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

Answer:

the current is 15.68 × $10^{5}$ A

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 = $\frac{F}{mass}$

a =  $\frac{4I}{1000}$ 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×  $\frac{4I}{1000}$ × $10^{4}$

solve we get I

I = 15.68 × $10^{5}$ A

so the current is 15.68 × $10^{5}$ A