Published on December 12, 2007
Physics 211: Lecture 1“Mechanics for Physicists and Engineers”Agenda for Today: Physics 211: Lecture 1 “Mechanics for Physicists and Engineers” Agenda for Today Course information and advice (how does the course work?) Class plus WWW Scope of this course Measurement and Units Fundamental units Systems of units Converting between systems of units Dimensional Analysis 1-D Kinematics (review) Average & instantaneous velocity and acceleration Motion with constant acceleration Course Info & Advice: Course Info & Advice Go to http://www.physics.uiuc.edu and follow “courses” link to the Physics 211 homepage. This is always your starting point. Course has several components: Discussion sections (tutorials, problem solving, quizzes) Labs: (group exploration of physical phenomena) Homework sets, Web based Lecture: (demos, discussion and i-clicker questions) What happens if you miss a lab or discussion section… Can’t make this up, will get ex or 0. Give excuse document to staff in 233 Loomis (Note from doctor or emergency dean or coach…) The first few weeks of the course should be review, hence the pace is fast. It is important for you to keep up! Lecture Organization: Lecture Organization Three main components: Lecturer discusses class material Follows lecture notes very closely Modified lecture notes posted each day… Lecturer does as many demos as possible If you see it, you gotta believe it! Look for the symbol Students work in groups on conceptual “Active Learning” (ACT) problems and vote on the answer using their i-clicker. About 3-4 times per lecture Slide4: on How would you best describe your high school physics class? I liked it and I remember quite a bit I liked it but I don’t remember much I didn’t like it but I remember quite a bit I didn’t like it and I don’t remember much I didn’t take one Turn on your i-clicker and vote: Show how to register Back to How Grades are Calculated: Back to How Grades are Calculated Your final grade for Physics 211 will be based upon your total score on all the components of the course. The total score is the sum of your scores on the final exam (300 pts), three exams (100 pts each), labs (200 pts total), homework/quizzes/lecture (200 pts total). Adds to 1000 Based on our experience from previous semesters, rough guidelines for letter grades (minimum score) this semester will be: A+(950), A(920), A-(900), B+(880), B(860), B-(835), C+(810), C(780), C-(750), D+(720), D(690), D-(610), and F(<610). Grades…: Grades… 10 labs (zero through 9) for 200 points (very important) Lecture participation (ACTS) 1 point per lecture – maximum of 20 points. Everyone gets a free point for today's lecture [9 quizzes + 14 HW(A+B) - 4 lowest] for 180 pts Where are the quizzes? Discussion section Where are the homework problems? On the web 3 midterm exams (100 pts each) for 300 pts One big final exam worth 300 pts Grades…: Grades… Notice that we do NOT use the common 90/80/70/60 breakdown for letter grades. The reason for this is that for some parts of the course the average score is typically very high. Example: suppose you keep up with things and average 95% on HW/Disc/Lab/Lect. This amounts to 380 points out of the 1000 What do you need on your exams, then? To get an A- (900) you need 520/600 = 0.87 To get a B- (835) you need 455/600 = 0.76 To get a C- (750) you need 370/600 = 0.62 Scope of Physics 211: Scope of Physics 211 Classical Mechanics: Mechanics: How and why things work Classical: Not too fast (v << c) relativity (325) Not too small (d >> atom) quantum mechanics (214, etc) Most everyday situations can be described in these classical terms. Path of baseball Orbit of planets etc... Fundamental Units: How we measure things! All things in classical mechanics can be expressed in terms of the fundamental units: Length L Mass M Time T For example: Speed has units of L / T (i.e. miles per hour). Force has units of ML / T2 etc... (as you will learn). Fundamental Units Units...: Units... SI (Système International) Units: mks: L = meters (m), M = kilograms (kg), T = seconds (s) cgs: L = centimeters (cm), M = grams (gm), T = seconds (s) British Units: Inches, feet, miles, pounds, slugs... We will use mostly SI units, but you may run across some problems using British units. You should know how to convert back & forth. Converting between different systems of units: Converting between different systems of units Useful Conversion factors: 1 inch = 2.54 cm 1 m = 3.28 ft 1 mile = 5280 ft 1 mile = 1.61 km Example: convert miles per hour to meters per second: Dimensional Analysis : This is a very important tool to check your work It’s also very easy! Example: Doing a problem you get the answer distance d = vt 2 (velocity x time2) Units on left side = L Units on right side = L / T x T2 = L x T Left units and right units don’t match, so answer must be wrong!! Dimensional Analysis Lecture 1, Act 1Dimensional Analysis : Lecture 1, Act 1 Dimensional Analysis The period P of a swinging pendulum depends only on the length of the pendulum d and the acceleration of gravity g. Which of the following formulas for P could be correct ? Lecture 1, Act 1 Solution: Lecture 1, Act 1 Solution Realize that the left hand side P has units of time (T ) Try the first equation (a) (b) (c) (a) Not Right !! Lecture 1, Act 1 Solution: (a) (b) (c) (b) Not Right !! Try the second equation Lecture 1, Act 1 Solution Lecture 1, Act 1 Solution: (a) (b) (c) (c) This has the correct units!! This must be the answer!! Try the third equation Lecture 1, Act 1 Solution Motion in 1 dimension: Motion in 1 dimension In 1-D, we usually write position as x(t). Since it’s in 1-D, all we need to indicate direction is + or . Displacement in a time t = t2 - t1 is x = x(t2) - x(t1) = x2 - x1 1-D kinematics: 1-D kinematics Velocity v is the “rate of change of position” Average velocity vav in the time t = t2 - t1 is: 1-D kinematics...: Consider limit t1 t2 Instantaneous velocity v is defined as: 1-D kinematics... t x t1 t2 x x1 x2 t so v(t2) = slope of line tangent to path at t2. 1-D kinematics...: 1-D kinematics... Acceleration a is the “rate of change of velocity” Average acceleration aav in the time t = t2 - t1 is: And instantaneous acceleration a is defined as: using Recap: Recap If the position x is known as a function of time, then we can find both velocity v and acceleration a as a function of time! x a v t t t More 1-D kinematics: More 1-D kinematics We saw that v = dx / dt In “calculus” language we would write dx = v dt, which we can integrate to obtain: Graphically, this is adding up lots of small rectangles: v(t) t + +...+ = displacement 1-D Motion with constant acceleration: Math 220: Also recall that If a is constant, we can integrate this using the above rule to find: Similarly, since we can integrate again to get: 1-D Motion with constant acceleration Recap: Recap So for constant acceleration we find: x a v t t t Ramp w/ lights Lecture 1, Act 2Motion in One Dimension : Lecture 1, Act 2 Motion in One Dimension When throwing a ball straight up, which of the following is true about its velocity v and its acceleration a at the highest point in its path? (a) Both v = 0 and a = 0. (b) v 0, but a = 0. (c) v = 0, but a 0. y Lecture 1, Act 2Solution : Lecture 1, Act 2 Solution x a v t t t Going up the ball has positive velocity, while coming down it has negative velocity. At the top the velocity is momentarily zero. Since the velocity is continually changing there must be some acceleration. In fact the acceleration is caused by gravity (g = 9.81 m/s2). (more on gravity in a few lectures) The answer is (c) v = 0, but a 0. Useful Formula: 1-D motion with constant acceleration: Useful Formula: 1-D motion with constant acceleration Plugging in for t: Recap:: Recap: For constant acceleration: From which we know: Washers Problem 1: Problem 1 A car is traveling with an initial velocity v0. At t = 0, the driver puts on the brakes, which slows the car at a rate of ab Problem 1...: Problem 1... A car is traveling with an initial velocity v0. At t = 0, the driver puts on the brakes, which slows the car at a rate of ab. At what time tf does the car stop, and how much farther xf does it travel? x = 0, t = 0 ab v0 Problem 1...: Problem 1... Above, we derived: v = v0 + at Realize that a = -ab Also realizing that v = 0 at t = tf : find 0 = v0 - ab tf or tf = v0 /ab x Problem 1...: Problem 1... To find stopping distance we use: In this case v = vf = 0, x0 = 0 and x = xf Problem 1...: Problem 1... So we found that Suppose that vo = 65 mi/hr = 29 m/s Suppose also that ab = g = 9.81 m/s2 Find that tf = 3 s and xf = 43 m Problem Solving Tips:: Problem Solving Tips: Read Carefully! Before you start work on a problem, read the problem statement thoroughly. Make sure you understand what information is given, what is asked for, and the meaning of all the terms used in stating the problem. Using what you are given, set up the algebra for the problem and solve for your answer algebraically Invent symbols for quantities you know as needed Don’t plug in numbers until the end Watch your units ! Always check the units of your answer, and carry the units along with your formula during the calculation. Understand the limits ! Many equations we use are special cases of more general laws. Understanding how they are derived will help you recognize their limitations (for example, constant acceleration). Recap of today’s lecture: Recap of today’s lecture Scope of this course Measurement and Units (Chapter 1) Systems of units (Text: 1-2) Converting between systems of units (Text: 1-3) Dimensional Analysis (Text: 1-4) 1-D Kinematics (Chapter 2) Average & instantaneous velocity and acceleration (Text: 2-1, 2-2) Motion with constant acceleration (Text: 2-3) Example car problem Don’t forget to register your i-clicker.