Question

For a railgun, determine the current required to accelerate a 1000kg space vehicle to earths escape velocity on 10km of track with a magnetic fied of 2T and a rail separation of 2m. Earths escape velocity is 11.2km/s

Answer 1

the current is 15.68 ×
`10^(5)` A

Step-by-step explanation:

mass = 1000 kg

magnetic fied = 2T

rail separation = 2m

escape velocity is 11.2km/s = 11.2 ×
`10^(3)` m/s

distance = 10 km =
`10^(4)` m

to find out

determine the current

solution

we know force F = I×L×B

here I is current and L is rail separation and B is magnetic field

so F = I ×2×2 = 4 I

so

acceleration is a =
`(F)/(mass)`

a =
`(4I)/(1000)` m/s²

so equation of motion

v²-u² = 2 a S

here u is initial velocity and S is distance and a is acceleration and v is final velocity

11.2 ×
`10^(3)` - 0 = 2×
`(4I)/(1000)` ×
`10^(4)`

solve we get I

I = 15.68 ×
`10^(5)` A

so the current is 15.68 ×
`10^(5)` A