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 30.0 g and electrical resistance 0.400 ? rests on parallel horizontal rails that have negligible electric resistance. The rails are a distance L = 9.00 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 = 0.131 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.

Find ?s , the coefficient of static friction between the rod and the rails.

Explanation / Answer

  Current I in the rod = V/R = 5/0.4 = 12.5A
Length through which B crosses = 0.09 m
Magnetic field B =.131T

Force acting on the rod = ILB = 12.5*0.09*.131 = 0.147 N

Frictional force = mg
Net force = 0.147 - mg = 0 when motion just begins.

= 0.147 / (0.03*9.8) = 0.5

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