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 0.300 Ohm rests on parallel horizontal rails that have negligible electric resistance. The rails are a distance L = 10.0 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 = 8.82 times 10^-2 T. Assume that the rod has a slightly flattened bottom so that it slides instead of rolling. Use 9.80 m/s^2 for the magnitude of the acceleration due to gravity. Find mu_s, the coefficient of static friction between the rod and the rails. Give your answer numerically.

Explanation / Answer

Current i = V/R = 5/0.300 = 16.67 A

Magnetic force Fb =iLB =16.67*0.10*8.82e-2

= 0.147 N

Static friction = magnetic force in order to balance forces,

umg = 0.147

u = 0.147/mg = 0.147/(0.030*9.8)

= 0.5 answer

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