Question

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Railgun weapons are not only popular in video games, they are actually being developed by the Navy for practical use. The figure below shows a simple model of how a railgun works. The entirety of the railgun is Immersed in a magnetic held of strength = 0.67 Tesi, With the switch open, the capacitor on the left is charged to a very high voltage V5500 volts. When the switch is dosed current will now through the bar and thereby exert a magnetic force on the bar pushing it to the right. The bar has a mass M-1,62 ko, a resistance R0.119 , and a length - 0.356 meters. We shall me that the rails have zero resistance, and that the bar slides without friction. The bar exits the rail gun after having accelerated over a distance of d - 3.05 meters Immersed in a Magnetic field MaM Resistance Length Switch D Calculate the current flowing through the bar when the switch is closed / Amps Calculate the force on the bar de to the magnetic Newtons Calculate the acceleration of the bara Assuming the bar experiences constant acceleration, find the velocity of the when it leaves the row)

Answer 1

When switch is closed, the voltage across the bar is same as that of the fully charged capacitor on left, which will send a current through the bar, given by,

I = V_o/R = (8500/0.119) A

= 71428.57 A

Force on the bar due to the magnetic field,

F = ILB = (71428.57*0.356*0.67) N

= 17037.14 N

Acceleration of the bar, a = F/M

= (17037.14/1.62) m/s²

= 10516.75 m/s²

Using, v² - u² = 2as, where, u = 0, s = d = 3.05 m, a = 10516.75 m/s², we have,

v² - 0² = 2*10516.75*3.05

Or, v = (64152.175)^1/2 = 253.28

Thus, velocity of the bar on leaving the rails will be, v = 253.28 m/s