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 m and electrical resistance R rests on parallel horizontal rails (that have negligible electric resistance), which are a distance L apart. (Figure 1^The rails are also connected to a voltage source V so a current loop is formed. The rod begins to move if the externally applied vertical magnetic field in which the rod is located reaches the value B Assume that the rod has a slightly flattened bottom so that it slides instead of rolling. Use g for the magnitude of the acceleration due to gravity. Find pi_s. the coefficient of static friction between the rod and the rails. Express the coefficient of static friction in terms of variables given in the introduction.

Explanation / Answer

Current I in the rod = V/R
Length through which B crosses = L
Force acting on the rod = ILB = VLB/R

Frictional force = mg
Net force = VLB/R - smg = 0 when motion just begins.
=> s = VLB/Rmg (Answer)

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