An electromagnetic rail gun can fire a projectile using a magneticfield and an e

Question

An electromagnetic rail gun can fire a projectile using a magneticfield and an electric current. Consider two parallel conductingrails, separated by .500 m,which run north and south. A 42 g conducting rod is placed across the tracksand a battery is connected between the tracks, with its positiveterminal connected to the east track. A magnetic field of magnitude0.750 T is directed perpendicular to the plane of the rails androd. A current of 2.00 A passes through the rod.

(b) If there is no friction between the rails and the rod, how fastis the rod moving after it has traveled 8.00 m down therails?
m/s

Explanation / Answer

F = IL X B, where L and B are vectors, and the cross product of those vectors.

Fnet = m*a

vf^2 = v0^2 + 2a(x-x0)

Firstly

F = ILXB

Cross product of L and B vectors LXB = LBsin(theta), but the angle between the L and B vectors is 90 degrees so sin(90) = 1

F = ILBsin(90) = I*L*B

F = 2.0A*0.5m*0.75T = 0.75 N

Now we use newton's law:

Fnet = m*a

0.75N/(42/1000 kg) = a = 17.86 m/s^2

. Since it is a constant force, we have constant acceleration and can use constant acceleration formulas.

Now we use:

vf^2 = v0^2 + 2a(x-x0) assuming it begins at rest, v0 = 0 so:

vf = root(2*17.86m/s^2*(8m)) = 16.90 m/s is the answer.

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