Physics 2514 Lecture 2

Transcription

1 Physics 2514 Lecture 2 P. Gutierrez Department of Physics & Astronomy University of Oklahoma Physics 2514 p. 1/17

2 Clicker To be or not to be, that is the question, but what is the answer? Please test your clicker by selecting any of the answers below. A) Yes. B) No. C) What? D) Why? E) Sounds good. Physics 2514 p. 2/17

3 Goal The goal of Chapter 1 is to introduce the concepts that are required to understand motion in a qualitative manner. Goals for today s lecture: Introduction to motion; Qualitative introduction to vectors; Introduction to the variables needed to describe motion; Introduction to velocity. Physics 2514 p. 3/17

4 Introduction The universe we live in is one of constant change and motion. In order to understand it, we need to find a set of principles and axioms that are based on observation. These can then be used to develop theories and models specific phenomena. Mechanics The science of motion. It consists of two branches: Kinematics The branch that concerns itself with the study of the motion independent of its cause; Originates with Galileo ( ) Dynamics The branch that concerns itself with the cause of the motion. Originates with Newton ( ) Further developed by D Alembert, Lagrange, Hamilton, Jacobi,... Physics 2514 p. 4/17

5 The Assumptions In order to discuss motion, any physics for that matter, we need to introduce the assumptions that we make: We will assume, at least for most of this semester, that all objects can be treated as point particles. A point particle has no size. Later in the semester we will see that this is correct if the point corresponds to the center of mass of the object. For a complete description we will also need to include the motion about the center of mass. We will also assume, unless told otherwise, that air resistance can be neglected. We will assume that relativistic and quantum mechanical effects can be ignored Physics 2514 p. 5/17

6 Motion Diagram Consider film of object in motion, then superimpose frames. Physics 2514 p. 6/17

7 Coordinate system To discuss motion, require a reference point. We use a right handed Cartesian coordinate system: Measure everything from origin. Measurement given as straight line distance or as distance along each of 3 perpendicular axis. PSfrag replacements 3 dimensions 2 dimensions Need to order things. (What cones first, second, etc. and how much later.) Define time, which depends on repeatability of measurements. Physics 2514 p. 7/17

8 Clicker Question What direction is the car traveling in? A) Left; B) Right; C) Can not tell, need to specify position of the car in each frame; D) Can not tell, need to specify the time at which each frame occurs; Physics 2514 p. 8/17

9 Units & Dimensions Before continuing we discuss units and dimensions For mechanics, the only quantities that we need to specify are time, position (length, distance), and mass. We will use SI units (Systeme Internationale d Unites) Time in second Position in meters Mass in kilograms All other measured quantities are given in terms of the dimensions of mass, length and time. Physics 2514 p. 9/17

10 Definitions Some more definitions Coordinate system Reference frame relative to which positions are measured. The standard reference frame is the Cartesian (rectangular) system with three perpendicular axis. Vector Mathematical object with magnitude and direction Scalar Mathematical object that is represented by a single number such as time, temperature distance,... Position vector Vector of length given by distance from fixed location to object, its direction points toward object. Position This can be defined as either the position vector or a set of numbers on a grid Physics 2514 p. 10/17

11 Vector Properties A + B B A placements A B A B A B 2 A Physics 2514 p. 11/17

12 Motion Diagrams To define position, set up a coordinate system. Note: that coordinate systems are arbitrary and do not affect the physics. Coordinate system 1 Coordinate system 2 y y ments PSfrag replacements t 1 r 1 t 1 r 1 x x Physics 2514 p. 12/17

13 Motion Diagrams Since we are interested in motion, lets consider two position vectors. ments Coordinate system 1 PSfrag replacements Coordinate system 2 y y t 1 r t 2 r 1 t 1 r 2 r t 2 r 1 r 2 x r = r 2 r 1 is the displacement vector which is the difference of two positions vectors. It specifies the separation between two positions and the direction the displacement occurs in ( t 2 > t 1 ) x Physics 2514 p. 13/17

14 Average Velocity We are now ready to define the rate at which an object changes its position in a quantitative manner. ments Even more definitions Average velocity is the displacement divided by the travel time. v avg = r t with { } r = r2 r 1 t = t 2 t 1 and t 2 > t 1 y r 1 t 1 r 2 r t 2 Constant velocity Displacement vector does not change for equal length time intervals x Physics 2514 p. 14/17

15 Speed IMPORTANT: Speed and velocity are not the same: Average Speed is the total distance traveled divided by the time required to travel the distance speed = distance time Example ments path r In this case path length > r, the time interval is the same, therefore speed > velocity velocity means the magnitude of the velocity. Physics 2514 p. 15/17

16 Clicker A ball 12 m from a wall travels toward the wall, bounces off of it and returns to the starting position. The total travel time is 5 s. What is the average speed and average velocity of the red ball? Assume that the ball is a point. cements 12 m average speed, average velocity A) 0 m/s, 0 m/s B) 4.0 m/s, 0 m/s C) 4.8 m/s, 0 m/s D) 4.8 m/s, 4.8 m/s Physics 2514 p. 16/17

17 Announcement Finish reading chapter 1. I will discuss motion and its description using displacements, velocity, and acceleration during Monday s lecture. Make sure you understand the sections on solving problems (1.7, 1.8) and the section on significant figures and units (1.9). Physics 2514 p. 17/17