The Force of a Ball
Bearing as a Function of Distance from a Magnet
Mark French, Tyler French, Hannah Peterson
Table of Contents:
Contents
2. Statement
3. Hypothesis
4. Materials
5. Method
6. Results
7. Raw
Data
8. Conclusion
10. Bibliography
11. Go
Up
Background
Information (Top):
Magnetism:
A Dipole is a magnet
with two poles, a north pole and a
south pole, each with opposite magnetic forces.
A magnetic field is the
magnetic effect of electric currents and magnetic materials. The magnetic field
at any given
point is specified by both a direction and a magnitude (or strength); as such
it is a vector field.
Concept 0 from Murray -
Magnetics 101
In an electric field, two dipole magnets are attracted
to each other. In the diagram, the bottom magnet positive end is attracted to
the top magnet negative end, while the bottom negative is repelled by the top
negative. The domains are aligned, and since the bottom + is closer than the
bottom -, the magnetic force is stronger between + - than - -.
The explains why our ball bearing will have a greater force
as it gets closer to the magnet.
A magnetic field
consists of imaginary lines of flux coming from moving or spinning electrically
charged particles. Examples include the spin of a proton and the motion of
electrons through a wire in an electric circuit.
The magnetic field of an
object can create a magnetic force on other objects with magnetic fields. That
force is what we call magnetism.
The magnetic field is a
dipole field. That means that every magnet must have two poles.
On the other hand, a
positive (+) or negative (−) electrical charge can stand alone.
Electrical charges are called monopoles, since they can exist without the opposite
charge.
Force:
Conservation of Energy:
“Energy is neither created nor destroyed.” When the marble is
slowing down, that means that it’s losing energy due to influences like gravity
and friction.
F=ma where F is Force, m
is mass, and a is acceleration.
We hope to develop a model
for the motion of a ball bearing based on the force-distance relationship. Our
independent variable is the distance of the ball bearing from the magnet, and
our dependent variable is the magnetic force between the bearing and magnet.
We believe the the force of the ball bearing will gradually decrease due
to friction and heat loss to the track underneath the ball as it moves to and
from the magnet. As the ball bearing moves towards the magnet, it will gain
force; however, as it moves away from the magnet, it will lose a greater amount
of force than it obtained. Thus, the ball bearing will slow down eventually at
the position of the magnet. The controlled variables include, but are not
limited to, the ball bearing, the grooved track, the position and type of
magnet, and the temperature of the environment.
- Two dixie cups
- Two smooth (cylindrical)
pencils
- Small ball bearing
(8.23 g used)
- Tape
- Sheets of paper
- Ruler
- Neodymium magnet
- Pen
- Video recording device
with slow motion function
First, construct the
experiment. See the diagram of the set-up for reference. Tape the two pencils
together at each end so they are completely parallel and flat. The groove in
between the two rounded surfaces will provide the track for the ball bearing to
follow. Tape the flat magnet in the middle of the attached pencils, ensuring
that the tape covers only one side of the pencils and does not completely
encircle them, which would obstruct the path of the ball bearing. Place the
track on a flat surface with the magnet face down. Mark the position of the
magnet’s center on the side of the track with the marker. This will be position
zero. Mark three additional points 0.5, 1.0 , and 1.5
cm to the left of the center. These will be the distances from which the ball
bearing will be released. Next, place the ends of the attached pencils on the
bottoms of the two overturned cups to elevate the track with the magnet facing
down. Position the pencil track so the downturned magnet is centered in the
space between the two cups and secure the track with tape. Lean the ruler
against the cups with its centimeter side facing out and a whole centimeter
value centered with the magnet. The ruler will provide a distance reference to
be used during the video analysis.
Conduct the experiment.
Hold the ball bearing away from the magnet at the 0.5 cm mark, turn on the
video recording device, and release the ball bearing. Stop recording when the
bearing has stopped moving. Conduct two more trials from the 0.5 cm release
point. Follow these steps for the 1.0 and 1.5 cm release points.
Up until this point, the
experiment has been conducted at an elevation of zero, as both cups are at the
same elevation and so the track is not angled. To angle the track, measure a
small stack of paper to a thickness of .25 cm and place under the right cup,
the side opposite from which the bearing is being released. Note that the ruler
may need to be re-centered with the magnet. Repeat the steps above using the same
release points. Next, repeat with the right cup elevated by a stack of paper
0.5 cm thick.
Explanation of method
for video analysis and data processing:
- Insert the video into Logger
Pro.
- Using the “Set Scale” option,
drag across one centimeter of the ruler to set the scale.
- Set the origin of the video to
the center of the magnet so data is precise.
- Using click-by-click
frame-by-frame analysis, record the movements of the magnet by maintaining
clicks on the center of the ball bearing as it moves.
- After clicking through all
frames of the video, Logger Pro automatically makes a position graph and a
velocity graph.
- Create a new data column, and
insert the function “derivative(“X Velocity”)” to
create the acceleration graph.
- Create a new data column and
insert the function “(“Acceleration”)(.00823) to
create the force graph.
- Repeat steps 1-7 for all 3
trials of all 3 distances for all 3 slopes.
- Once done, average all trials
of each distance and slope for a total of 9 average force graphs.
Diagram of Set-up:
Results (Top):The variations between the graphs of the
different trials were very slight and so it isn’t necessary to include all
graphs. However, the lack of variation helps to prove our hypothesis in that
regardless of incline or starting distance from the magnet, force does decrease
as a function of distance from the magnet.
Data: .cmbl files
Our hypothesis was
correct, as the force of the ball bearing did decrease over time. Though it was
not measured in the experiment, this force decreased as a result of heat loss
to and friction with the track. In this experiment, the position of the magnet
was designated as zero and thus whenever the ball bearing was to the right of
the magnet its position was positive, while whenever it was to the left of the
magnet its position was negative, which accounts for the negative values on the
position graph. The graph of the force indicates that the ball bearing’s force
decreased exponentially over time. The Intermediate Value Theorem proves that
while the force was zero at position 0 as well as at the positions farthest
away from the magnet, the force must had been the
greatest somewhere in between the two.
There were likely
procedural errors in the experiment that could be improved to mitigate the
error. An example of this would be the fact that the ball bearing was held in
place and released by a finger, which could have resulted in some human error
such as pushing or dragging the ball bearing when releasing it or some
variation in the position from which it was released. This error could be
removed by having a sort of sliding gate to hold the ball bearing in place and
release it uniformly. Such a gate could be placed at each of the desired
release points. Another possible source of error includes the video analysis of
the ball bearing. To track the bearing, a point was manually placed onto the
bearing by clicking on it, with the goal of clicking on its center for
consistency; however, it’s likely that the tracked points were not always
completely centered on the bearing, which resulted in inconsistency in the
bearing’s position. To resolve this, more accurate video analysis could be
used, such as using digital software to track the ball bearing.
·
http://www.skf.com/us/products/bearings-units-housings/ball-bearings/index.html Conduct this experiment at home by purchasing
your very own ball bearing here! You will cherish it forever.
·
https://en.wikipedia.org/wiki/Magnetic_field Concise, basic information on magnetic fields,
because Wikipedia rocks.
·
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html This website was helpful because it provided
information on the magnetic fields of bar magnets,
which was the kind used in this experiment.
·
https://www.kjmagnetics.com/blog.asp?p=gauss-guns Our experiment was inspired by Gauss guns.
·
http://www.nyu.edu/classes/tuckerman/adv.chem/lectures/lecture_2/node4.html Conservation of energy played an important
role in the results of our experiment.
·
http://cutepugpics.com/ This
experiment may be mundane to some, so we highly recommend viewing these
adorable Pug pictures.
Bibliography (Top)::
"Bar Magnet." Magnets and Electromagnets. HyperPhysics, n.d.
Web. 28 Nov. 2015.
"Magnetic
Field." Wikipedia.
Wikimedia Foundation, n.d. Web. 28 Nov. 2015.http://65.media.tumblr.com/7ecfd67b68f85ef3aad0bd1e0f76755f/tumblr_nr6q2zaMUq1uuz88lo1_500.jpg
Kurtus, Ron. "Basics of Magnetism."
By Ron Kurtus. School
For Champions, 29 Jan. 2013. Web.
14 Dec. 2015.
http://65.media.tumblr.com/7ecfd67b68f85ef3aad0bd1e0f76755f/tumblr_nr6q2zaMUq1uuz88lo1_500.jpg