Rail guns have been suggested for launching projectiles into space without chemi
ID: 2155338 • Letter: R
Question
Rail guns have been suggested for launching projectiles into space without chemical rockets, and for ground-to-airantimissile weapons of war. A tabletop model rail gun as shown in the figure below, consists of two long parallel horizontal rails2.50 cm apart, bridged by a bar BD of mass 3.00 g. The bar is originally at rest at the midpoint of the rails and is free to slide without friction. When the switch is closed, electric current is very quickly established in the circuit ABCDEA. The rails and bar have low electrical resistance, and the current is limited to a constant30.0 A by the power supply.(a) Find the magnitude of the magnetic field1.25 cm from a single very long, straight wire carrying current 30.0 A.
1 T
(b) Find the vector magnetic field at point C in the diagram, the midpoint of the bar, immediately after the switch is closed. (Hint: Consider what conclusions you can draw from the Biot-Savart law.)
( 2i + 3j + 4k ) T
(c) At other points along the bar BD, the field is in the same direction as at point C, but greater in magnitude.Assume that the average effective magnetic field along BD is five times larger than the field at C. With this assumption, find the vector force on the bar.
( 5i + 6j + 7k ) N
(d) Find the vector acceleration with which the bar starts to move.
( 8i + 9j + 10k ) m/s2
(e) Does the bar move with constant acceleration?
11
yes
no
Explain.
12
(f) Find the velocity of the bar after it has traveled 130 cm tothe end of the rails.
( 13i + 14j + 15k ) m/s
Explanation / Answer
sol: suppose that, velocity of the bar F = ma might help a little bit. Do you know the mass of the bar? F = bil (flux density x current x length of bar) velocity of the bar So then you have the force to find a. Now you have: acceleration (a) displacement (s) original velocity (u) and want final velocity (v) you can use: velocity of the bar v^2 = u^2 + 2as! to give you v! answer
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