AP Free Response Question
2003 B3
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A rail gun is a device that propels a projectile using a magnetic force. A simplified diagram of this device is shown above. The projectile in the picture is a bar of mass
M
and length
D
, which has a constant current
I
flowing through it in the +y-direction, as shown. The space between the thin frictionless rails contains a uniform magnetic field
B
, perpendicular to the plane of the page. The magnetic field and rails extend for a distance
L
. The magnetic field exerts a constant force
F
on the projectile, as shown. Express all algebraic answers to the following parts in terms of the magnitude
F
of the constant magnetic force, other quantities given above, and fundamental constants.
(a) Determine the position
x
of the projectile as a function of time
t
while it is on the rail if the projectile starts from rest at x = 0 when t = 0.
(b) Determine the speed of the projectile as it leaves the right-hand end of the track.
(c) Determine the energy supplied to the projectile by the rail gun.
(d) In what direction must the magnetic field
B
point in order to create the force
F
? Explain your reasoning.
(e) Calculate the speed of the bar when it reaches the end of the rail given the following values.
Topic Formulas
Description
Published Formula
Faraday's Law
magnetic field around a current-carrying wire
magnetic flux
magnetic force on a current-carrying wire
magnetic force on a moving charge
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Ampere's Law
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Eddy Currents plus a Lab Simulation
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Electricity and Magnetism Background
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Introduction to Magnetism
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Magnetic Field Along the Axis of a Current Loop
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Magnetic Forces on Particles (Part II)
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Magnetism: Current-Carrying Wires
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Maxwell's Equations
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Meters: Current-Carrying Coils
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Torque on a Current-Carrying Loop
Worksheet:
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Maggie
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The Tree House
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Magnetism
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Bar Magnets
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Magnetic Forces
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Meters and Motors
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Magnetic Forces on Current-Carrying Wires
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Magnetic Forces on Moving Charges
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Practice with Ampere's Law
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36A: Magnets, Magnetic Fields, Particles
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36B: Current Carrying Wires
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Exercises on Current Carrying Wires
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