Transcript PIT AND PENDULUM

PIT AND THE PENDULUM
Did Edgar Allen Poe know His Math?
Sharon Wiest
DO YOU KNOW THE STORY?
(Do your students?)
• LET ME TELL YOU A STORY ……..
• You could start by going to you-tube:
• And choose either video (but not today) :
•
•
•
•
Pit and the Pendulum
Pit and Pendulum Rap
Pit and the Pendulum (part 2 of 2)
Vincent Price -- Pit & Pendulum part II
Details from the story:
As the pendulum descends to within 3 inches,
and is 10 to 12 swings away from starting to
cut his clothes before cutting his body, the rats
cut the ropes, and the main character is free
to roll off the table.
MATH STANDARDS
• WRITE/CREATE A MATHEMATICAL EQUATION
TO REPRESENT A GIVEN SITUATION
• DRAW A FIRST QUADRANT GRAPH IN THE
COORDINATE PLANE TO REPRESENT
INFORMATION IN A TABLE OR SITUATION
• REPRESENT A PROBLEM SITUATION, DESCRIBE
THE PROCESS USED TO SOLVE THE PROBLEM,
AND VERIFY TO REASONABLENESS OF THE
SOLUTION
• Extract and organize mathematical
information from symbols, diagrams, and
graphs to make inferences, draw conclusions
and justify reasoning
• Make and test conjectures based on data (or
information) collected from explorations and
experiments
• Represent proportional relationships using
graphs, tables, and equations
• Determine slope and y-intercept of a linear
function for given table of data
• Determine and justify whether a given verbal
description represents a linear relationship
• Create a scatterplot for two-variable data set,
and use trend lines to make predictions
• Extract information from graphps to make
inferences and draw conclusions
• Represent a function four ways: symbolic
expression, graph, table, verbally. Make
connections among these representations
• Evaluate the argument and conclusion
• Verify accuracy in context of the original
problem
TIME TO
EXPLORE!
WHAT DATA DID WE COLLECT?
(which order do you want to use?)
Length of the pendulum OR
Time for one complete swing (period)
Time for one complete swing (PERIOD)
OR Length
SLOPE
Let’s calculate a couple of slopes using pairs of data by
hand.
Slope (m) = (y2 – y1)
(x2 – x1)
Using:
1.
2.
3.
4.
first two points
second and third points
first and third points
a set of points which pique your interest
OBSERVATIONS
• What units are we using?
• Is your first slope the same as others here?
Are the slopes approximately the same for the
first few points?
• If other people’s first slope is very different,
are the two slopes reciprocals?
• Comparing the slope calculations for several
of the smallest data pairs – Do we think the
relationship between period and length is
linear?
• Let’s create a linear equation using one of our
slope values: y– y1 = m(x – x1)
• What do we expect the time of a complete
period to be if the length of the pendulum is 5
ft?
Let’s put our data in your calculator or
in FATHOM
Refresher for calculator:
• STAT/EDIT/ highlight L1/CLEAR/ENTER
• CLEAR LIST 2 also
• Enter data
• Quit
• STATPLOT/TURN PLOT 1 ON(or some other plot)
• Check to make sure that the lists named for x and
y match your data
• ZOOM/ ZOOMSTAT
Does the last answer fit with our
results?
• Let’s look at the scatterplot of the complete
data set.
• Do we think really think this is a linear
relationship?
Regression Analysis for Data that is not
Linear
• How can we use the calculator or fathom to
get a non-linear equation for the data?
• What equation do we get?
Let’s use our new equation
• Predict the time for a complete period for some
pendulum length within the domain of our data
(interpolation)
• How do this value fit with our data?
• HOW LONG DOES THE PRISONER (Mark) HAVE TO
GET OFF THE TABLE ? Do we need to make some
assumptions?
• QUESTION:
Has anyone else BEFORE us investigated the
relationship between period and length of the
pendulum?
• From Physics:
Period of a Pendulum = 2*Pi * sqrt(length/gravity constant)
• T = 2π√(L/g)
• How does OUR equation compare to the accepted
physics relationship?
• Note: Units revisited ----- trials and
tribulations in trying to jog an old memory