A rail gun uses electromagnetic forces to accelerate a proje

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 = 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 = 0.218 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. Find the coefficient of static friction between the rod and the rails

Solution

I = V / R = 5.00 / 0.400 = 12.5 A

Length = 9 cm = 0.09 m , B = 0.218 T

Force acting on the rod = I L B = 12.5 * 0.09 * 0.218 = 0.245 N

Frictional force = mu m g

Net force = 0.245 - mu m g = 0

mu = 0.245 / (50 * 10^-3 * 9.8)

mu = 0.500