Mastering Physics Solutions: Rail Gun

Rail Gun

Part A = out of the plane of the figure
Part B = The rod will accelerate but the magnitude of the acceleration will decrease with time; the velocity of the rod will approach but never exceed a certain terminal velocity.
Part C = (V – B * L * vr(t)) * (L * B) / (R * m)
Part D = V / (B * L)

Solution Below:

A conducting rod is free to slide on two parallel rails with negligible friction. At the right end of the rails, a voltage source of strength V in series with a resistor of resistance R makes a closed circuit together with the rails and the rod. The rails and the rod are taken to be perfect conductors. The rails extend to infinity on the left. The arrangement is shown in the figure. Part A

There is a uniform magnetic field of magnitude B, pervading all space, perpendicular to the plane of rod and rails. The rod is released from rest, and it is observed that it accelerates to the left. In what direction does the magnetic field point?

• into the plane of the figure
• out of the plane of the figure

out of the plane of the figure

Part B

Assuming that the rails have no resistance, what is the most accurate qualitative description of the motion of the rod?

• The rod will accelerate but the magnitude of the acceleration will decrease with time; the velocity of the rod will approach but never exceed a certain terminal velocity.
• Under these idealized conditions the rod will experience constant acceleration and the velocity of the rod will increase indefinitely.
• The rod will accelerate indefinitely with acceleration proportional to its (increasing) velocity.

The rod will accelerate but the magnitude of the acceleration will decrease with time; the velocity of the rod will approach but never exceed a certain terminal velocity.

Part C

What is the acceleration ar(t) of the rod? Take m to be the mass of the rod.
Express your answer as a function of V, B, the velocity of the rod vr(t), L, R, and the mass of the rod m.

• The rod will accelerate but the magnitude of the acceleration will decrease with time; the velocity of the rod will approach but never exceed a certain terminal velocity.
• Under these idealized conditions the rod will experience constant acceleration and the velocity of the rod will increase indefinitely.
• The rod will accelerate indefinitely with acceleration proportional to its (increasing) velocity.

(V – B * L * vr(t)) * (L * B) / (R * m)

Part D

What is the terminal velocity vt reached by the rod?

V / (B * L)