Question

It has been suggested that rail guns based on this principle could accelerate payloads into earth orbit or beyond. Find the distance the bar must travel along the rails if it is to reach the escape speed for the earth (11.2 km/s).
Let B = 0.86 T , I = 2300 A , m = 20 kg , and L = 55 cm . For simplicity, assume the net force on the object is equal to the magnetic force, as in parts A and B, even though gravity plays an important role in an actual launch into space.
Express your answer using two significant figures.

Answer 1

Answer:

The distance of the bar D = 1153 km

Explanation:

The electric force is the one that takes place between electric charges.

The electric force with which two point charges are attracted or repelled at rest is directly proportional to their product, inversely proportional to the square of the distance that separates them and acts in the direction of the line that joins them.

Recall that:

Electrical force(F) = I*B*L

where;

I = the current,

B = the magnetic field strength,

L = the length of the bar

However;

From the second equation of motion,

F = Ma

Since; (F) = I*B*L

Then,

Ma = IBL,

where;

M is the mass;

a is the acceleration

Making the acceleration (a) the subject of the formula, we have

a = IBL/M

Similarly;

From the third equation of motion;

v^2= u^2+2as,

where v and u are the final velocity and the initial velocity respectively

Here u = 0

Also; let distance s = D

Then

v^2 = 2aD

where;

a = IBL/M

Making the distance D  the subject of the formula, we get:

D = v^2/2a = v2*M/(2IBL)

D = 11200² × 20/(2×2300×0.86×0.55)

D = 1153047.155 m

D = 1153 km