Varying electrical conductivities of different, non-magnetic metals appears to affect the magnitude of magnetically damped motion. To determine the relationship between magnetic damping and conductivity an experiment was designed using different length tubes of aluminium, copper and brass. The tubes had the same diameter and similar wall thickness. A short, cylindrical neodymium magnet was dropped through the tubes of and the time for the magnet to traverse the tube was recorded using a smartphone camera. These times allowed for the terminal velocity to be calculated for each metal length and the average terminal velocity for each metal was determined. This data was then processed to compare the terminal velocity with known conductivity values. The relationship between the terminal velocities of aluminium, brass and copper and their respective conductivities was found to be inversely proportional; as conductivity increases, terminal velocity decreases. Through this relationship, copper was identified as most effective in magnetically damping motion, exhibiting the largest terminal velocity of all metals and the highest conductivity

Akhtar, Kalem

English

Illinois Mathematics and Science Academy: DigitalCommons@IMSA

Queensland Academy for Science, Mathematics and Technology"4 Perfect IB Scores Kalem Akhtar  The relationship between electrical  conductivity and magnetically damped motion"Research Question: In regards to electrical conductivity, which metal allows for maximum magnetic damping to be achieved?  Context: Magnetic damping is used in magnetic braking systems for high speed trains.  Contribution: This research quantifies the degree of magnetic braking with different metals and alloys due to conductivity Background"•  Faraday’s and Lenz’s Law of Induction shows the magnitude of induced voltage when a magnetic field passes through a wire or coil   where 𝛆 represents the electromotive force, ​Ф↓𝑩  represents the magnetic flux and 𝒕 represents time. •  Stronger magnetic fields, greater electrical conductivities and faster changes in field result in greater eddy currents formed, and greater magnetic fields produced. 𝜀= − ​𝑑​Ф↓𝐵 /𝑑𝑡 	Methodology"Setup: •  Cylindrical Neodymium Magnet •  Various metal tubes •  Retort stand, clamp and plastic tub •  Camera and accessories •  Whiteboard and accessories 1.  Apparatus and camera were set up.  2.  A camera recording was taken as the neodymium magnet was dropped through the tube into the plastic tub. Trial details were recorded on the whiteboard for each trial. 3.  The process was repeated 5 times for each tube.  Methodology"•  In the experiment, the type of metal tube was varied to measure the time taken for a magnet to pass through the tube •  All other variables were controlled Variables	Measured	 Possible	Effect	On	Results	How	The	Variable	Was	Controlled	Temperature	Increasing	will	increase	resis-vity	of	metal,	increasing	𝑡	 Experiment	was	undertaken	with	a	constant	temperature	Mass,	shape	and	strength	of	magnet	Varying	will	increase	𝑡	and	therefore	reduce	terminal	velocity	The	same	magnet	was	used	in	each	trial	Thickness	of	tube	 Increasing	will	increase	𝑡	and	therefore	reduce	terminal	velocity	Tubes	were	of	very	similar	thickness	and	had	similar	inner	diameters	Raw Data"y	=	0.2437x	+	0.0035	R²	=	0.9999	y	=	0.4852x	+	0.0107	R²	=	0.97859	 y	=	0.2408x	-	0.0121	R²	=	0.99789	0.00	0.50	1.00	1.50	2.00	2.50	0.00	 1.00	 2.00	 3.00	 4.00	 5.00	 6.00	 7.00	 8.00	 9.00	Displacement	(m)	Time	(s)	Average	Terminal	Velocity	of	Different	Metals	Copper	 Brass	 Aluminium	This graph shows the displacement of the magnet through the tube against time taken for the magnet to fall through the tube for all the metal types. The gradient represents terminal velocity as the gradient is displacement over time. Analysis"To determine a relationship between terminal velocity and conductivity, the raw data was processed using:   This was tabulated with the respective calculated uncertainties as well as the literature values for conductivities.  𝑇𝑒𝑟𝑚𝑖𝑛𝑎𝑙 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦= ​𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡/𝑡𝑖𝑚𝑒 	Tube	Material	ConducBvity	(S/m)	Terminal	Velocity	(m/s)	Mean	 Uncertainty	Aluminium	 3.77×107	 0.2437	 ±	0.0169	Brass	 1.54×107	 0.4852	 ±	0.0689	Copper	 5.95×107		0.2408	 ±	0.0403	Results"y	=	5E+06x-1.582	R²	=	0.91781	0	10,000,000	20,000,000	30,000,000	40,000,000	50,000,000	60,000,000	70,000,000	80,000,000	0	 0.1	 0.2	 0.3	 0.4	 0.5	 0.6	 0.7	Conduc-vity	(σ)	Terminal	Velocity	(ms-1)	Conduc-vity	vs	Terminal	Velocity	for	the	three	metal	tubes	This graph shows the average terminal velocity of each metal plotted against their respective conductivities. The trendline produced is inversely proportional. Evaluation"The graph produced indicates an inversely proportional relationship between terminal velocity and conductivity; however, it is not possible to draw strong conclusions with only three metal types. 		INVERSELY PROPORTIONAL Sources of Error"Random errors: •  variations in dropping the magnet •  variation in timing the magnet  Systematic Error: •  Appropriateness of the selected frame rate for the camera 		Improvements"-  Increase accuracy of set up e.g. camera with higher frame -  Standardised release of magnet e.g. electromagnetic release Conclusion"The experiment was successful in identifying the metal with the maximum dampening effect to be copper, and the hypothesis was proven to be correct as the terminal velocity was inversely proportional to conductivity. Eddy currents have many practical applications as the unique properties of the currents allow for a very smooth dampening of motion. Some examples where eddy currents could be used are in the safe braking of high speed trains or in emergency stopping for dangerous machinery. Knowledge of the relationship between magnetic braking and conductivity would allow for the use of different metals in different applications enabling optimisation. Possible Extension"To further the investigation, the following variables could be explored:  -  Additional types of metal -  Different thickness of tubes -  Different magnet shapes, sizes and strengths -  Experimentally determining metal conductivities Bibliography"•  Tsokos, K. A. (2014). Physics for the IB Diploma. Cambridge: Cambridge University Press. •  Sawicki, C. (1997). A dynamic demonstration of Lenz’s law. Phys. Teach. 35, 47–49. •  Gates, J. (May 2011). A teachable moment uncovered by video analysis. Phys. Teach. 49, 284–285 •  Clack, J. and Toepker, T. (1990) Magnetic induction experiment Phys. Teach. 28, 236 •  Halliday D., Resnick R. and Walker J. (1997) Fundamentals of Physics, 5th ed. Wiley p. 641. •  Lenz Law and Eddy Current Demonstration (2016). Retrieved 7 November 2017, from:http://emagnetsuk.com/magnet_products/measurement_and_experimentation_tools/lenz_law_and_eddy_current_demonstration.aspx  Acknowledgements"•  Dr Kirsten Hogg for organising equipment and assisting with poster construction •  Aryaman Sud for assisting with recording trials •  Deanna Iannantuono for assisting with poster construction	

The relationship between electrical conductivity and magnetically damped motion

The Relationship between Electrical Conductivity and Magnetically Dampened MotionKalem AkhtarQASMTToowong, Queensland, AustraliaJune/July 2018A magnet falling through a metal tube will reach terminal velocity due to induced eddy currents.  The time taken to reach terminal velocity depends on the conductivity of the metal tube.Research Question: Does the conductivity of different metal tubes (Aluminium, Copper and Brass) determine the time a falling magnet takes to reach terminal velocity?Background: Faraday’s Law of Induction:The slow fall of a magnet through a metal tube is a demonstration of Lenz’s Law.  The changing magnetic flux from the falling magnet induces an emf in the metal tube.Raw Data: Analysis and Evaluation:The terminal velocity of the magnet was determined for each metal type using a graph like the one shown in Figure 3.  The maximum and minimum slopes were used to determine the uncertainty.  The terminal velocities were tabulated along with the conductivities of the metals.Although it is not possible to establish a trend with only three metal types it appears that conductivity is inversely proportional to terminal velocity. Sources of error in the experiment arise from random errors associated with dropping and timing the magnet’s fall through the tube.  These errors were minimised by using a video camera to record the motion.  By carefully reviewing the film frame by frame the time interval was accurately determined.  Multiple trials ensured the results were reliable.Conclusion:The experiment was successful in identifying the metal with the maximum dampening effect to be copper, and the hypothesis was proven to be correct as the terminal velocity was inversely proportional to conductivity.Applications:Eddy currents have many practical applications as the unique properties of the currents allow for a very smooth dampening of motion. Some examples where eddy currents could be used are in the safe braking of high speed trains or in emergency stopping for dangerous machinery.  Knowledge of the relationship between magnetic braking and conductivity would allow for the use of different metals in different applications enabling optimisation.where ε represents the voltage, ФB represents the magnetic flux and t represents time.Eddy currents:Eddy currents are formed as a result of the emf and produce their own magnetic field which opposes the initial field. This causes dampened motion, as the two fields oppose each other, balancing the force of gravity on the magnet.When the magnetic force equals the gravitational force the magnet reaches terminal velocity.  The terminal velocity of the magnet will be measured for varying length tubes of aluminium, copper and brass.It is expected that metals with greater electrical conductivities will have greater eddy currents formed, and the magnet will reach terminal velocity faster.Methodology: 1. The apparatus was assembled as shown in Figure 1, with the metal tube clamped by the retort stand and the plastic tub positioned below the tube. The experiment was un-dertaken in front of a whiteboard for a clear background.2. The video camera was attached to the tripod and was set at a quality of 1080p and a frame rate of 30fps.3. The metal type, tube length and trial number was noted on the whiteboard with the whiteboard marker and video recording was started.4. The neodymium magnet was dropped into the tube and once it landed in the plastic tub beneath video recording was stopped.5. The process was repeated until 5 trials had been recorded for each tube.Table 1. Raw data from the aluminium tube lengths Table 2. Processed data for three metals.  Terminal velocity calculated from 5 trials of 6 lengths for each metal.Figure 2. Photograph of the experimental setupFigure 3. Graph of Aluminium tube times used to calculate terminal velocity of the magnetFigure 4. Conductivity and terminal velocity for the three metal tubes.Figure 1. Schematic of apparatus setup-3-1135790 0.5 1 1.5 2Time (s)Length (m))Time vs Length for Aluminium TubeMaximum Slope TrendlineMinimum Slope TrendlineBest Fit Trendline010000000200000003000000040000000500000006000000070000000800000000 0.1 0.2 0.3 0.4 0.5 0.6 0.7Conductivity (S/m)Terminal Velocity (m/s)Conductivity vs Terminal Velocity for the three metal tubes

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The relationship between electrical conductivity and magnetically damped motion

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Illinois Mathematics and Science Academy: DigitalCommons@IMSA