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Physics 1408-002 Principles of Physics Sung-Won Lee [email protected] Lecture 3 – Chapter 2 & 3 – January 15, 2009 Announcement I Lecture note is on the web Handout (4 slides/page) http://highenergy.phys.ttu.edu/~slee/1408/ HW Assignment #1 is placed on MateringPHYSICS, 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. 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. !! 107 out of 198 registered so far (~26% -> 54% now) !! 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. Displacement •! Defined as the change in position during some time interval –! Represented as !x; !x = xf – xi (f = final, i = initial) 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. The displacement is written: 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:Instantaneous Velocity The instantaneous velocity is the average velocity, in the limit as the time interval becomes infinitesimally short. Ideally, a speedometer would measure instantaneous velocity; in fact, it measures average velocity, but over a very short time interval. Reminder!! 2.4 Acceleration Acceleration deals with change of velocity. i.e. Acceleration is the rate of change of velocity. 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. The instantaneous acceleration is the average acceleration, in the limit as the time interval becomes infinitesimally short. Motion at Constant Acceleration We now have all the equations we need to solve constant-acceleration problems.Velocity and acceleration are related Knowing an objects’ acceleration is the key to finding its velocity at later instants of time. Motion with Constant Acceleration i.e. uniformly accelerated motionIMPORTANTConstant Acceleration- Falling Objects Near the surface of the Earth, all objects experience approximately the same acceleration due to gravity. GALILEO!!!! Multi-flash photograph of a falling apple, at equal time intervals. The apple falls farther during each successive interval, which means it is accelerating. Falling Objects In the absence of air resistance, all objects fall with the same acceleration, although this maybe hard to tell by testing in an environment where there is air resistance. A ball and a light piece of paper are dropped at the same time. Freely Falling Objects The acceleration due to gravity at the Earth’s surface is approximately 9.80 m/s2. At a given location on the Earth and in the absence of air resistance, all objects fall with the same constant acceleration. A rock and a feather are dropped simultaneously (a) in air, (b) in a vacuum.Falling Objects The acceleration due to gravity at the Earth’s surface is approximately a =g = 9.80 m/s2 afree fall = (9.80 m/s2 , down) ay = -g = -9.80 m/s2 Suppose that a ball is dropped (v0 = 0) from a tower 70.0 m high. How far will it have fallen after a time t1 = 1.00 s, t2 = 2.00 s, and t3 = 3.00 s? **Ignore air resistance. Reminder!!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 live in a 3 + 1 dimensional world"•! 3 space dimensions •! 1 time dimension"(string theorists tell us it’s 10 + 1)"2 Dimensions"x1 y1 x and y coordinates of point ( x1, y1) Cartesian Coordinate System •! Also called rectangular coordinate system •! x- and y- axes intersect at the origin •! Points are labeled (x,y); requires two numbers Used to describe the position of a point in space can also specify a position by giving "distance and direction from origin """y"x"r"r, ""Polar Coordinate System •! Point is distance r from the origin in the direction of angle !, ccw from reference line •! Points are labeled (r,!)Polar to Cartesian Coordinates •! Based on forming a right triangle from r and !"•!x = r cos ! •!y = r sin ! Cartesian to Polar Coordinates •! Relationship between r and !"•!! must be ccw from positive x axis for these equations to be valid 2 2tanyxr x y!== +Vectors and Scalars A vector has magnitude as well as direction. Some vector quantities: displacement, velocity, force, momentum A scalar has only a magnitude. Some scalar quantities: mass, time, temperature Car


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TTU PHYS 1408 - Describing Motion

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