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ELECTROMAGNETIC CANNON
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Question
A solenoid can be used to fire a small ball. A capacitor is used to energize the solenoid coil. Build a device with a capacitor charged to a maximum 50V.
Investigate the relevant parameters and maximize the speed of the ball.
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Outline
Experimental setup Experimental procedure Typical result Statistics and explanation Relative parameters
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Experimental Setup
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Experimental Procedure
Charge the capacitor five times longer than its time constant.
Connect the capacitor to the solenoid. Measure the distance the bar flies to
estimate the initial speed. Repeat the procedure above.
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Typical Result
Video
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Qualitative Explanation
The “steel” ball is magnetized, with the same direction as the magnetic field in the solenoid. Faraday’s Law Curie’s Law
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Why It Moves
A magnetic dipole in magnetic field tends to move toward where the magnetic potential is less (i.e. the middle of the solenoid) Magnetic domain model Loop model
Bdx
dF
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How Fast It Moves
The magnetic field is associated with the discharging process of the capacitor, and the position of the ball.
The dipole moment is associated with the changing rate of the magnetic field, and the magnetization of the ball.
Bdx
dF
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Parameters
Voltage Solenoid
Length Layer Diameter
(→Inductance) Capacitance Resistance
(→frequency)
Magnetic field Ball
Magnetic permeability
Resistance Mass Shape Initial position
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Experiment I
Speed vs. Voltage Parameter : Voltage (from 30V ~50V) Initial Condition :
Capacitance: 1470μF Number of Layers: 5 layers Length: 1.5 cm Position of Cannon: In front of the solenoid (0
mm) Mass: 0.014 g
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Voltage
Speed is positively related to the voltage.
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Experiment II
Speed vs. Capacitance Parameter : Capacitance (from 470μF to
3300μF) Initial Condition :
Voltage: 50 V Number of Layers: 5 layers Length: 1.5 cm Position of Cannon: In front of the solenoid (0
mm) Mass: 0.014 g
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Capacitance
A peak occurs at 1470 μF.
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Experiment III
Speed vs. Number of Layers Parameter : Number of layers (4~8 layers) Initial Condition :
Voltage: 50 V Capacitance: 1470 μF Length: 1.5 cm Position of Cannon: In front of the solenoid (0
mm) Mass: 0.014 g
1 2 3 4 5 6 7 81.5 cm
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Numbers of Layers
A peak occurs at 5 layers.
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Experiment IV
Speed vs. Solenoid length Parameter : Length (1, 1.5, 2, 2.5, 3 cm) Initial Condition :
Voltage: 50 V Capacitance: 1470 μF Number of Layers: 5 cm Position of Cannon: In front of the solenoid (0
mm) Mass: 0.014 g
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Length
A peak occurs at 1.5 cm.
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Experiment V
Speed vs. Position Parameter : Position (0~10 mm) Initial Condition :
Voltage: 50 V Capacitance: 3700 μF Length: 1.0 cm Mass: 0.083 g
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Position
Speed reaches maximum when the ball is at the front of the solenoid.
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Summary
The fastest speed we achieve is 31.4 m/s, which happens under V=50 V C=1470 μF Layers=5 Solenoid Length=1.5 cm Position: At the front Ball mass=0.014g Material: Iron
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Summary
In this case, energy stored in the capacitor is 1.84 J.
Energy transferred to the projectile is 6.91*10-3 J.
Ratio=3.76*10-3
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Thank you!