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 20.0g and electrical resistance 0.100 ohms rests on parallel horizontal rails that have negligible electric resistance. The rails are a distance L = 5.00cm apart. (Figure 1) The rails are also connected to a voltage source providing a voltage of V = 5.00V . The rod is placed in a vertical magnetic field. The rod begins to slide when the field reaches the value B = 3.92X10^-2 T . Assume that the rod has a slightly flattened bottom so that it slides instead of rolling. Use 9.80m/s^2 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 = 5/0.2 = 25 A
Length through which B crosses = 0.08 m
Magnetic field B = 7.35e-2 (No unit is given)

Force acting on the rod = ILB = 25*0.08*7.35e-2 = 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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