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# Physics I PHYS 150

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This 5 page Study Guide was uploaded by Madyson Sporer on Monday October 5, 2015. The Study Guide belongs to PHYS 150 at Christian Brothers University taught by Staff in Fall. Since its upload, it has received 39 views. For similar materials see /class/219458/phys-150-christian-brothers-university in Physics 2 at Christian Brothers University.

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Date Created: 10/05/15

PHYS 150 STUDY GUIDE FOR PART ONE VECTORS AND BASIC MOTION INTRODUCTION In this first quarter ofthe course we consider I what physics is 2 the concept of vectors and 3 the basic description of motion We first of all consider what physics is A first attempt at a definition might be this Physics is the science that considers the basic structure of matter the basic properties of matter the basic interactions between pieces of matter and the basic descriptions of motion Physics attempts to describe as many natural phenomena happenings as it can in terms of as few basic principles laws as it can Note Natural phenomena are usually very complex things and to start with we will be making many idealizations and simplifying assumptions Once the basic principles are known you can begin to consider removing some ofthese simplifying assumptions and try to obtain more and more accurate descriptions of real phenomena ote This is a physics course and not an applications course We will consider some applications as examples but the applications are not the primary aim ofthe course They are only a very nice side benefit We are primarily seeking the basic structure properties interactions and descriptions You can deal with more applications in engineering courses or on your own if you understand the basic principles you should be able to do this but time puts a severe limit on our discussion of applications in this class If you wish to talk about applications outside of class I will be glad to talkto you Physics is a science which means that it involves measurements We discuss measurements and the associated units and dimensions This leads to the metric system Next we discuss the idea of vectors and coordinate systems in anticipation of the ideas of force and motion You must learn to think in terms of components of vector quantities if you are to work successfully in physics and hence in engineering Our first lab experiment deals with these ideas Finally we consider the basic description of motion position velocity and acceleration You must be able to distinguish velocity and acceleration they are not the same Our second lab experiment deals with this PHYSICS AND MEASUREMENT OUTLINE 1 Introduction a de nition of physics b review of math S1 0 measurements dimensions and units d the metric system e dimensional analysis f order of magnitude estimates Su lementa Problems 8 1 Given the following three equations solve them for x y and z ax by 02 5 where abc are the last three digits of your phone number eg 3213448 means a4 b4 08 dx ey fz 8 where def are the last three digits ofyour social security number gx hy kz 0 where ghk are the last three digits of your zip code HINT In the look back stage step 7 check your answers by substituting in your answers into the equations to show that they indeed work PHYS 150 Study Guide for Part 1 page 2 DIRECTED QUANTITIES VECTORS OUTLINE 1 Positions a lengths b angles 0in radians sr sarclength rradius S234 c coordinate systems and transformations between systems 1 rectangular Xy X r cos0 y r sin0 2 polar r0 r X2 yz 0 arctanyX 2 Vectors 85 a position is a vector b idea ofa vector magnitude and direction c components of a vector MOST IMPORTANT 1 rectangular X and y components 2 polar magnitude and direction 3 two three and more dimensions 3d coordinate systems include rectangular spherical cylindrical d addition and subtraction of vectors 1 add rectangular components 2 can NOTjust add nonrectangular components Su lementa Problems 8 2 lfthe arc length is 30 meters and the radius is 15 meters what is the angle a in radians b in degrees c in revolutions 3 lfthe diameter ofthe moon is 3476 km and its distance from the earth is 384500 km what angle does the moon make with the eye a in radians b in degrees c in cycles Hint DRAWA GOOD and CLEAR DIAGRAM showing both given distances and the angle at the eye 4 What is the displacement ofthe point of a wheel initially in contact with the ground when the wheel rolls fonNard 34 of a revolution the radius of the wheel is 39R39 and the 39Xaxis39 is the fonNard direction Hint DRAWA GOOD and CLEAR DIAGRAM showing the initial and final positions and the displacement vector between them 5 A car drives ve blocks East turns North for two blocks then turns back West for 2 blocks What is the nal position ofthe car relative to the initial position Express in both rectangular and polar form ANSWERS TO Supplementam Problems 2 a 020 radians b 1146 c 0032 revolutions 3 a 00090 radians b 0518 c 00014 cycles 4 571 R 100 R or 580 R 99 5 3 blocks East 2 blocks North or 361 blocks 337 North of East PHYS 150 Study Guide for Part 1 page 3 MOTION IN ONE DIMENSION OUTLINE 1 Introduction Motion is change in position with time 2 Velocity a average velocity vxavg AXAt AX X na Xinmal b velocity is a vector magnitude speed and direction polar form v 6V rectangular form vx vy c instantaneous velocity vX dXdt need Xt Acceleration 86 A v a average acceleration axavg AvXAt b acceleration is a vector magnitude and direction polar form a ea rectangular form ax ay c instantaneous acceleration aX dedt need vxt since add only in rectangular must differentiate only in rectangular d distinguish between velocity and acceleration A v The inverse of differentiation is integration S789 tf b AX to vxt dt Xtf Xo to nd Xtf need X0 a AvX if axt dt Vxtf vxo to nd Vxtf need vxo c nding position from acceleration rst nd vxt then Xt need vxo amp X0 01 v A particular case constant acceleration S101112 a formulas X Xt Xo vxot 12axt2 vX vxt vxo axt aX const b freely falling bodies ay gearth 98 ms2 const nearthe earth PHYS 150 Study Guide for Part 1 page 4 Su lementa Problems 8 6 Below is a graph of Xt On the graphs beside it sketch vt and at 7 Below is a graph of axt On the graphs beside it sketch Xt and vxt assuming that Xo gt O and vxo lt O PHYS 150 Study Guide for Part 1 page 5 8 Below are the numerical values of velocity at speci c times as well as the functional expression for velocity a Using the numerical method calculate both the average acceleration during each second between t0 and t8 seconds and calculate the position at each second in the range t0 to t8 seconds You should assume that x10 m when t0 ie X0 10 m b To check yourself use the functional form for vxt to nd axt and Xt using calculus again assume X0 10 m calcualte the acceleration att 75 sec and compare it to the average acceleration between 7 and 8 sec and evaluate the position at t8 sec and compare to what you got using the numerical procedure HINT remember for the numerical method you use vXavg AXAt and amg AvXAt where AX X1 X At t1 t NUMERICAL dATA vx0 sec 2500 ms vx5 sec 1000 ms vx1 sec 2488 ms vx6 sec 092 ms vx2 sec 2404 ms vx7 sec 1616 ms vx3 sec 2176 ms vx8 sec 3644 ms vx4 sec 1732 ms FUNCTIONAL FORM vxt 25 ms 012 ms4t3 9 For the situation in problem 8 above graph vxt vs t From this graph qualitatively graph Xt vs t and axt vs t Be sure to indicate the initial conditions on your graphs 10 A car accelerates assume uniformly from rest with an acceleration of 18 ms2 a How long a time will it take forthe carto reach a speed of 25 ms b How far will the car have gone in this time c How fast will the car be going after 10 seconds d How far will the car have gone after 10 seconds 11 A ball is thrown upwards from the top of a building 14 meters high with an initial speed of 25 ms a How long will it take the ball to reach it39s highest point b How high will this highest point be c How long will it take the ball to hit the ground at the bottom of the building d How fast will the ball be going when it hits the ground 12 An airplane on an aircraft carrier takes off from rest and needs to reach a speed of 80 ms 80 ms 180 mph but the wind and the speed of the carrier make this an effective speed of 225 mph The carrier has a deck 110 meters long for the takeoff Assume the acceleration of the plane during takeoff is constant a What is the acceleration necessary for the plane during take off b What is this acceleration in 39gees39 c How long in duration is the takeoff Answers to Supplementam Problems 69 You are on your own on all these For problem 8 make sure your answers to the numerical and calculus ways are close For problem 9 you should be able to check your graphs with your answers to problem 8 above 10 a 1389 sec b 17361 m c 18 ms d 90 m 11 a 255 sec b 4589 m c 561 sec d 2999 ms 12 a 2909 ms2 b 297 gees c 275 sec

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