TIMS Laboratory Investigations
Work, Energy, and Simple Machines
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(ISBN 0-7872-4144-X, middle): This investigation is designed to be a basic and simple introduction to the concept of work. Using the force gauge, the children find out how much force is needed to raise the TIMS cart vertically three different distances. They calculate the work done for each distance and plot the results. A variety of proportional reasoning questions follow including questions using different masses. We then relate the external work to the “internal” work done by the heart, lungs, etc., study the conversion of N-m to calories, and look at the calorie content of different foods. The children learn how many calories they need to burn to do a specific amount of work and find out that a very few calories go an awfully long way.
Several Ways to Reach the Top: An Introduction to Simple Machines
(ISBN 0-7872-4145-8, middle): A cart is raised 60 cm in three
ways: straight up, along a 90-cm incline, and along a 120-cm incline.
In each case the pulling force, measured by a force gauge, is
parallel to the direction of motion of the cart. The distance
moved, l, is the manipulated variable, the responding variable is the
pulling force, F||. For each value of l, the work done to move the cart is calculated. The children find
that F|| is inversely proportional to l and that the work done is constant. These two observations lead
to multiple-step logic problems that explore the interrelationship
among F||, l, and W. Having found the external work necessary to do a job,
the children find the equivalent internal work and relate that
to how many calories are burned and how many bowls of cereal are
needed to make up for the lost calories.
The Unequal Arm Balance: The Lever
(ISBN 0-7872-4146-6, middle): A ruler is balanced by its center
hole. Two washers are taped three inches left of the center, and
the number of washers required on the right to balance at varying
distances is found. One finds that we need more washers on the
right the closer one gets to the center. Based on their data,
the children can deduce the unequal arm balance relationship that
FL x lL = FR x lR. Problems with more than one set of washers on the right, as
well as multiple sets of washers on the left, test the children’s
understanding of this basic concept.
The Gravitational Pendulum
(ISBN 0-7872-4147-4, middle): Washers, tied to the end of a string,
are set in back-and-forth motion. The children carry out four
investigations to determine which variables affect the period,
T, of this gravitational pendulum. They are asked to study T vs.
the amplitude of motion, A, the mass of the washers, m, the length
of the string, l, and a variable of their own choosing. A plot of l vs. T yields a nonlinear relationship requiring them to straighten
out the curve. A variety of multistep problems follow as we busily
change A, l, and m to predict T. Algebra and proportional reasoning are used.
We conclude with a practical look at pendulums in clocks and at
the circus.
Working Against Friction
(ISBN 0-7872-4148-2, middle): Using the force gauge, the students
drag the TIMS cart upside down, measure the dragging force and
the distance moved, and calculate the work done. Force diagrams
and basic algebra are used. They find that the work vs. distance
is a linear relationship and so can predict values of the work
for various distances moved and for various forces used. The children
compare lifting to dragging to see which requires less force.
They predict what would happen to the work vs. distance relationship
if one adds mass to the cart, and then check their prediction.
The children also determine the internal work they have to do
to drag an object, how many calories this will cost them, and
how much they have to eat to break even in terms of calories.
Free Fall III: Work and Kinetic Energy
(ISBN 0-7872-4149-0, middle): The students did work against gravity
when they steadily raised the TIMS cart a distance d. They also let objects free fall and found that v increased
linearly with time. In this investigation we use these old ideas
to break new ground. The work done by gravity on a freely falling
object, Wg, will be the manipulated variable. The object’s instantaneous
velocity, v, after falling a distance, d, will be the responding
variable. Its mass will be held fixed. The children should know
how to make all the measurements. The result will be a surprise.
W vs. v is not a straight line! On straightening out the curve,
the students will find that Wg is proportional to v2, and that the proportionality constant is M/2! So, the children
will have discovered kinetic energy of translation (KET), and for an object that starts from rest, the work-kinetic energy
equation. This becomes a jumping-off point for expanding the Work
Kinetic-Energy equation to situations where the initial velocity
is not zero, and then on to all kinds of problems involving work,
force, distance, mass, and velocity which will require nice orderly
multistep logical thinking.
The Case of the Missing Energy
(ISBN 0-7872-4150-4, middle): In Free Fall III, we defined the
concept of the kinetic energy of translation (KET = 1/2MV2) and related it to the work done by gravity on an object falling
freely from A to B: WgAB = KEgTB – KEgTA. In The Case of the Missing Energy, the children learn that the
above equation is not true when objects roll down an incline.
Using three different objects, the children calculate Wg, measure v, calculate KET, and find that Wg and KET do not add up. Kinetic energy seems to be missing! Why? Where
did it go? Did someone take it? Like a good detective, the children
gather evidence, search the evidence for clues, and piece together
the clues to find the thief. Along the way they will learn about
kinetic energy of rotation, how the distribution of mass affects
the kinetic energy of rotation, and how the interchange between
KET and KER determines how fast an object moves. Sherlock Holmes, eat your
heart out!
One for Two: The Idea of Potential Energy
(ISBN 0-7872-4151-2, middle): Our lab starts with an e-mail message
from the eighth graders at the Royal Mount School to the eighth
graders at the Willow School. They have discovered something neat
and they ask the Willow students to check it out. When they roll
a 1" steel sphere and separately a 1 1/4" steel sphere down an
incline from four different heights, Dh, and measure the distance, d, that each sphere pushes a slider,
they find two linear curves if they plot d vs. Dh (one for each mass), or four linear curves when they plot d
vs. M (one for Dh). But when they plot the product M x h vs. d, something marvelous
happens, all the data coalesces into a single straight line. Do
the Willow students see the same thing? Using the new graph and
proportional relationship, the Willow students are challenged
to make all kinds of predictions, check them out, and find percentage
differences. But why these results? The Royal Mount students think
they have worked out the reason and the Willow students are challenged
to do the same. The Royal Mount folks then excitedly explain a
new concept they came across called Potential Energy (PE), and
how it is related to KE and how it also explains what is going
on in the lab. Potential energy problems follow with a final note
of some further PE studies bending rods and stretching rubber
bands. So, there is more to come.
A Potentially Good Launcher
(ISBN 0-7872-4152-0, middle): This investigation continues our
study of force, work, and kinetic and potential energy. So far
we have used the constant force of gravity to do work, to store
potential energy, and to convert work to kinetic energy. But there
are other forces in nature, besides gravity, that are important
in doing work and storing potential energy. In A Potentially Good
Launcher, the students study, for the first time, a nonconstant
force—one that varies with distance, and which plays an important
role in many applications. In Part I we use the force gauge blade
to see how such a force can store PE and find out how much PE
it can store. We have the children experience a nonconstant force,
show that this one increases linearly with distance, find the
average of such a force, and by straightening out a curve to discover
how PE is related to how much the force gauge is bent. In Part
II, the children release that PE by having the force gauge launch
their cart. The students determine the relationship between the
stored PE and the launch velocity of the cart and see how the
stored PE and the launch KE are related. Some KE will be missing,
and so the search is on.
Going Up!
(ISBN 0-7872-4153-9, middle): By tying a hanging mass, m, via
a pulley to the cart and using the force gauge to launch the cart,
we convert the launcher to an elevator. This enables us to stop
off at several floors and explore some old ideas and some new
ones. The investigation is rich in variables, including the responding
variable, h, the height to which m rises, and three manipulated
variables: Dl1, the distance we push back the blade; M, the mass of the cart;
and m. Together they give us the opportunity to carry out three
investigations, the associated analysis of each, and lots of neat
predictions. This will give us the opportunity to test the children’s
experimental skills in this more complicated setting. In the analysis,
the children relate h to the other variables. We could stop here,
but going up one more floor, so to speak, gives us the opportunity
to review the concept of potential energy, now for both the launcher
and gravity in one system, and to use the concept of PE to derive
the final experimental results. This blending of theory and experiment
is not always available to us and so we try to take full advantage
of it. There will be lots of data collecting, graphing, straightening
out curves, and proportional reasoning, along with the chance
to do some independent thinking.
Blast-Off
(ISBN 0-7872-4154-7, middle): This is an end-of-the-year assessment
investigation where the students use a rubber band to launch a
cart. We define four experimental tasks: to calibrate the rubber
band; to find the relationship between the amount the rubber band
is stretched and the launch velocity of the cart; to find the
effect of the mass of the cart on the launch velocity; and the
relationship between the stored PE and the launch velocity. There
are no data tables or instructions on how to proceed. At a minimum,
the students should be able to draw pictures, define variables,
set up data tables, carry out multiple trials, and find the graphical
relationship between variables. But there is more. They will have
an opportunity to straighten out curves, look at an inverse proportional
relationship, and use proportional reasoning. They will have a
chance to explain, in words, what is going on as well as use equations
to solve problems. The topics include length, velocity, acceleration,
the second law, kinetic energy (all kinds), and potential energy.
There is nothing in the lab that has not been covered previously.
But, as we shall see, the rubber band is a peculiar beast and
so there will be an opportunity for the children to do some thinking
that extends beyond their past experiences.
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Copyright © 1997 by Kendall/Hunt Publishing Company
Copyright © 1999 Institute for Mathematics and Science Education.
All rights reserved.
UIC—University of Illinois at Chicago