2003B3.
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.
B=5TL=10mI=200AM=0.5kgD=10cm