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 50.0 g and electrical resistance 0.400 ? rests on parallel horizontal rails that have negligible electric resistance. The rails are a distance L = 5.00 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 = 0.392 T . Assume that the rod has a slightly flattened bottom so that it slides instead of rolling. Use 9.80 m/s2for the magnitude of the acceleration due to gravity.

Give your answer numerically.

Explanation / Answer

Given,

Current I in the rod = V/R = 5/0.4 = 12.5 A

Length through which B crosses = 0.05 m

Magnetic field B = 0.392 T

Force acting on the rod = ILB = 12.5*0.05*0.392 = 0.245 N

Frictional force = ?mg

Net force = 0.245 - ?mg = 0 when motion just begins

? = 0.245 / (0.05*9.8) = 0.5

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