Question

Rail guns can accelerate an object by using the magnetic force on a current carrying device. A rail gun is constructed to accelerate a length of copper wire, having a radius of 5.1 x 10-4 m and density,  = 8960 kg/m3. The rails have a length L = 1.0 m and are in a constant magnetic field B = 2.0 T, oriented perpendicularly to the plane defined by the rails. The wire forms an electrical connection across the rails at one end of the rails. The wire starts from rest at this end of the rails, and when triggered, a current of 10 KA flows through the wire. Calculate the speed of the wire as it leaves the rail. {2.34 km/s}

Answer 1

v = 2.33 103 m / s

Step-by-step explanation:

The magnetic force is

F = q v x B = i L X B

Where L is wire length and B the magnetic field

Let's calculate the value of the force

F = i L B

Now we can calculate the acceleration using Newton's second law

F = m a

a = F / m

Density is

ρ = m / V

V = π r² L

ρ = m / π r² L

m = ρ π r² L

a = I L B / (ρ π r² L)

a = 10 10³ 2.0 / (8960 π (5.1 10⁻⁴)²)

a = 2.73 10⁶ m/s²

Having the acceleration we use the kinematic equation

v² = v₀² + 2 a x

v = √ 2 ax

v = √ (2 2,723 10⁶ 1.0)

v = 2.33 103 m / s