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 0.85 m?resistance and a mass of 4.4 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 5.0 cm ?

Explanation / Answer

given that

V = 1.2 V

R = 0.85 mohm

B = 0.80 T

L = 15 cm = 0.15 m

m = 4.4 g

from ohm's law

i = V/R = 1.2/.85*10^(-3)

i = 1.41*10^3 A

we know that

F = B*i*L

F = 0.80 * 1.41*10^3 * 0.15 = 169.2 N

we also know that

F = m*a

a = F/m = 169.2 / 4.4*10^(-3)

a = 38454.54 m/s^2

from neuton's equation of motion

v^2 =u^2 + 2*a*x        ( u = 0)

given

x = 5 cm = 0.05 m

v = sqrt (2*a*x)

v = sqrt ( 2 * 38454.54*.05)

v = 62.01 m/s

answer

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