PhysicsLAB 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.

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