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 0.400 Ω rests on parallel horizontal rails that have negligible electric resistance. The rails are a distance L= 5.00 cm apart. (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 = 0.392 T . Assume that the rod has a slightly flattened bottom so that it slides instead of rolling. Use 9.80 m/s2for the magnitude of the acceleration due to gravity.

Answer 1

Find \(\mu_{z}\), the coefficient of static friction between the rod and the rails? Current carrying conductor experiences a magnetic force in horizontal direction as \(\mathrm{B}\) is in z-direction and current flow is in y-direction. Conductor slides when B becomes \(0.392 \mathrm{~T}\). This should be equal to frictional force. Hence, we should have \(\mu_{z} m g=B I L\)

$$ \begin{array}{l} \Rightarrow \mu_{i}=\frac{B \times \frac{V}{R} \times L}{m g} \\ =\frac{(0.392)\left(\frac{5}{0.400}\right)(0.05)}{\frac{50}{1000} \times 9.8} \\ =0.5 \end{array} $$