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 50.0 g and electrical resistance 0.200 O rests on parallel horizontal rails that have negligible electric resistance. The rails are a distance = 6.00 apart. The rails are also connected to a voltage source providing a voltage of = 5.00. 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 0.200 O rests on parallel horizontal rails that have negligible electric resistance. The rails are a distance = 6.00 apart. The rails are also connected to a voltage source providing a voltage of = 5.00. The rod is placed in a vertical magnetic field. The rod begins to slide when the field reaches the value B = 0.163 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.

Explanation / Answer

Force on a current carryingconductor in magnetic field F = B*I*L*sin? B = Magneticfield = 0.163T I = Current = V/ R = 5 /0.2 = 25 A L = Lengthof rod = 6 cm = 0.06 m ? = Anglebetween B andL = 90 degree When the rod just startssliding, the force due to magntic field is has just overcomefrictional force. Force offriction = B*I*L*sin? µ*m*g = B*I*L*sin? µ = 0.163* 25 * 0.06 * sin 90 / (50 * 10-3* 9.8) µ = 0.49 Coefficient of friction µ = 0.49

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