Unit: Graphing Motion

1
Unit Graphing Motion Objectives Describe types
of straight line motion. Design experiments to
collect data and analyze motion. Use graphs to
describe the motion of the object. Book
Assignment Physics A Reading 2.7 and Appendix
C Physics Honors Read 2.8 Question s 17
and 19 Problem s 51 - 59 Work with the
person next to you, create a list of different
types of linear (straight line) motion. What is
acceleration vs. velocity?
2
Work with the person next to you, create a list
of different types of linear (straight line)
motion. Compare acceleration to velocity
3
Demonstrations Constant Velocity Bowling ball
rolling on floor Air Hockey Puck What role does
friction play in these? Sketch graphs of the
motion on the axes below.
4
Constant Acceleration Bowling Ball rolling down
a ramp Dropping a book above a table Dropping a
sheet of paper uncrumpled vs. crumpled What role
does friction play in these? Sketch graphs of
the motion on the axes below.
5
Air Resistance Drafting
6
Constant Deceleration Bowling Ball rolling up a
ramp Pushing cart across floor - roll to a
stop Book sliding to rest on a table What role
does friction play in these? Sketch graphs of
the motion on the axes below.
7
Activity Graphing the Motion of a Toy
Buggy Observe the buggy. What type of motion is
this? What role does friction play in this case?
8

• Buggy Rules
• Cheap and Fragile
• Dont drop it.
• Dont push it with the motor off.
• Dont restrain the buggy from motion.
• Objective
• In a group of 4, collect displacement/time data
  and graph
• it. You should have at least four data points.
• 2. Determine the actual velocity of the buggy.
• Materials
• Buggy
• Stop Watches
• Meter Sticks
• Graph paper or computer

9

• General Lab Conduct THESE APPLY ALL YEAR!
• Treat others with respect.
• If you put any marks on the floor, remove them.
• When in the hall, be respectful of other classes.
• Clean up all materials - leave the room in better
  condition
• than you found it.
• 5. Failure to follow these rules will result in
  boring lab lectures
• instead of activities.
• Any questions?
• You may begin. As you are collecting your data,
  on a
• separate piece of paper, create a data table, a
  sketch of your
• set-up and a brief description of the procedure.
  Then we can
• process the data before graphing.

10

• What is good data?
• As many data points as reasonable.
• A set of data points is for a given run of the
  buggy.
• Be consistent with measurements, ie always use
  the same
• spot on the object.
• Appropriate units.
• Correct experimental design.
• For example, a rolling start in this case.
• 6. Consider sources of error - avoidable ones vs.
  unavoidable
• ones.
• 7. Why was it easier to set the distance and
  measure the time?

11
Refer to Handout Steps for Creating a Graph in
Excel
12

• Add the following steps to this handout.
• Making a good graph
• 1. Start with the end in mind (have an idea of
  what the graph
• should look like).
• Make sure the scale/numbers is/are appropriate -
  data takes
• up at least 3/4 of the graph.
• Label all axes with titles and units.
• Title graph (Y Title vs. X Title).
• Do not connect the data points. Draw a trend
  line.
• In an Excel graph, make sure the background is
  white!
• Be sure to put your name in the header,footer or
  text box.
• In the Excel graph, turn on major and minor
  gridlines.
• Follow these rules and create a graph of your
  data.

13
Here is a graph of some sample data
14
Did you draw a trendline? Did you label the
axes? In Physics class, the units are as
important as the numbers. SLOPE RISE/RUN
What is the rise? METERS What is the
run? SECONDS What is the rise/run? METERS/SECO
ND Does this have any physical meaning for this
graph? (What is this a measurement
of?) VELOCITY This method of unit analysis
works for any graph to see what the graph is
measuring.
15
What are some shapes that you can calculate the
area of? Rectangle base x height, Triangle
1/2 base x height Look at your graph, do you see
a triangle? What are the units of the
base? SECONDS What are the units of the
height? METERS What would the units of the area
of this triangle be? SECONDS x METERS Does the
area under the line have any physical
meaning? Not in this graph, but it may depending
on the graph. You should always check the slope
and area of any graph to see if they have any
physical meaning.
16

• When calculating slope, you should always use
  points that are
• far enough apart to be accurate.
• Steps for Calculating Slope
• Determine the numerical value of each division on
  the X and
• Y axes. Remembering that each box does not
  necessarily
• equal one unit.
• Select two points that are far apart on your
  line. These are
• not actual data points, because data points
  rarely fall on
• the trendline.
• Carefully label their X,Y coordinates.
• Determine slope using change in Y over change in
  X. Dont
• forget the UNITS and SHOW ALL WORK!
• Just for fun, convert your slope to miles/hour.
• The next slide will show you what your graph
  should look like.
• Who had the fastest vehicle in the class?

17
rise
run
18
Pick three points on your displacement time graph
and determine the velocity at those points. You
should pick points one in the beginning, one
in the middle and one at the end of the
run. Create a data table on your graph of these
times and velocities.
19
Time (seconds) Velocity (meters/sec)
1 0.27
3 0.27
5 0.27
20
Create a graph of velocity vs. time using the
data table from the displacement time graph.
21
(No Transcript)
22
SLOPE RISE/RUN What is the
rise? METERS/SECOND What is the
run? SECONDS What is the rise/run? METERS/SECOND
/SECOND METERS/SECOND2 Does this have any
physical meaning for this graph? (What is this
a measurement of?) ACCELERATION
23
Here are a few questions about acceleration What
does acceleration tell you about the motion of
the object? It tells you how fast the velocity
is changing and if the object is speeding up or
slowing down. Describe how you would feel in your
car if you were undergoing a rapid
acceleration. What would happen to a cup of
coffee on your dash board? The cup of coffee
would slide off of the dash board toward the
back of the car. Does the cup of coffee ever
really move backwards relative to the
road? No. See the following video clip of
Richard Feynman (Nobel Prize Physics 1965)
discussing a similar situation.
24
(No Transcript)
25
Describe how you would feel in your car if you
were undergoing a rapid deceleration. What
would happen to a cup of coffee on your dash
board? The cup of coffee would slide into the
windshield. Watch the following demonstration
with a rolling cart and a mass on the rolling
cart.
26
(No Transcript)
27
What shape is between the line and the X axis
(under the line)? RECTANGLE What are the units
of the base? SECONDS What are the units of the
height? METERS/SECOND What would the units of
the area of this rectangle be? METERS Does the
area under the line have any physical
meaning? Yes, displacement.
28
What is the velocity at 2 seconds? 0.27 m/s You
obtain this by reading directly off the graph.
29
What is the acceleration at 2 seconds? To obtain
the answer, calculate the slope of the line. Pick
two points far apart on the graph.
30
What is the displacement between 2 and 4
seconds? To obtain the answer, calculate the area
under the line.
31
Pick three points on your velocity time graph and
determine the acceleration at those points. You
should pick points one in the beginning, one
in the middle and one at the end of the
run. Create a data table on your velocity time
graph of these times and accelerations.
32
To obtain the answer, calculate the slope of the
line. Pick two points far apart on the graph.
Time (seconds) Accel (m/s2)
1 0
3 0
5 0
Use this data table to create an acceleration
time graph.
33
What does this graph tell us about the velocity
of the buggy? The velocity is not changing, but
we dont know what the velocity is.
34
What would an acceleration time graph look like
if the buggy wasnt turned on? The graph would
look the same. What would an acceleration time
graph look like of a car on cruise control
driving down a straight road? The graph would
look the same. The point is that sitting still or
going fast will look the same on an acceleration
time graph as long as the velocity is not
changing.
35
Put this table in your notes or on the back of
your directions for Graphing in Excel!
Type of Graph Read the Graph Calculate the Slope Calculate the Area
Displacement vs. Time Displacement (m) Velocity (m/s) Nothing (m?s)
Velocity vs. Time Velocity (m/s) Change in Velocity or Acceleration (m/s/s or m/s2) ? Velocity Displacement (m)
Acceleration vs. Time Acceleration (m/s/s or m/s2) Change in Acceleration (m/s/s/s or m/s2/s or m/s3) ? Acceleration Velocity (m/s)
36
To complete the Toy Buggy Activity, you should
have the following Page 1 Sketch, raw data
and description of procedure. Page 2
Displacement vs. Time Graph with associated
work. Page 3 Velocity vs. Time Graph with
associated work. Page 4 Acceleration vs. Time
Graph Page 5 Toy Buggy Worksheet (see next
slide)
37
(No Transcript)
38
Demonstration Roll bowling ball across the
floor. After the bowling ball is released,
describe its motion. Sketch this motion on the
three axes below. Assuming the bowling ball
leaves my hand at 1 m/s, how much distance will
it cover in the first second of travel compared
with the last second of travel? Should be 1 m
for both times. On the same axes in a different
color, sketch the bowling ball rolling at a
constant speed of 2m/s. Compare the lines on each
graph.
39
Now lets talk about accelerated motion (velocity
is changing). Demonstration Roll bowling ball
from rest down ramp. Describe the velocity as the
ball rolls down the ramp. The velocity
increases. How is velocity represented on a
displacement time graph? The steepness (slope)
of the line. So what must happen to the slope on
a displacement time graph for the bowling ball
rolling down the ramp? The slope becomes steeper
as time goes on. Sketch the graphs below. Explain
your lines to your neighbor.
40
(No Transcript)
41
Most of you have heard the term free fall, what
do you think it means? Demonstration Drop book
and paper. Which one of these is in free
fall? The book. Air resistance is counteracting
gravity on the paper so the paper is not free
to just fall. What could we do to the paper to
help it fall more freely? Crumple it up. On the
three axes below, sketch graphs for the book
falling assuming it is a constant acceleration.
42
Assuming no air resistance, what is the constant
acceleration of gravity near the surface of the
earth? 9.8 m/s2, but it is ok to use 10 m/s2
except when dealing with data. Galileo
measured this concept of acceleration, using
ramps to slow the effect of gravity, and bells
to measure where the ball was. Lets talk
about what this means, an acceleration of 10 m/s2
is means that the speed of a freely falling
object changes by 10 m/s every second. Lets
Review
43
Assuming no air resistance, what is the constant
acceleration of gravity near the surface of the
earth? 9.8 m/s2, but it is ok to use 10 m/s2
except when dealing with data. Galileo
measured this concept of acceleration, using
ramps to slow the effect of
gravity, and bells to measure where the ball
was. Galileos Finger Galileo's Ramp Lets talk
about what this means, an acceleration of 10
m/s2 means that the speed of a freely falling
object changes by 10 m/s every second. Lets
Review
44
Lets look at some sample data for an object in
free fall dropped from rest.
Time (s) Velocity (m/s)
0 0
1 10
2 20
3 30
4 40
How does this data represent constant
acceleration? The change in velocity per second
is always 10 m/s.
Time (s) Velocity (m/s)
0 0
1 10
2 20
3 30
4 40
45
The idea of constant acceleration has some
important consequences on your graphs. The
main one is that your velocity time graphs must
be straight lines. Why is this true? The slope
of the velocity time graph is acceleration and
therefore can only have one numeric value. The
second consequence is that your acceleration time
graphs must be horizontal straight lines.
46
Now lets analyze the motion of the bowling ball
rolling down a ramp more accurately. Do you
think this will be constant acceleration like the
book in free fall? How will this experiments
start compare with the start of the Toy Buggy
Experiment?
47

• Objective Organize as a class and collect
  displacement time
• data. Refer to your notes for collecting good
  data and make sure
• that you have at least five data points.
• Materials
• Bowling Ball
• Wooden Ramp
• Stop Watches
• Meter Sticks
• Graph paper or computer
• Any questions?
• You may begin. As you are collecting your data,
  on a
• separate piece of paper, create a data table, a
  sketch of your
• set-up and a brief description of the procedure.
  Then we can
• process the data before graphing.

48

• For review What is good data?
• As many data points as reasonable.
• A set of data points is for a given roll of the
  bowling ball.
• Be consistent with measurements, ie always use
  the same
• spot on the object.
• Appropriate units.
• Correct experimental design.
• For example, a stationary start in this case.
• 6. Consider sources of error - avoidable ones vs.
  unavoidable
• ones.
• 7. Why was it easier to set the distance and
  measure the time?

49
What do you think the shape of the line will be
on the displacement time graph? Curved upward
because the velocity increases and therefore the
slope of the line increases. Plot your data, but
do not draw a trendline yet. Can you see a curved
upward line? Are there any points that seem like
they dont fit? These are called outliers.
50
Here is some sample data of an actual data
51
Complete the graph by adding a trendline. See the
Excel Handout for details. If you are using
Excel, make sure you fit the points with a
second order polynomial. This is a fancy way of
saying that the line has one curve.
52
Pick three points on your displacement time graph
and determine the velocity at those points. You
should pick points one in the beginning, one
in the middle and one at the end of the
run. How is this process going to differ
compared to the constant velocity buggy? You
need to take the slope at the points of interest
because the slope changes.
53
Draw tangent lines at your points of interest.
54
Pick two points on the tangent line and determine
the slope
(4.6,3.2)
(2.7,1.4)
55
This means is that at 2.5 s the bowling ball was
traveling at 0.95 m/s. Look at the velocity
(slope) of the line before 2.5 s. How do you
think it will compare to the velocity you just
found? The velocity will be less than 0.95
m/s. Look at the velocity (slope) of the line
after 2.5 s. How do you think it will compare to
the velocity you just found? The velocity will
be more than 0.95 m/s. Pick a time before 2.5 s,
draw a tangent line and calculate
the velocity. Pick a time after 2.5 s, draw a
tangent line and calculate the velocity. Warning
Do not pick points to close to the beginning or
end of your curve or you will not be able to
draw a tangent line. Warning Do not pick your
original data points because they are not part
of the trendline.
56
Here is a sample graph with all work shown for
all three velocities.
57
Create a graph of velocity vs. time using the
data table from the displacement time graph. It
should look like this
58
What will the slope of this line tell
us? Acceleration. You need to graph acceleration
vs. time. How will you do it? Find the slope of
the trendline. Do not use your data points.
Select two points, one at the beginning and one
at the end, on your trendline.
59
Time (s) Accel (m/s2)
0 0.37
1 0.37
2.5 0.37
4 0.37
(3.2, 1.2)
(0.5, 0.2)
60
Use this data table to create an acceleration
time graph.
61
What is the velocity at 2 seconds? 0.76 m/s You
obtain this by reading directly off the graph.
62
What is the acceleration at 2 seconds? To obtain
the answer, calculate the slope of the line. Pick
two points far apart on the graph.
63
What is the displacement between 1 and 3
seconds? To obtain the answer, calculate the area
under the line.
64
To complete the Bowling Ball Activity, you should
have the following Page 1 Sketch, raw data
and description of procedure. Page 2
Displacement vs. Time Graph with associated
work. Page 3 Velocity vs. Time Graph with
associated work. Page 4 Acceleration vs. Time
Graph Page 5 Bowling Ball Worksheet (see next
slide)
65
(No Transcript)
66
(No Transcript)
67
(No Transcript)
68
(No Transcript)
69

• The Bike Lab
• Objective To design and execute experiments that
  demonstrate
• constant velocity, constant acceleration and
  constant
• deceleration. Create the motion graphs and answer
  questions
• that analyze the motion.
• Materials
• Bike
• Helmet
• Stop Watches
• Tape Measure
• Chalk

70
Your instructor will break the class into three
groups. Each group is responsible for designing
an experiment for one of the types of motion
that includes jobs for everyone in the class.
The class will collect data together. The data
will be graphed and analyzed in groups of two.
71
To complete the Bike Lab, you should have the
following 1. Sketch, raw data and description
of procedure for each type of motion on a
separate page. 2. Displacement vs. Time Graph
with associated work for each type of motion on
a separate page. 3. Velocity vs. Time Graph with
associated work for each type of motion on a
separate page. 4. Acceleration vs. Time Graph
for each type of motion on a separate page.
Note Deceleration is just a negative
acceleration. 5. Bike Lab Worksheet (see next
slide)
72
(No Transcript)
73
Assemble the finished Bike Lab according to your
instructors directions.
74
Assemble the finished Bike Lab in the following
order! Graph 1A Displacement vs. Time for
Constant Velocity Bike Graph 1B Velocity vs.
Time for Constant Velocity Bike Graph 1C
Acceleration vs. Time for Constant Velocity
Bike Graph 2A Displacement vs. Time for
Constant Acceleration Bike Graph 2B Velocity
vs. Time for Constant Acceleration Bike Graph 2C
Acceleration vs. Time for Constant Acceleration
Bike Graph 3A Displacement vs. Time for
Constant Deceleration Bike Graph 3B Velocity
vs. Time for Constant Deceleration Bike Graph 3C
Acceleration vs. Time for Constant Deceleration
Bike Answers to Bike Activity Worksheet showing
all formulas and work on graphs.
75
You now have everything you need to complete the
worksheet Packet. Complete it! Physics is not a
spectator sport Additional Resources Physics
Education Technology Website The main site can be
found at http//phet.colorado.edu Moving Man
JAVA Applet
76
Looking at the graphs of the bowling ball on the
ramp or the bike on the hill, what is important
about the acceleration? It is constant, like
free fall. If acceleration is constant, the
velocity changes by equal increments every
second. As a ball falls, how much does its
velocity change by each second? 10 m/s every
second. Now imagine riding in a car with a stick
shift as someone shifts through the gears, how
do you feel? Would it feel the same as if you
were the ball falling? How are these motions
different? Things in nature rarely have constant
acceleration. This means that acceleration is
changing every second.
77
Hills on ski slopes are good examples of
non-constant acceleration. Imagine skiing down
these hills below, sketch an acceleration vs.
time graph for each. Keep in mind, free fall has
an acceleration of 10 m/s2 and a flat surface
has an acceleration of 0 m/s2.
78
Line at Line start Line start at less
than higher than last 0 m/s2, rise to 10
m/s2. and end 0 m/s2. less than 10m/s2.
Last two graphs have lines that are not really
straight.
79
If velocity changes for an object in motion, we
say that the object is undergoing
acceleration. When acceleration changes in your
car, you often jerk forward or backward. If
acceleration changes for an object in motion, we
say that the object is undergoing jerks.
80
Activity Graphing the Motion of a Real Car Get
some real data Try this http//www.car-videos.com/
performance or any other source Complete the
worksheet on Real Car Motion
81
(No Transcript)
82
(No Transcript)
83
(No Transcript)
84
(No Transcript)
85
(No Transcript)
86
(No Transcript)
87
(No Transcript)
88
(No Transcript)
89
(No Transcript)
90
(No Transcript)
91
(No Transcript)
92
(No Transcript)
93
(No Transcript)
94
(No Transcript)
95
(No Transcript)