Representing MotionPHYSICS 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/829b6d8b023204e4efd61dde1f28fc38f544d002/68747470733a2f2f646576656c6f7065722e6c6561706d6f74696f6e2e636f6d2f646f63756d656e746174696f6e2f696d616765732f4c6561705f417865732e706e67

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/xAxisNegativeDisplacement.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/page3/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?

0 1 2 3 4 5 60

5

10

15

20

25

30

35

Chart Title

Time (s)

Posi

itio

n (

m)

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.gif

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?

0 15 25 35 45 55

-100

-50

0

50

100

150

200

250

300

Chart Title

Series1 Series2 Series3

Time (s)

Posi

tion (

m)

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

0 1 2 30

1

2

3

4

5

6

7

Chart Title

Red Jogger Blue Jogger

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 direction0 1 2 3 4 5 6 7 8 9

0

2

4

6

8

10

12

14

Chart Title

Column1 Column2 Column3

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