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 40.0 g and electrical resistance 0.300 rests on parallel horizontal rails that have negligible electric resistance. The rails are a distance L = 10.0 cmapart. (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 = 0.118 T . Assume that the rod has a slightly flattened bottom so that it slides instead of rolling. Use 9.80 m/s2 for the magnitude of the acceleration due to gravity.

A.) Find s, the coefficient of static friction between the rod and the rails.

Give your answer numerically.

Explanation / Answer

We can find the force on the conducting rail, due to the current and magnetic field.

Only the magnetic field will be responsible for this force (not electric field).

So we have F = q*v x B, where Force, v and B are vectors. We can rewrite q*v as I*L, where I is electric current, and L is length.

Find the current = Voltage/resistance = (5 V) / (0.3 ) = 16.67 A. Change length to SI units of 0.10 m, then we have I*L = q*v = (16.67 * 0.10) = 1.667 Coulomb*m/s. Multiply this by the magnetic field 0.118 Tesla and it gives the force as 0.196706 Newton. This is the force just enough to overcome the friction.

Static Friction = (Normal Force)(static coefficient). In our case, the Normal Force is the weight = (0.04 kg)(9.80 m/s^2) = 0.392 Newton

So,

Static coefficient = static friction/normal force = 0.196706/0.392 = 0.5018 (ans)

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