A conducting bar with mass m and length L slides over horizontal rails that are

Question

A conducting bar with mass m and length L slides over horizontal rails that are connected to a voltage source. The voltage source maintains a constant current I in the rails and bar, and a constant, uniform, vertical magnetic field B fills the region between the rails (see the figure (Figure 1)

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 = 0.73 T , I = 2200 A , m = 30 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.

Explanation / Answer

We know that electrical force = IBL , where I is the current, B is the magnetic field strength, L is the length of the bar

From 2nd law of motion, F = Ma
=> Ma = IBL, where M is the mass of the bar and a is the acceleration

=> a = IBL/M
From 3rd equation of motion, v2= u2+2as, where v is the final velocity and u is the initial velocity

Here u = 0 and let distance s = D
=> v2 = 2aD
D = v2/2a = v2*M/(2IBL)
D = 112002*30/(2*2200*0.73*0.55)
D = 2130193 m = 2130 km

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