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 the figure. 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 0.78mΩ resistance and a mass of 5.6g. Ignore the resistance of the rails.

(Figure 1)

What is the magnitude of the force on the wire?
-180 N

What will be the wire's speed after it has slid a distance of 6.5cm? 

Answer 1

The current is

             I = V/R

               = (1.2 V)/(0.78 x 10^-3 ?)

               = 1538.46 A

b) right

c) The magnitude of the force on the wire is

             F = BIL

                =(0.80 T)(1538.46 A)(0.15 m)

                = 184.6152 N

d) The acceleration of rod is

                a = F/m

                  = ( 184.6152 N)/(5.4 x 10^-3 kg)

                  =34187 m/s2

The speed of the rod is

        v = [u^2 + 2as]^1/2

           = (2(34188 m/s2 )(0.06 m))^1/2

             =64.05 m/s