A rail gun accelerates a projectile from rest by using the magnetic force on a c

Question

A rail gun accelerates a projectile from rest by using the magnetic force on a current-carrying wire. The wire has radius r = 5.63·10-4 m and is made of copper having a density of ? = 8960 kg/m3. The gun consists of rails of length L = 1.48 m in a constant magnetic field of magnitude B = 2.07 T, oriented perpendicular to the plane defined by the rails. The wire forms an electrical connection across the rails at one end of the rails. When triggered, a current of 1.03·104 A flows through the wire, which accelerates the wire along the rails. Calculate the final speed of the wire as it leaves the rails. (Neglect friction.)

Explanation / Answer

mass of wire = pi R^2 * length of wire * density Force on wire = length of wire * current * B field (note: the first responder made a mistake by confusing length of the rails and length of wire. They are not the same thing.) acceleration of wire = force on wire / mass of wire = = length of wire * I B / pi R^2 * length of wire * density = = I B / pi R^2 * density = 10300 * 2.07 / pi * 0.000563^2 * 8960 = = 2389637 m/s^2 Now using basic kinetmatics: v final squared = 2 * acceleration * distance traveled = = 2 * 2389637 * 1.48 = 7073325 take sq root... final speed = 2660 m/s

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