How fast is the rod moving after it has traveled 8.00 m down the rails?

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An electromagnetic rail gun setup is described, involving a 49.0 g conducting rod on parallel rails with a magnetic field of 0.750 T and a current of 2.00 A. The discussion revolves around calculating the speed of the rod after it has traveled 8.00 m, with attempts to apply the equations of motion and magnetic force. The initial calculations using the wrong formulas led to confusion, prompting requests for clarification on the correct approach. Key formulas discussed include F = ma and Fm = ILB, which relate the magnetic force to the current and magnetic field. Ultimately, the correct method for deriving the rod's speed was confirmed, resolving the initial misunderstanding.
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Homework Statement


An electromagnetic rail gun can fire a projectile using a magnetic field and an electric current. Consider two parallel conducting rails, separated by 0.530 m, which run north and south. A 49.0 g conducting rod is placed across the tracks and a battery is connected between the tracks, with its positive terminal connected to the east track. A magnetic field of magnitude 0.750 T is directed perpendicular to the plane of the rails and rod. A current of 2.00 A passes through the rod.
If there is no friction between the rails and the rod, how fast is the rod moving after it has traveled 8.00 m down the rails?

Homework Equations



a=(IL(([mu0(I))/(2\pi*r)))/m
v=sqrt{2ad}

The Attempt at a Solution



(2(.530)(4pi-7(2))/(2pi(.53))/.049 = 1.63e-5
sqrt{2*1.63e-5*8}=.016

this answer is wrong. can you please tell me what i am doing wrong and help me out?Thanks.
 
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Sweet, I don't recognize that formula! Can you derive it from basic formulas for us? I would expect you to use Fm = I*L*B in this problem - the formula for the magnetic field causing a force on a current.
 
i got the answer, thanks for trying to help
 
Sorry, I'm still not with you. I see you are using F = ma but why not
F =ILB? Where does the mu and pi come from? I would begin with
F = ma
ILB = ma
 
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