Assume that a rail gun accelerates a projectile from rest by using the magnetic

Question

Assume that a rail gun accelerates a projectile from rest by using the magnetic force on a current-carrying wire. The wire has radius r = 5.10 times 10^-4 m and is made of copper having a density of rho = 8960kg/m^3. The gun consists of rails of length d = 1.48 m in a constant magnetic field of magnitude B = 2.07 T, oriented perpendicular to the plane defined by the rails (out of plane). The wire forms an electrical connection across the rails at one end of the rails. When triggered, a current I = 1 times 10^4 A flows through the wire of length L = 30 cm, which accelerates the wire along the rails. a) Show the directions of the current and the B-field on the free-body diagram. b) Calculate the final speed of the wire as it leaves the rails. (Neglect friction.)

Explanation / Answer

Given,

Length of wire, l = 30 cm

Magnetic field, B = 2.07 T

Radius of wire, r = 5.10 x 10-4 m

Length of rail, d = 1.48 m

Current, I = 104 A

Mass of wire, m = x r2 x l x

Force on wire, F = l x current(I) x B

Acceleration of wire, a = force on wire / mass of wire

= (length (l) x current (I) x B) / ( x r2 x l x )

= I B / ( x r2 x )= (10000 x 2.07) / (3.14 x (5.10 x 10-4)2 x 8960

Acceleration, a = 28273014.17 m/s2

Now using basic kinetmatics:

v2 = 2 x acceleration x distance traveled = 2 x 28273014.17 x 1.48 = 8368812.195

Therefore, final speed, v = 2892.89 m/s

(Please rate my answer if you find it helpful, good luck....)

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