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 10.0g and electrical resistance 0.500ohms rests on parallel horizontal rails that have negligible electric resistance. The rails are a distance = 6.00cm apart. The rails are also connected to a voltage source providing a voltage of = 5.00V .
The rod is placed in a vertical magnetic field. The rod begins to slide when the field reaches the value = 8.17×10-2T . 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 the coefficient of static friction between the rod and the rails.

Explanation / Answer

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 30.0g and electrical resistance 0.200 ohms rests on parallel horizontal rails that have negligible electric resistance. The rails are a distance L = 8.00 cm apart. 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 = 7.35e-2 Assume that the rod has a slightly flattened bottom so that it slides instead of rolling. Use 9.80 m/s for the magnitude of the acceleration due to gravity. 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 = µmg Net force = 0.147 - µmg = 0 when motion just begins. µ = 0.147 / (0.03*9.8) = 0.5

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