The Force of a Ball Bearing as a Function of Distance from a Magnet                                         Mark French, Tyler French, Hannah Peterson

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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:

1. Insert the video into Logger Pro.
2. Using the “Set Scale” option, drag across one centimeter of the ruler to set the scale.
3. Set the origin of the video to the center of the magnet so data is precise.
4. 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.
5. After clicking through all frames of the video, Logger Pro automatically makes a position graph and a velocity graph.
6. Create a new data column, and insert the function “derivative(“X Velocity”)” to create the acceleration graph.
7. Create a new data column and insert the function “(“Acceleration”)(.00823) to create the force graph.
8. Repeat steps 1-7 for all 3 trials of all 3 distances for all 3 slopes.
9. 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.