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Video Modules 1 & 2
Understanding Kinetic Energy
There are many ways to explore the relationship of mass and speed to kinetic energy. Hot
Wheels™ system was chosen rather than a professional system for studying force and motion,
such as the systems sold by Pasco, for two reasons.
First, a way to perform this investigation that was minimally expensive was offered so that it
could be done even in classrooms with very limited resources. The components for this Hot
Wheels system can be obtained for less than $100, which is substantially less cost than a Pasco
system.
Second, the students are thought to find the Hot Wheels system more engaging because many
students are likely to be familiar with Hot Wheels products and the thrill of racing and playing
with them.
Nevertheless, a similar investigation can be performed with Pasco or other related types of
professionally manufactured equipment. Indeed, such equipment provides a higher level of
reproducibility and accuracy. If the teachers happen to have access to such equipment and have
all of the components that they may need, they may decide to use that instead. Or the teachers
may decide to use the Hot Wheels set up first so as to engage student interest and then move to a
Pasco system to refine their observations.
All of the information that they need to be able to acquire the components and construct a system
based on a Hot Wheels track set is provided, as shown in these videos, and use that system to
perform the investigation that was presented.
Our initial tests with the Hot Wheels system showed that the pendulum’s potential energy at its
apex was markedly less than the kinetic energy of the car calculated from the car’s mass and
speed. This would make the system unsuitable for this demonstration. However, after some
investigation, this inequality in the kinetic energy of the car and the potential energy of the
pendulum was found to be most likely due to energy that was absorbed through deformation of
the car and/or the pendulum in the collision. This energy absorption could be greatly reduced by
attaching strong neodymium magnets to the face of the car and the pendulum bob, with the same
poles of the magnets facing each other. Thus the repulsive magnetic fields mediate the collision
and due to the elastic nature of this interaction, nearly all of the car’s kinetic energy is transferred
to the pendulum. Then, as the pendulum rises, its kinetic energy is gradually converted to
potential energy until at its apex, all of its kinetic energy is converted to potential energy. The
potential energy of the pendulum can be calculated from its height. Thus determining the
pendulum’s height at its apex can be used as a measure of the car’s kinetic energy at the moment
that it collided with the pendulum. This is the key feature of this demonstration – providing a
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way for students to visually observe the effects of variation in mass and speed on kinetic energy
by watching and measuring the deflection of the pendulum.
Constructing the Hot Wheels Track, Car, & Pendulum System
The Hot Wheels Set
Hot Wheels V-Drop Super Velocity Track Set (currently available from Amazon.com for $20)
was used. Other Hot Wheels track sets also may work as long as the teacher has at least two
meters of straight track. The teacher also will need at least one meter of track that is all at the
same level and a section of track that can be elevated without raising the final one-meter section.
The Hot Wheels V-Drop Super Velocity Track Set
The V-Drop track set includes two cars, but additional cars that had flat tops and flat front ends
were purchased. The flat roof facilitated attaching metallic lead sheets to increase the mass. The
flat front end facilitated attaching the magnet used to reduce energy loss in collisions. Of course,
it looks more appropriate if the car’s front end is used, but the car could run in reverse if it is
found easier to attach the magnet to the rear end of a car. These cars were tested and the one that
was the fastest was selected. The fastest car was also likely to have the lowest friction. This
reduces interference from friction in the relationship of mass, speed, and kinetic energy and thus
makes this relationship more evident to students.
The track was assembled as described in the instructions accompanying the Hot Wheels kit
except that the start of the track was supported using a clamp on a ring stand rather than
suspending it from a door. This allowed an easily and reliably change in the speed of the car by
changing its launch height.
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The mass of the car is varied by adding pieces of metallic lead sheets. Lead sheet 1/16” thick that
can be easily cut to smaller sizes, can be obtained from chemical supply companies such as
Fisher Science Education. The type of lead metal sheet used was Catalog No. S75144 and
available at a price of $18.20 for one 500 g sheet from this vendor: http://www.fishersci.com
Neodymium rare earth magnets
The magnets were obtained from K & J Magetics, Inc. http://www.kjmagnetics.com/ - Disc
magnets that were axially magnetized were used; 1 inch diameter, 1/8 or 1/4 inch thick, N52
grade. The exact size of the magnets is not crucial and the teacher can experiment to determine
what works best in their system. These magnets are very brittle and very powerful. It is important
to use care in handling them to prevent two magnets from attaching to each other abruptly
because the force involved may be sufficient to cause the magnets to break. Also, once two of
these powerful magnets have attached to each other it can be extremely difficult to separate
them. The easiest way to separate them is to slide them apart but even that can be extremely
difficult. It is probably worthwhile to order some extra magnets due to the relatively high
probability that some magnets will be broken during their use.
Adhesive Putty
Reusable adhesive putty such as BlueStik™ was used to attach magnets to cars and pendulum
bobs and to secure metallic lead sheets to cars. The smallest amounts that were sufficient to
securely make attachments were utilized. Use of excess putty should especially be avoided for
attaching the magnets to the car and the pendulum since it might allow for energy absorption in
the collision that would reduce energy transfer to the pendulum. If the pendulum bob is
ferromagnetic no putty will be needed for that attachment. Some putty was placed at key points
on both sides of the track throughout the level section to secure the track to the table and to
minimize its movement during use.
The Pendulum system
For the pendulum support a piece of 3/4 inch plywood 12 inches high X 34 inches long was used
to attach aluminum supports that were made using a T.I.G welder. These dimensions are not
critical – these just happened to be the dimensions of a piece that were available, so the teacher
should feel free to adjust this for their circumstances. Indeed, this board is longer than what
would be needed, but the extra length for the placement of the support brackets in locations were
used and did not interfere with pendulum movement. Manufactured aluminum or wood shelf
support brackets could be used instead of custom made supports and the shelf support brackets
can be attached using screws.
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Pendulum Support Board with Support Brackets
The pendulum using a ball bearing such as those that can be obtained from McMaster-Carr was
constructed. An example of a suitable ball bearing can be found at:
http://www.mcmaster.com/#60355k35/=2ezllg
The bearing shown on that web page is Part No. 60355K35, 9/32” thick, 7/8” OD with a 3/8”
opening for the pendulum support rod and currently is listed at $5.32.
The bearing was mounted by drilling or boring a hole of the appropriate size (7/8” for the
McMaster-Carr bearing referenced above) in a block of aluminum. Three set screws on each of
three sides secured the bearing in place. The block of aluminum was machined to create a 3/4
inch slot that allowed it to be mounted on the pendulum support board.
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Bearing Holder Assembly Illustration
By mounting the bearing in this aluminum block one is able to easily adjust the position of the
bearing on the board. However, the bearing could also be mounted directly in the pendulum
support board by drilling a hole of suitable size through the face of the board near the top of the
board and drilling a hole through the edge of the support board to mount a set screw to hold the
bearing in place.
A pendulum support rod should be selected that has a diameter to fit the bearing opening (3/8”
for the bearing referenced above). This support rod should be cut to an appropriate length (e.g.,
3/4 to 1 inch) and press-fit into the bearing.
A hole through the pendulum support rod was drilled to fit the pendulum rod. A brass pendulum
rod 1/8 inch in diameter was used. Drill the hole in the pendulum support rod slightly larger than
the diameter of the pendulum rod so that it is easy to mount and remove the pendulum rod and
drill and tap a hole for a set of screws to secure the pendulum rod inside the pendulum support
rod as shown in the photo above.
The teacher could use a different type of metal for the pendulum rod but select a material that is
light and stiff. It is better for the pendulum support rod to be as light as possible so that the center
of mass of the pendulum is as close to the bottom as possible. This simplifies the calculations of
the pendulum’s potential energy. It is also beneficial for the pendulum rod to be as stiff as
possible to prevent bending after collision that will absorb energy and thus reduce the conversion
of car kinetic energy into pendulum potential energy.
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Rectangular blocks of metal were used as pendulum bobs. A hole was drilled through the side of
the bob to accommodate the pendulum rod and a set screw hole was drilled and tapped on one
face of the bob to secure the bob on the pendulum rod. For complete transfer of momentum from
the car to the pendulum bob, the bob must be the same mass as the car. The greater the difference
in mass of the car and the bob, the more incomplete momentum transfer will be. When the mass
of the car is varied, a bob could be used that is the average of these masses, but for more accurate
results vary the bob mass with the car mass so that the bob in use always has the same mass as
the car. This will also require using a different potential energy scale for each bob since the bob
potential energy depends on its mass. Alternatively you could use a scale that is marked in height
of the pendulum rather than in PE units and then the same scale could be used for all of the
pendulum bobs.
The size of the metal block needed for a pendulum bob can be determined once the car masses
that will be tested are known, by using the density of the metal block material. The density can
be determined by dividing the mass of the metal block the teacher starts with by its volume. Its
volume can be determined by multiplying its length, by its width by its thickness. For instance, if
one wants a bob that has a mass of 80 g, and they have metal stock that has a density of 8.40
g/cm3 and is 2.4cm X 2.6cm X 20 cm long, they would cut a piece from this rod that is 80 g ÷
8.40 g/cm3 ÷ (2.4 cm X 2.6 cm) = 1.52 cm long.
Be sure to orient the face of the pendulum bob so that it is exactly perpendicular to the travel of
the pendulum. Thus the magnet on the front of the car and the magnet on the pendulum bob are
exactly parallel to each other. This will help to maximize momentum transfer in the collision.
The pendulum system was positioned so that the pendulum bob rested exactly at the end of the
track as shown in the photo below of the pendulum potential energy scale.
Potential Energy Scale
A potential energy scale was made by attaching a white sheet of heavy paper to the pendulum
support board using double-sided tape, in the area behind the swing of the pendulum. The center
of gravity of the pendulum was determined by finding the point at which it balanced after
removing it from the pendulum support rod. That point was marked on the pendulum and the
pendulum was remounted in the support rod. The pendulum’s arc of travel was marked by
placing a pen or pencil next to the side of the pendulum at its center of gravity with the point of
the pen or pencil touching the paper. The pendulum was then moved through its arc of travel
with pen or pencil marking that arc. A horizontal line was drawn parallel to the bottom of the
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pendulum support board at the point of rest of the pendulum center of gravity to represent zero
potential energy. The height of the arc above that line and the mass of the pendulum is used to
calculate the pendulum’s potential energy at convenient intervals. Be sure to include the magnet
when measuring the mass of the pendulum but be cautious because the powerful magnet may
influence the balance so the teacher may need to place the pendulum in a tared container to
isolate the balance from the magnet’s field. The pendulum’s potential energy PE is calculated
using the equation:
PE = pendulum mass X acceleration of gravity X height above rest level
Example:
PE = 80 g X 9.8 m/s2 X 0.010 m = 7.84 mJ
Note that millijoules (mJ) were used as the unit for energy, which corresponds to g•m2/s2. Thus
for the equations to be valid, the heights must be converted to meters and the velocities
converted to meters/second.
The Pendulum PE Scale
The pendulum scale can be marked either with the height of the pendulum’s center of gravity or
the pendulum potential energy or both. One might mark pendulum height on the top side of the
arc and pendulum potential energy on the bottom side of the arc. If the teacher labels the scale
with only the height of the pendulum’s center of gravity then the students can calculate the
potential energy as part of the process of investigating the car’s kinetic energy. The photo above
shows the scale marked for PE in units of mJ.
To calculate at which heights to mark specific magnitudes of PE the following equation can be
used:
Height above rest point (mm) = PE ÷ pendulum mass (kg) ÷ 9.8 m/s2 X 1000 mm/m
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Example:
Height = 5 mJ ÷ 80 g ÷ 9.8 m/s2 X 1000 mm/m = 6.4 mm
An Excel spreadsheet will be provided titled “Pendulum Height Calculations” that the teacher
can use to calculate the heights above the rest position at which to mark the various PE intervals.
This spreadsheet can be found on our web site in the Supplemental Materials section for this set
of videos. Be sure that the marks have sufficient visual contrast that they will be easily seen and
read when the pendulum’s apex is measured.
Using the Hot Wheels System to Investigate Kinetic Energy
An important and essential first step of any learning activity is to engage the interest of the
learners. The student video that is provided is intended to help with this goal. It should give
students a sense of how kinetic energy is related to the speed and mass of an object. But the
student video is only intended to be an introduction sufficient to pique student interest and
curiosity. Hopefully, they are then motivated to explore this relationship through hands-on
inquiry.
It is recommended to start with a showing of the assembled Hot Wheels system and a
demonstration of how the pendulum’s movement is an indication of the kinetic energy of the car.
One can observe how the pendulum moves higher when the mass or speed of the car is increased.
Students can then be asked to predict which will increase the motion of the pendulum more,
doubling the cars mass or doubling its speed. If students comprehend the video, they should
predict that speed will have the greater effect. They should then test this prediction with the
system.
Students can be challenge to determine the exact mathematical relationship of the car’s mass and
speed to its kinetic energy. They can do this by measuring the kinetic energy (KE) of the car
while varying the mass and speed.
Record the car’s speed over the end section of track that is level. This section of the track should
be at least one meter long. If the level section of track is not at least one meter long, adjust the
position of the elevated portion of the track so that a longer portion of the track is level. Put a
clear and easily seen mark on the track at the timing start point and measure the exact distance
from this point to the pendulum. Set the car at the launch position and release it. Time the car’s
travel using a stop watch beginning as the front of the car reaches the timing start point and end
the timing as the front of the car just reaches the pendulum. Record this time. Repeat this
measurement at least three times to increase the accuracy of this measurement. It is expected that
there is some variation in this measurement because of differences in the number of small
collisions of the car with the sides of the track as it travels the track. These minor collisions
represent variations in friction that slightly alter the car’s speed. Students can be introduced to
the concept of determining the arithmetic mean of multiple measurements as a method for
reducing experimental uncertainty with this part of the procedure. While there is a delay in
pressing the stopwatch button due to human reaction time, that delay should be about the same
for both the start and finish so that should cancel in determining the overall time. If the teacher
happens to have some other device for measuring the car’s speed such as a motion sensor, they
may use that instead to obtain measurements that may be more accurate. However, measuring the
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travel time with a stopwatch has been found to provide adequate accuracy for observing the
correct mathematical relationship of speed with KE.
At the same time that some students are measuring the car’s speed, others can also measure the
apex of the pendulum’s travel. One way this can be accomplished is by mounting a video camera
on a tripod so that the video camera can record the pendulum’s travel after the collision. Then by
rewinding the recording and stepping through the recording of the pendulum’s travel one frame
at a time, the teacher can easily determine the magnitude of the pendulum’s apex with a high
degree of reliability. If a video camera is not available, then the apex must be judged by visual
observation. If the teacher uses this method it is suggested that they assign two students to watch
for each measurement and take the average of the two measurements. The teacher should neglect
results if the car lost speed due to a bad launch or because it was excessively bouncing against
the sides of the track. It is best to carefully adjust the track to minimize gaps between track
sections and to align the track so that the car can travel as smoothly as possible to minimize the
effects of friction.
It may be helpful to have a student stationed near the pendulum to catch the pendulum after it
reaches its apex and before it fully rebounds to where the car is resting so that it doesn’t come in
contact with the magnet on the car. It was often found that during the rebound, the pendulum and
car magnets are able to move in such a way that they reorient themselves to maximize their
attractions. Due to the strength of these magnets, the magnets are then strongly attracted to each
other and once they attach to each other it can be very difficult to separate them.
Thus for each measurement several students can be involved. One student can release the car
from the launch point, one student can time the car’s travel, one student can catch the pendulum
after it reaches the apex and before it returns to the resting position, one student can operate the
video camera or two students can visually observe the pendulum’s apex, and one student can
record the results. Another student can be responsible for varying the car’s mass and another for
varying the launch height.
At least three measurements should be recorded for each set of values of the variables, mass and
speed. An Excel spreadsheet titled “KE Data Template” is provided that can be used to record
the data. This spreadsheet includes the formula for calculating the car’s KE (equal to the
pendulum’s PE at its apex).
It will work better to have measurements that include at least a doubling of the car’s mass and a
doubling of its speed so that the magnitude of the differences will enable observing noticeable
differences in the mathematical relationships.
When the teacher has recorded a complete set of measurements, they may ask their students
which of the following equations best fit the data:
KE = car mass X car speed
KE = 1/2 car mass X car speed
KE = 1/2 (car mass)2 X car speed
KE = car mass X (car speed)2
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They can check this by calculating the car’s KE using each of these equations and determining
which gives results that are closest to what they measure for the car’s KE using the pendulum
system. It is most likely that they will not observe perfect agreement due to experimental
variation so they should decide which of these equations is the best fit – which gives results that
are closest to those they actually measured. This is the way that scientists select the best
explanations for other phenomena that they observe. There is always some experimental
variation that results in less than absolute perfect agreement so scientists search for the simplest
explanation that best fits the evidence.
However, in this case, the teacher should also call students’ attention to the fact that a very large
number of other scientists have verified that KE does indeed equal 1/2 mass X speed2 based on
many thousands of highly accurate and carefully verified experimental measurements. Thus there
is a very high level of confidence that this equation is the best fit for this data. If students fail to
find this equation has the best fit for their data, because there is so much other evidence that
indicates this equation is the best fit, they should search for an explanation in the nature of their
data for the failed fit to this equation. A possible explanation is a pendulum that is not
functioning well. For instance, it may not be swinging freely so it is not showing the car’s full
kinetic energy. Or the students may have made errors in measuring some of the variables such as
the car’s mass or speed or the pendulum apex.
Teachers are encouraged to experiment with this system to find ways to make the measurements
more reliable and reproducible and to further reduce friction and other complicating factors.
Hopefully, they will find this system to be a useful way to guide Their students’ exploration of
these concepts. Best wishes to the teachers and their students’ further inquiries into ways that
nature behaves.
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