A rail gun uses electromagnetic forces to accelerate a projectile to very high v

Question

A rail gun uses electromagnetic forces to accelerate a projectile to very high velocities. The basic mechanism of acceleration is relatively simple and can be illustrated in the following example. A metal rod of mass 40.0 g and electrical resistance 0.500 ? rests on parallel horizontal rails that have negligible electric resistance. The rails are a distance L = 7.00 cm apart. (Figure 1) The rails are also connected to a voltage source providing a voltage of V = 5.00 V . The rod is placed in a vertical magnetic field. The rod begins to slide when the field reaches the value B = 0.280 T . Assume that the rod has a slightly flattened bottom so that it slides instead of rolling. Use 9.80 m/s2 for the magnitude of the acceleration due to gravity.

Explanation / Answer

Find the Current I in the rod

I = V/R = 5 / 0.5 = 10 A

Length through which B crosses = 7 cm = 0.07 m

Magnetic field B = 0.280 T

Now, find the force acting on the rod

F = ILB = ( 10 A ) ( 0.07 m ) ( 0.280 T ) = 0.196 N

Expression for the frictional force:

Fr= mg

Thus, the net force =0.49 N - mg

At the time the motion is just begin, F_net = 0

0.196 N - mg =0

= 0.196 / (0.04*9.8) = 0.5

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