Magnetic forces can be used to accelerate projectiles to very high speeds in a so-called railgun. In the simplified version shown below, a voltage source drives current down two parallel ideal wires to a section of metal in contact with both wires. The metal has a resistance 0.6 mΩmΩ and weights 6 grams. We assume that the contacts between the wires and the section of metal are friction-less and that the metal can slide along the wires for a total distance of 1 m before exiting the railgun as a projectile. Our goal is to calculate what voltage that will cause the metal projectile to leave the railgun at the speed of sound (343 m/s), assuming it starts from rest. First, what constant force (in N) will accelerate the rod to the speed of sound in 1 m? Give your answer to 3 significant digits. Next, which voltage V will generate the necessary current to create this constant force? Give your answer to 3 significant digits.
Magnetic forces can be used to accelerate projectiles to very high speeds in a so-called railgun. In the simplified version shown below, a voltage source drives current down two parallel ideal wires to a section of metal in contact with both wires. The metal has a resistance 0.6 mΩmΩ and weights 6 grams. We assume that the contacts between the wires and the section of metal are friction-less and that the metal can slide along the wires for a total distance of 1 m before exiting the railgun as a projectile. Our goal is to calculate what voltage that will cause the metal projectile to leave the railgun at the speed of sound (343 m/s), assuming it starts from rest.
First, what constant force (in N) will accelerate the rod to the speed of sound in 1 m? Give your answer to 3 significant digits.
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