A device called a railgun uses the magnetic force on currents to launch projecti

Question

A device called a railgun uses the magnetic force on currents to launch projectiles at very high speeds. An idealized model of a railgun is illustrated in (Figure 1). A 1.2 V power supply is connected to two conducting rails. A segment of copper wire, in a region of uniform magnetic field, slides freely on the rails. The wire has a 0.92 m ohm resistance and a mass of 5.6 g Ignore the resistance of the rails. The power supply is switched on. What will be the wire's speed after it has slid a distance of 7.0 cm? Express your answer with the appropriate units.

Explanation / Answer

A)Current, I =V/R =1.2/(0.92*10-3) A

Force on the wire, F = IBLsin90o = 1.2*0.8*0.15/(0.92*10-3) N = 157 N

B) Acceleration of the wire, a=F/m = 157/(5.6*10-3) m/s2 = 28035.7 m/s2

Let v be the speed of the wire after sliding a distance of 7 cm,

Using,    v2 - u2 = 2as

we have,     v2 - 0 =2*28035.7*0.07

or   v = 62.65 m/s

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