TIMS Laboratory Investigations
Inertia, Balanced Forces, and
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(ISBN 0-7872-4129-6, middle): The students use the force of the Earth’s gravity to calibrate their force gauges in newtons. They hang different masses on a force gauge and mark the position of the gauge’s thin blade on a card. By using masses in the range of 0–100 grams, they create a scale from 0–1 newton. Using masses up to 1 kilogram, they calibrate the gauge’s thick blade up to 10 newtons. The force gauge is then used extensively in a variety of investigations.
Weight vs. Number
(ISBN 0-7872-4130-X, middle): This is the first force investigation
the children try after building their force gauge. The investigation
is in the spirit of our ___________ vs. Number labs, where the
manipulated variable is a whole number of objects, N, and the
responding variable is the variable of interest, in this case
weight, Wt. Chalk, washers, plastic rulers, 1" Lucite spheres or 1/2" steel
spheres can all be used as the object. The units of weight will
be in newtons. The resultant curve of N vs. Wt is a straight line through (0,0). Using proportional reasoning,
the children learn to count the number of identical objects by
weighing them. Along with this and the new ideas in the experiment
such as units of force, the concept of weight, the direction of
gravity, and the idea of balanced forces, the children make force
diagrams and use simple algebra to solve problems. The ideas just
outlined will be an intrinsic part of every one of the balanced
force investigations, making this lab the next big step in the
children’s intellectual development.
Galileo’s Classic Experiment
(ISBN 0-7872-4131-8, middle): With this investigation Galileo
overturned 2000 years of misconception about what causes motion.
Aristotle (384 b.c.–322 b.c.) held that all motion requires force.
That view prevailed until Galileo rolled a sphere down one incline
and up another. As Galileo did, the children hold the initial
release point and the height of the short ramp fixed. They then
measure the distance, l, the sphere rolls up the long incline,
and height, y, to which it rolls. The number of blocks, N, supporting
the long incline is varied. The children then plot l vs. N and
y vs. N. They see what Galileo saw, and we try to draw out of
the children the conclusion that Galileo made, that the sphere
has an “…inclination to motion…exercised through an intrinsic
property and without need of a particular mover….” This will not
be easy since, as Piaget found, children and adults naturally
hold Aristotle’s view. Along the way toward discovering inertia
and getting rid of our prejudices, we will tackle problems relating
N and l which require inverse proportional reasoning, something
else that is not well understood by the children. Altogether,
a challenging lab.
Buoyant Force
(ISBN 0-7872-4132-6, middle): Various numbers of washers, hanging
from the force gauge, are suspended first in air and then in water.
Using the two force measurements, a force diagram, and some basic
algebra, the children determine the buoyant force, FB of water on the washers. After finding that FB depends linearly on the volume of the washers, the children do
a bit of detective work to see if the shape of the objects or
their mass affects the magnitude of the buoyant force. The children
answer questions using proportional reasoning and algebra and
then, in an open-ended extension of the lab, see if FB depends on the density of the liquid and, if so, what the relationship
is between FB and rliquid . An optional discussion of how to relate sinking
and floating to the buoyant force and to density of the object
is given in the Teacher Lab Discussion.
Adhesion
(ISBN 0-7872-4133-4, middle): If the children dip their hands
into water, they will find that some of the water will stick,
or adhere, to their fingers. It is the goal of this investigation
to study this adhesive property of water. Using the force gauge,
the children pull off the surface of water plastic pieces of different
areas. Using this gauge reading, as well as the force of gravity
acting on the piece, a force diagram, and some algebra, the children
determine the adhesive force between the object and water and
show that it is linearly related to the area of the piece. Once
again putting on their thinking caps, they see if the adhesive
force also depends upon the shape of the piece, its perimeter,
or its mass. The children are further challenged with questions
involving proportional reasoning and algebra. As an optional extension
of the lab, you can have the children investigate the effects
of the type of liquid and the type of material on the adhesive
force. A variety of applications of adhesion and cohesion (water
sticking to itself) are given in the Teacher Lab Discussion.
Friction
(ISBN 0-7872-4134-2, middle): In this investigation the children
study sliding friction and try to understand how it depends upon
the type of surface, on the mass of the sliding object, and on
the area in contact between the two surfaces. The children pull
a weighted block along four different surfaces using the force
gauge. The force gauge reading, along with the concept of balanced
forces and some simple algebra, allows the children to calculate
the frictional force. A couple of surprises await the children.
The first is that the frictional force and mass of the block are
linearly related; the second is that if one controls for the mass,
the frictional force is independent of area. Moving from surface
to surface, from mass to mass, and from area to area, the children
solve problems dealing with proportional reasoning, algebra, and
inductive logic. In spite of friction, there is no slowing down
in this lab.
The Inertial Pendulum
(ISBN 0-7872-4135-0, middle): Three different masses are attached
to the end of the thin blade from the force gauge and set into
horizontal motion. The number of oscillations, N, in 10 sec are
counted. The mass, M, is the manipulated variable, N is the responding
variable, and the blade and oscillation time are held fixed. What
the child will find is that N decreases nonlinearly as M increases.
This gives the children an opportunity to make difficult interpolation
and extrapolation predictions, and in so doing, learn how to deal
with such curves. But the bulk of the questions deal with the
practical applications of what they have learned, from how to
measure mass in outer space, to why it is hard for a lion to catch
a gazelle. The answers, clear from the investigation, are bound
up with the idea of inertia, of how a mass changes its motion
in response to a given force. It is this changing response that
makes our system an inertial balance.
The Magnetic Force
(ISBN 0-7872-4136-9, middle): The lab is in three parts. In Part
I we trace some of the high points in the history of magnetism
from 400 b.c. to 1600 a.d. The children learn how to find the
magnetic poles of a small cylindrical bar magnet, show that like
poles repel and unlike attract, and deduce the cause of the Earth’s
magnetism. In Part II, the children study the strength of the
magnetic force as a function of the separation between two magnets
by using their force gauge and pieces of paper. The nonlinear
relationship is a jumping-off point for predicting and checking
the values of the magnetic force at various separations. In Part
III the children study the magnetic lines of force surrounding
a single magnet and around orientations of two magnets. A small
compass is used to trace out the lines of force and the children
explain what they see using the results from Parts I and II. The
magnetic force is a wide-ranging lab using old concepts to introduce
new ideas.
The Elektric Force
(ISBN 0-7872-4137-7, middle): We introduce Part I with a story
relating the accidental discovery of “elektricity” about 2600
years ago. The children then learn how to make a detector for
determining the sign of the charge, discover that there are two
kinds of forces, one repulsive and one attractive, and that, therefore,
there must be two kinds of charge. We help the students understand
how to build a macroscopic model of charge transfer, and then
discuss the charge structure of the atom. In Part II, the students
build an electric force measurer and use that to estimate the
value of the force between charged objects. We discuss Coulomb’s
Law, and then the students use Coulomb’s Law to estimate the amount
of charge that produced the above forces. We take the students
back to the microscopic world and use the mass of the proton and
the charge of the proton and electron to estimate the number of
electrons transferred between the charged objects, the total electrons
in each charged object, and even how many electrons the children
have. Mathematically, the children deal with the powers of ten,
negative exponents, and lots of ratios.
Induced Magnetism
(ISBN 0-7872-4138-5, middle): In Part I the children discover
that some materials can be magnetized, others cannot. They try
to find which ones and what is special about them. They will find
they can flip the polarity of an induced magnet, can demagnetize
it, and yet, if left alone, will see that an induced magnet, fragile
as it is, can remain magnetized a long time. In Part II the children
study the strength of the induced magnetic force, see how it falls
off with distance, and compare its strength to that of the magnetic
force between two permanent magnets. Interpolation and extrapolation
questions follow. The children also try to find an analytic relationship
between the force and the separation. We have structured the student
write-up so that the lab is in an open-ended format. There are
no special instructions, data tables, etc. Instead there are a
series of leading questions which will help guide the students
in both their qualitative and quantitative investigation of induced
magnetism.
The Electric Dipole Force
(ISBN 0-7872-4139-3, middle): In Part I, the students repeat Thales’
discovery of “elektricity” using the charged vinyl strip (instead
of amber) and paper (instead of papyrus). The children are challenged
to explain what is going on using the atomic model they studied
in The Elektric Force. The children then go Thales one better
and measure the strength of this induced electric force using
ever longer pieces of paper. In Part II, the students first play
around with a stream of water and a charged strip and see what
variables affect how much water bends. We help the students explore
the atomic structure of the water, and how the structure of water
can explain what they just investigated. We follow this with a
TIMS Super Challenge Take-Home Experiment, where the students,
using a sink at home, find the relationship between the distance
the water bends and the distance of the charged strip from the
water stream. We try to use all this hard-won knowledge to answer
some questions about water and the real world. Exploring the microscopic
world of the atom is never easy, but studying the electric dipole
force is a good way to introduce the students to the wonderful
world of the very small.
Catching Up with Newton I: Cause and Effect
(ISBN 0-7872-4140-7, middle): As the children learned in Galileo’s
Classic Experiment, once an object gets going it can move with
a constant velocity with no forces acting on it. Newton, in his
first law, extended Galileo’s Law of Inertia to systems where
the sum of the forces vanish (SF = 0). The children have used
this idea in many TIMS force investigations. In this lab, guided
by a letter from Dr. M. Jordan to his student Ms. Carsons, the
children take the next big step and find the relationship between
the net force (SF = FNet) when it is not equal to zero and the
resulting acceleration, a. To do so, in this open-ended investigation,
they will have to manipulate two variables, control the mass,
measure the accelerations, and plot FNet vs. a. By tilting the
incline and using the force gauge, the TIMS cart, and a stopwatch,
the children can achieve all of these goals. Having found the
linear relationship between FNet and acceleration for the cart,
the children answer a variety of questions relating FNet to the
acceleration, and solve multistep logic problems involving four
variables, FNet, acceleration, distance, and time. They also get
a chance to apply what they have learned to some real world problems
involving cause and effect, i.e., FNet vs. a.
Catching Up with Newton II: Mass and the 2nd Law
(ISBN 0-7872-4141-5, middle): In Catching Up with Newton I, we
controlled M, varied F, measured a, and learned that F was proportional
to a. In this experiment, M is varied, a is measured, and F is
now controlled. This is done using the incline set horizontally,
the TIMS cart, a pulley, a hanging mass, and a stopwatch. 
By the end of this lab, the children will have discovered the
key relationship between a and M, and using the result of the
earlier investigation, explore the relationship among a, M, and
F. Along the way, we will define Newton’s second law, learn how
to solve proportion problems using three variables, and how to
use the second law to learn about forces acting both on us and
around us. The children will have the chance to do some good experimental
work, make some massive masses, check predictions, and work on
proportional reasoning, multistep logic, and basic algebra. The
lab is set up as a series of letters between Dr. Jordan and Ms.
Carsons because we wanted to establish a dialogue with the children
about some of the key ideas. They will do a lot of filling in
the blanks as part of the dialogue. With this lab, we have almost
caught up with Newton. There is still the third law.
Catching Up with Newton III: The 3rd Law
(ISBN 0-7872-4142-3, middle): At long last Ms. Carsons and Dr.
Jordan try to come to terms with the last of Newton’s laws. Quoting
Newton’s statement of the third law, Dr. Jordan claims, “It makes
no sense.” And in this he is in good company. Few people understand
the third law. But Ms. Carsons leads him through three observations,
not experiments—there is no data collection in this lab—which
she hopes will help Dr. Jordan (and the students) understand the
third law. Both during and following observations there is an
exchange of questions both qualitative and quantitative which
further illustrate the third law and tests the children’s understanding
of the first and second as well. During the course of the questions,
we bring out three paradoxes and use the third law to explain
how rockets work, birds fly, and about locomotion in general,
and learn how to use the third law along with the first and second
to solve problems. Notice the role of the teacher and pupil have
been reversed in this lab. This is not uncommon in research where
the student becomes the expert and guides the professor. We all
learn from one another.
Count Down
(ISBN 0-7872-4143-1, middle): In this three-part investigation,
the students build and launch their own balloon rocket. They start
in Part I by measuring the burn time of their rocket engine and
calculate the rate at which it ejects fuel (i.e., mass) vs. the
length of the engine (i.e., the balloon). In Part II, the students
fuel the engine, mount it in a paper bag, and launch it along
a horizontal nylon line. By measuring the distance and time that
it travels, and using the burn time and glide distance, the students
try to find the thrust of the rocket and the friction opposing
its motion. Then in Part III, the students design and build a
better rocket and compare it to the paper bag model. It should
be no contest. Since this is an end-of-the-year lab, we have thrown
in the kitchen sink, so to speak. The students will need to find
areas and volumes, determine mass using density, find velocity
and accelerations, make force diagrams, and use the second law
to find forces. There will be data tables and graphs, proportional
reasoning and algebra, and some nice multistep-logic thinking.
All in all, a good piece of work for our TIMS astronauts.
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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