Physics EEI: Magnetic Braking - Sliding on Incline, Conductor Study

This Physics EEI report investigates the effects of conductor thickness and conductivity on magnetic braking. The experiment compares aluminum and copper conductors by measuring the velocity of a magnet sliding down an inclined plane. The results indicate that increasing conductor width decreases the magnet's velocity, demonstrating a relationship between braking force and conductor properties. Copper is shown to be a more effective material for magnetic braking compared to aluminum. The experiment uses a simple setup to study eddy current braking, and the data analysis includes linear regression to quantify the relationship between conductor width and magnet velocity. The report concludes by discussing error analysis and recommendations for future experiments, highlighting the practical applications of magnetic braking in various technologies. Desklib provides access to similar solved assignments and past papers for students.

0
2019
Physics EEI
Krystina Cheng
ID: 018237
Teacher: Miss Branch
Magnetic Braking -Sliding down an incline

1
Abstract
This experiment is aimed to compare magnetic braking properties of aluminum and copper
conductors and then investigate the effects of the thickness of conductor sheet on magnetic
braking properties of a conductor.
A simple and cheap experimental setup applicable in the study of eddy current brake by sliding a
magnetic along an inclined conducting surface using the basic principles in physics. A
quantitative experiment on the variation of velocity of magnet sliding on an inclined plane with
the conductor sheet width has shown that as the conductor width is increased, the velocity of the
magnet declines.The findings of this experiment also shows that copper is better than alluminium
in terms of magnetic brakibg systems.

2
Table of Contents
Abstract.......................................................................................................................................................2
Introduction.................................................................................................................................................4
Objectives of the Experiment..................................................................................................................4
Theory Review.........................................................................................................................................4
Hypothesis...............................................................................................................................................5
Justification..............................................................................................................................................5
Results.........................................................................................................................................................6
Analysis and Discussion...............................................................................................................................7
Error Analysis..........................................................................................................................................8
Conclusion...................................................................................................................................................9
Recommendations.......................................................................................................................................9
References...................................................................................................................................................9

3
Introduction
Research question and Aim: What effects does the thickness and conductivity of metal have on
the velocity of a magnet down an incline plane? To investigate the effects of the thickness of
conductor sheet on magnetic braking properties of a conductor. The aim of our investigation was
to test variables of different metals and thickness of the metal sheets to see what effect it had on
the velocity of a magnet travelling down an inclined plane. Magnetic braking depends on eddy
currents. Since 1851 French physicist Léon Foucault discovered that the eddy current is an
electrical phenomenon. It is caused when a conductor is exposed to a changing magnetic field
due to relative motion of the field source and conductor. For example, when a permanent magnet
moves over a sheet of metal (such as aluminum), eddy currents are set up in the metal and these
can act as a brake on the motion (Lenz's Law).
To compare magnetic braking properties of aluminum and copper conductors
To investigate the effects of the thickness of conductor sheet on magnetic braking properties of a
conductor.
Theory Review
According to Lenz’s law, the flow of eddy currents in a conducting material produces another
magnetic field that acts in such a way that it opposes the magnetic field that initially produced it.
For instance, a magnet sliding down on a conductive material’s surface will experience an
opposing force or drag that slows down its motion. This is as a result of eddy currents induced on
the surface of the material. This principle is widely applied in rapidly decelerating moving or
revolving machines or machine parts (Van Saders et al., 2016).). The use of eddy currents to
slow down moving machines is considered safer than conventional methods because the process
is smoother (Matt, MacGregor, Pinsonneault, & Greene, 2012).), especially in cases where the
magnet and the conducting plane are not in contact. Furthermore, factors such as rain do not
affect the process. It is worthwhile to mention that, the magnetic breaking cannot bring a moving
device to a complete stop since the braking torque declines with a fall in speed (Van Saders et
al., 2016).). For example, the speed can be cut down from about 25 to 5 m/s after which another
method is applied to reduce the speed further.
The flow of eddy currents in a material generates heat due to the resistance presented by the
material and as it is with all work done against resistance, heat is produced which corresponds to
energy loss. Thus the kinetic energy of the material is converted to heat energy with the result
being that the magnet slows down.
Magnetic induction phenomenon can be investigated by deceleration of a magnet falling through
a conductor. As a magnet falls through an inclined plane, the falling magnet induces an eddy
current in the conductor. The resulting eddy current resist the increase in flux. As the induced
eddy current and the magnet interacts, a damping force results (Martins et al., 2010). This causes
the magnet to have a low velocity as it falls. As the magnetic force increases, its speed increases
too. This continues until a point when the magnetic force equalizes magnet’s weight. This result
into constant velocity (Matt, MacGregor, Pinsonneault, & Greene, 2012). This magnetic braking

4
forms the center of various technological application. This concept can be demonstrated in the
laboratory using readily available equipment.
Figure 1: Interaction between the magnetic field due to eddy currents and that due to the conducting
plane. a) is the main magnetic field, b) Shows the magnetic field due to eddy currents and c) The
resulting field.
Hypothesis
It was hypothesized that as increasing thickness of the conducting plane the magnetic braking
force will reduce. It was hypothesized that aluminum is better conductor in magnetic braking
applications.
Justification
When a magnet slides down an incline surface, magnetic flux along the conductor’s track
changes. A change in induced emf is then experienced inside the conductor resulting into eddy
current. This exerts magnetic force on the eddy conductor portion that is found inside the
external magnetic field that results from magnetic action as proposed by Lenz’s law (Qian et al.,
2010). This force is then propagated within the metallic track thus retarding the sliding process.
The resulting force can be explained by Newton’s third law of motion (Li, Krasnopolsky, &
Shang, 2011).
Magnetic braking force is directly proportional to the velocity and is evaluated using the formula
in the equation below where b is the damping coefficient. This coefficient depends on the
parameters of the systems; v is the magnet’s velocity. This velocity is a function of the dynamic
emf while the velocity is proportional to the conductor’s length (Van Saders et al., 2016). This
velocity is of low magnitude. Suppose m is considered as the mass of the magnet sliding down
the plane, its motion as result of its weight, the mechanical friction between the magnet and the
surface as well as the braking force are obtained from Newton’s second law of motion as
follows:

5
Solution of the above differential equation yields
Subjecting a mass to an opposing force that is proportional to its velocity forms the basis of
various experiments. This experiment provides an opportunity to investigate this induction
phenomenon.
Planning & Preliminary trials:
For the preliminary trial of experiments, the retort stand was set up and plank of wood was
clamped to the stands. It was measured 30 cm high form the top of the plank and the angle was
calculated as 30 degrees. A sheet of width of 0.9mm aluminum was clamped on the top of tank, a
sheet of plastic was taped on top of the mental.
The magnet was put on the top of plank and slide down from
incline. But the motion of magnet can’t be tracked by the
motion sensor because the magnet is so small so that the
motion sensor can’t detect the motion of magnet. To make
the motion sensor can track the motion of the magnet, a sheet
of paper was cut into a rectangle with one side equal to the
circumference of the magnet, the paper was bluetacked to the
top of magnet in a cylinder and ensure the cylinder wasn’t
touching the bottom. The motion sensor was put at the
bottom of the plank, but sometimes the motion can’t be track
exactly. So the position of motion sensor was changed to the top of the plank to make it recorded
more accurately. Then the motion sensor was plugged into computer. The data of thickness of
0.9mm aluminium was recorded for preliminary trails as the graph shown.
Equipment:
 Wooden plank
 2x Retort stands
 2x Clamps
 Metre ruler
 Motion sensor
 Laptop
 Smooth plastic sheet
 Disk magnet
 4x Copper sheets (thicknesses of 0.5mm, 0.9mm,
1.05mm & 1.2mm)

6
 5x Aluminium sheets (thicknesses of 0.6mm, 0.9mm, 1.2mm, 2.4mm, 3mm)
 Paper
 Scissors
 Blue tack
 Adhesive tape
Method
(1) The retort stand was set up: -put clamp on retort stand
-plank of wood was clamped to the stands (It was measured 30cm high from the top of the
plank, angle was calculated as 30 degrees)
(2) A sheet of mental was clamped on the top of the plank
(3) A sheet of plastic was taped on the top of the mental sheet (Ensuring the bottom of the
plastic reached the bottom of the board)
(4) Motion sensor was attached (using bluetack) at the top of the plank
(5) Motion sensor plugged into computer
(6) The flag was made on the magnet which can tacked by motion sensor
(7) Magnet was released from 40cm middle of plank (directly in front of motion sensor) the
Capstone started recording
(8) Magnet slid down the incline and reached the bottom the Capstone stopped recording
(9) Results were recorded in a distance vs time graph
(10) Repeated the previous steps but changed the different mental sheets (Aluminium and
copper) one with no metal sheet which is control one -and different thickness of variables metal
sheets – four trials of each sheet
Copper sheet thickness (mm)
o 0.5
o 0.9
o 1.05
o 1.2
Aluminium sheet thickness (mm)
o 0.6
o 0.9
o 1.2
o 2.4
o 3
(11) All the results were recorded into Capstone then find the linear function of every trail
Results
Aluminum
Width (mm) Trial Velocity (gradient
of graph) (m/s)
Error Average (m/s)

7
0.6 1 0.111 4.4 ×1 0−4 0.10975
2 0.108 3.3 ×1 0−4
3 0.11 3.9 ×1 0− 4
4 0.11 5.5 ×1 0− 4
0.9 1 0.0908 4.7 × 1 0−4 0.097275
2 0.0995 5.6 ×1 0−4
3 0.0898 4.6 × 10−4
4 0.109 5 ×1 0−4
1.2 1 0.0698 1.9 ×1 0− 4 0.072425
2 0.0758 4.2 ×1 0−4
3 0.0695 5.9 ×1 0− 4
4 0.0755 2.8 ×1 0−4
2.4 1 0.0483 6.1 ×1 0−5 0.04795
2 0.0463 7.3 ×1 0−5
3 0.0486 1.0 ×1 0−4
4 0.0486 7.0 ×1 0−5
3 1 0.0578 1.5 ×1 0− 4 0.0864
2 0.0569 2.1 ×1 0−4
3 0.0585 1.1 ×1 0−4
4 0.0577 1.1 ×1 0−4
Copper
Width (mm) Trial Velocity (gradient
of graph) (m/s)
error Average (m/s)
0.5 1 0.0879 4.9 × 10−4 0.08725
2 0.0892 2.1 ×1 0−4
3 0.0887 2.7 ×1 0−4
4 0.0832 3.9 ×1 0− 4
0.9 1 0.0519 1.6 ×1 0−4 0.0512
2 0.0494 1.6 ×1 0−4
3 0.0497 2.2 ×1 0−4
4 0.0538 1.1 ×1 0−4
1.05 1 0.0519 1.1 ×1 0−4 0.04925
2 0.0475 1.2 ×1 0−4
3 0.0489 1.0 ×1 0−4
4 0.0487 1.5 ×1 0− 4
1.2 1 0.0424 8.6 ×1 0−5 0.044925
2 0.0428 1.4 ×1 0−4
3 0.0467 1.6 ×1 0−4
4 0.0478 3.1 ×1 0−4

8
Analysis and Discussion
Aluminum
Copper

9
Control
The magnet was observed to reach a terminal velocity almost instantaneously and then slides
down at a constant velociy as the net force approached zero. The curves in the two graphs are
least square linear lines repersenting the relationship between velocity and the width of the
metallic sheet. The coefficint of determination for the aluminium sheets is 0.9606 while that
copper is 9419 indicating that results copper sheet width is relatively more related to the
magnet’s velociy compared to alluminium.
From beckground theory magnetic braking force (F)=-bv hence

10
F is proportional to v
The obtained curves are negatively sloping, it can thus be concluded that as the width increases,
velocity of the magnet declines. This implies that sheets of lower width offers more braking
force. This findings are in line with the theoritical framework of the relationship between fluxes
and amount of current induced in conductors as supported by the findings of (Machida, Inutsuka,
& Matsumoto, 2011). Furthermore, the value of the coefficient of determination is quite high
which shows that the model fits the data to a high degree of accuracy and only a fairly low
percentage of the variance in the velocity is unexplained by the change in width of the
conducting material.
A comparison between the findings of aluminum sheet and copper sheets reveals copper is a
better material in magnetic braking copared to aluminium. This attributed to the relatively high
velocity in aluminium sheet of the same width as that of copper. Copper sheet of a similar
thichkness offers more resistance hence a better material in the braking process. This is shown
by the general the velocities realised in aluminum procedure are more than those obtained from
cooper. The change in velocity with respect to width was found to be greater in coppper sheets
compared to aluminium sheets. This findings conforms to the finding of Li, Krasnopolsky, &
Shang (2013) who conluded that copper offers better braking properties compared to
alluminium based on the nature difference in the magnet’s velocities.
The relatively high velocity of the magnet on alumium sheet shows that it will require
comparitively larger drag force in aluminium compared to copper. This implies that copper
condictors offers a better braking properties compared to allumium. Copper is thus a better
material in magnetic braking systems.
Error Analysis
The results obtianed are subject to some experimental errors. Theoritically, a linear relationship
between the velocity obtained and width should have all the data points within a straight line
because tmagnetic braking force is linearly related to velocity in the form of F=-bv.
Experimental results however shows some deviation with the value of R-square <1. The errors
are in the collected data can be attributed to the following sources of errors:
Possible misreading might have resulted into incorrect recording of the velocities from the
associated graphs.
Failure to account for the effects of other factors such as the earth’s magnetic field might have
affected the findings.
Physical variations. The pysical properties such as difference in the sizes of aluminum and
copper used might have resulted into inconsitent results.
Recommendations
The accuracy of this experiment can be improved by designing another experiment to determine
the contribution of the earth’s magnetic field to the overall breaking force experienced by the
magnet.

11
Conclusion.
This report has presented the results the magnetic braking properties by exmining sliding
characterestics of a magnet on an incline conducting plane. The experiment was conducted using
easily aquired materials. Based on the results and their analysis, it can be seen that magnetic
braking force increases as the conductor gets thinner. The analysis of the results obtained also
shows that copper is better conuctor to be used in magnetic braking compared to aluminium. The
experiment was thus a success as the objectives were achieved.