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 50.0g and electrical resistance 0.500? rests on parallel horizontal rails that have negligible electric resistance. The rails are a distance L = 8.00cm 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 = 0.306T . Assume that the rod has a slightly flattened bottom so that it slides instead of rolling. Use 9.80m/s2for the magnitude of the acceleration due to gravity.

Explanation / Answer

force F = B*I*L

I = V/R

F = B*L*V/R

F = 0.306*5*.08/0.5 = 0.2448 N

F = friction = u*N

0.2448 = u*mg

0.2448 = u*50x10^-3*9.8

u = 0.499

u = 0.5

coefficient of friction u = 0.5

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