Question

Rail guns have been suggested for launching projectiles into space without chemical rockets. A tabletop model rail gun (see figure below) consists of two long, parallel, horizontal rails (= 3.60 cm apart, bridged by a bar of mass m = 2.75 g that is free to slide without friction. The rails and bar have low electric resistance, and the current is limited to a constant I = 27.0 A by a power supply that is far to the left of the figure, so it has no magnetic effect on the bar. The figure shows the bar at rest at the midpoint of the rails at the moment the current is established. We wish to find the speed with which the bar leaves the rails after being released from the midpoint of the rails. Find the magnitude of the magnetic field at a distance of 1.80 cm from a single long wire carrying a current of 27.0 A. It For purposes of evaluating the magnetic field, model the rails as infinitely long, magnitude direction --- Using the result of part (a), find the magnetic field at the midpoint of the bar. Argue that this value of the field will be the same at all positions of the bar to the right of the midpoint of the rails. At other points along the bar, the field is in the same direction as at the midpoint, but is larger in magnitude. Assume the average effective magnetic field along the bar is five times larger than the field at the midpoint. A V This answer has not been graded yet With this assumption find the magnitude of the force on the bar. N With the assumption find the direction of the force on the bar. Find the velocity of the bar after it has traveled a distance d m/s 110 cm to the end of the rails.

Answer 1

fo I 2ty 44X10 X 27 20x 0,018 3X104T B = 1² x 3x104 T (-2) + 2x3x154 T (-ŷ) 3X10 T direction - y a) B-IX = P7A ( 0.036 m2) * [sx3xio} 1.458X103N = ta m Direction a = EP = 1.458X10N 0.00275kg 0.53 m/s² ug" =v2 + zax ug2 = of 2 x 0.33 X 11 vf direction tx T.08 mis