Physics chapter 2 Ms. Pollock Representing Motion Physics chapter 2 Ms. Pollock

2.1 Picturing Motion Using measurement and calculation to analyze motion Allow determination of how fast and how far an object will move Perception of motion instinctive – eyes naturally notice moving objects more than stationary ones http://www.pbs.org/wgbh/nova/assets/img/special-relativity-nutshell/image-03- large.jpg

All Kinds of Motion Motion = change in position along path of straight line, circle, arc, or back-and-forth Study begun with motion along straight line – simplest motion Motion related to space and time http://www.scott-eaton.com/wp/wp-content/bodies_in_motion_II_ballet.jpg

Motion Diagrams Series of intervals showing location of object at regular time intervals Everything in background in same position Only object being observed in motion http://www.physicsclassroom.com/Class/1DKin/U1L2c3.gif

The Particle Model Tracking motion easier if following single point on object Particle motion simplified version of motion diagram Size of object must be smaller than size of motion https://s-media-cache- ak0.pinimg.com/736x/86/7f/82/867f82d4e3fc19096e542a92cc083d74.jpg

2.2 Where and When? Measurements of motion possible with addition of standard measuring devices Important to set coordinates for reference https://camo.githubusercontent.com/829b6d8b023204e4efd61dde1f28fc38f544d002/6 8747470733a2f2f646576656c6f7065722e6c6561706d6f74696f6e2e636f6d2f646f63756d656 e746174696f6e2f696d616765732f4c6561705f417865732e706e67

Coordinate Systems Coordinate system – location of zero point of variable being studied and direction in which values of variable increase Origin – point at which both variables have zero value Arrows representing position https://math-e-motion.wikispaces.com/file/view/250px-Cartesian-coordinate- system.svg.png/32885411/250px-Cartesian-coordinate-system.svg.png

Coordinate Systems Position – separation between object and origin Length of arrow indicates distance Negative position possible, if measurement to left of origin http://zonalandeducation.com/mstm/physics/mechanics/kinematics/1DMotion/xAxisN egativeDisplacement.png

Vectors and Scalars Magnitude – size Vector – quantity with both magnitude and direction Scalar – quantity without direction Vector represented in boldface and scalar represented in regular type in this text https://www.grc.nasa.gov/www/k-12/airplane/Images/vectors.jpg

Vectors and Scalars Familiar with scalar addition Vectors altered by direction and unit Example p. 35 Resultant – sum of vectors; always points from tail of first vector to tip of last vector http://www.cyberphysics.co.uk/graphics/diagrams/forces/vector_components3.gif

Time Intervals and Displacements Time interval – difference between two times; t = tf – ti Position – vector with tail at origin of coordinate system and tip at place Displacement – change in position; d = df – di Initial and final at beginning and end of any chosen interval Complete description of displacement require distance traveled and direction moved http://192.185.174.48/~thescienceclassr/wp-content/uploads/2013/11/distance-and- displacement.png

Time Intervals and Displacements Distance and displacement not the same; distance scalar, displacement vector Displacement same in any coordinate system Displacement often used in study of motion http://cnx.org/resources/ac2fc1d2bb61772caaefbaf319bee755bcae7049/PG10C2_008 .png

2.3 Position-Time Graphs Often helpful to represent motion in different ways Helpful in determining displacement Graphs often helpful in organizing information https://www2.southeastern.edu/Academics/Faculty/rallain/plab193/page1/page26/p age3/files/page3_1.jpg

Using a Graph to Find Out Where and When Position-time graph – line graph with time data on horizontal axis and position data on vertical axis Graph not picture of object’s path– picture of object’s speed Can be used to estimate position beyond what is known http://demo.webassign.net/ebooks/cj6demo/art/images/c02/nw0058.gif

Example Problem 1 When did the runner whose motion is described in Figure 2-12 reach 30.0 m beyond the starting point? Where was he after 4.5 s?

Practice Problems P. 39 # 9 - 13

Position vs. Time Instantaneous position – position of object at particular point in time, represented by d Representations of motion equivalent – important to learn which are best for solving different kinds of problems Can also be done for multiple objects http://www.physicsclassroom.com/getattachment/calcpad/1dkin/problems/prob12.gi f

Challenge Problem Niram, Oliver, and Phil all enjoy exercising and often go to a path along the river for this purpose. Niram bicycles at a very consistent 40.25 km/h, Oliver runs south at a constant speed of 16.0 km/h, and Phil walks south at a brisk 6.5 km/h. Niram starts biking north at noon from the waterfalls. Oliver and Phil both start at 11:30 AM at the canoe dock, 20.0 km north of the falls. 1. Draw position-time graphs for each person. 2. At what time will the three exercise enthusiasts be within the smallest distance interval? 3. What is the length of that distance interval?

Example Problem 2 When and where does runner B pass runner A?

Practice Problems P. 41 # 14 - 18

2.4 How Fast? Displacement and time needed to show how fast an object is moving Recall slope calculation (rise over run) With distance and time, velocity (slope) can be calculated. Red slope = (6.0 m – 2.0 m) / (3.0 s – 1.0 s) = 2.0 m/s Blue slope = (3.0 m – 2.0 m) / (3.0 s – 2.0 s) = 1.0 m/s

Average Velocity Change of position related to time interval v = d / t = (df – di) / (tf – ti) Slope of position time graph not speed, but velocity – has magnitude and direction http://hyperphysics.phy-astr.gsu.edu/hbase/images/vela6.gif

Average Speed Absolute value of position-time graph slope Speed – how fast object is moving Sign of slope direction of motion http://www.mentorials.com/site/monographs/high-school/physics/images/uniform- speed-graph-bus-journey.png

Example Problem 3 The graph at the right describe the motion of a student riding his skateboard along a smooth, pedestrian-free sidewalk. What is his average velocity? What is his average speed? v = d/t = (df – di) / (tf – ti) v = (12.0 m – 6.0 m) / (8.0 s – 4.0 s) v = 6m / 4 s V = 1.5 m/s in positive direction

Practice Problems P. 45 # 25 - 28

Instantaneous Velocity Average velocity describing what happened at several different times during the motion of the object Instantaneous velocity – speed at specific time within motion of object May indicate stop or change in direction http://teacher.nsrl.rochester.edu/TeachingPresentations/NCUR99/IMG016.GIF

Average Velocity on Motion Diagrams Vectors related to magnitudes of motions Average velocity equation of motion d = vt – di Direction specified by positive and negative charge