu/~slee/1408/ HW Assignment #1 will be placed on MateringPHYSICS “today”, and is due by 11:59pm on Tuesday, 1/20 1408 Lab News: on-going now!! *** 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 starting this Thursday. On-lime Homework !! To access MateringPHYSICS, you must register at http://www.masteringphysics.com/ !! Instructions are in the Student Access Kit. !! Your course ID is LEE2009 !! Once you are registered, you will be able to download the HW assignment. !! 52 out of 198 registered so far (~26%) !! If you do not have the Student Access Kit which comes with a new textbook, you can purchase one on the MasteringPHYSICS site. Please do it ASAP.Chapter 2 Describing Motion: Kinematics in “One” Dimension 1.! Reference Frames & Displacement 2.! Average Velocity 3.! Instantaneous Velocity 4.! Acceleration 5.! Motion at Constant Acceleration 6.! Solving Problems 7.! Freely Falling Objects The directions of the car’s velocity and acceleration are shown by the green (v) and gold (a) arrows. Motion is described using the concepts of velocity and acceleration. We examine in detail motion with constant acceleration, including the vertical motion of objects falling under gravity. Equations of Constant Acceleration Equations we need to solve constant-acceleration problemsKinematics-Description of Motion •! Reference Frames and Displacement •! Average Velocity •! Instantaneous Velocity •! Acceleration •! Motion at Constant Acceleration •! Solving Problems •! Falling Objects •! Graphical Analysis of Linear Motion Kinematics •! Describes motion while ignoring the agents that caused the motion •! For now, will consider motion in one dimension –! Along a straight line Position •! Defined in terms of a frame of reference –! One dimensional, so generally the x- or y-axis •! The object’s position is its location with respect to the reference frame (see next slide) Reference Frames and Displacement Any measurement of position, distance, or speed must be made with respect to a reference frame e.g. If you are sitting on a train and someone walks down the aisle, their speed with respect to the train is a few miles per hour, at most. Their speed with respect to the ground is much higher. A person walks toward the front of a train at 5 km/h. The train is moving 80 km/h with respect to the ground, so the walking person’s speed, relative to the ground, is 85 km/h. Reference Frames and Displacement Distinction between distance and displacement. Displacement (blue line) is how far the object is from its starting point, regardless of how it got there. Distance traveled (dashed line) is measured along the actual path. A person walks 70m east, then 30m west. The total distance traveled is 100 m (path is shown dashed in black); but the displacement, shown as a solid blue arrow, is 40m to the east.Reference Frames and Displacement The displacement is written: Left: Displacement is positive Right: Displacement is negative •! Defined as the change in position during some time interval –! Represented as !x; !x = xf – xi (f = final, i = initial) –! SI unit = meters (m) –! !x can be positive or negative The arrow represents the displacement x2 – x1 Average Velocity Speed: how far an object travels in a given time interval Velocity includes directional information: •! Velocity v is the “rate of change of position” •! Average velocity vav (or v) in the time !t = t2 - t1 is: vav!x(t2) " x(t1)t2" t1=#x#tt t1 t2 x1 x2 ! t trajectory Vav = slope of line connecting x1 and x2 ! x Uniform Motion •! The simplest form of motion is uniform motion. An object’s motion is uniform if its position-versus-time graph (x,t) is a straight-line. (see Fig) Fig shows how uniform and non-uniform motion appear in (x,t) graphs. For uniform motion the (average) velocity remains constant: Example •! You start in Chicago at 9 am and drive straight west down Iowa,stopping for tolls, arriving in Aurora 100 km west at 10 am. What is your average velocity? •! Let x be the displacement west. Let t1=0 be 9 a.m. and let t2= 1 hour be the arrival time. •! Let x(t1 )= x1=0 km be Chicago, and x(t2 )=x2= 100 km be Aurora. •! The displacement, x2- x1= 100 km •! The time interval, t2- t1= 1 hour = 3600 s •! The average velocity, x2- x1 /t2- t1 = 100 km/hrInstantaneous Velocity The instantaneous velocity is the average velocity, in the limit as the time interval becomes infinitesimally short. These graphs show (a) constant velocity, (b) varying velocity. Ideally, a speedometer would measure instantaneous velocity; in fact, it measures average velocity, but over a very short time interval. Instantaneous Velocity What was my velocity at the instant t = 1s?Finding Position from VelocityReminder!!2.4 Acceleration Acceleration deals with change of velocity. i.e. Acceleration is the rate of change of velocity. Velocity changes if: the magnitude of the velocity (speed) changes the direction of the velocity changes Change of velocity Average acceleration = Time interval Position, time, and velocity are important concepts, and they might appear to be sufficient. But that is not the case. Sometimes an object’s velocity changes as it moves. Note the same pattern: !v !r aavg = vavg = !t !t Three vector quantities: r displacement meters v velocity meters/second a acceleration meters/(second)2 " " " " ! ! ! 2.4 Acceleration Acceleration is a vector, although in one-dimensional motion we only need the sign (e.g. + or -) Left-hand Fig:: positive acceleration (“increase”) Right-hand Fig:: negative acceleration (“decrease”) 2-4 Acceleration There’s a difference between negative acceleration and deceleration: Negative acceleration is acceleration in the negative direction as defined by the