[math-fun] More high school physics: the railgun revealed
FYI -- High school physics teachers: sharpen your #2 pencils! Data: 32' barrel 4500 mph exit velocity 25# projectile 25 Mwatts power plant 125 mile range 10x per minute Q: What is the average acceleration? Q: What is the kinetic energy on exit? Q: At a rate of 1 shot per every six seconds, what is the minimum average power of the power supply required? Q: If the power plant is 25 Mwatts, what is the power efficiency? Q: (Extra credit/calculus) If the projectile is a pure iron cylinder of minimum surface area, what are its dimensions? Q: (Extra credit/calculus) What is the magnetic strength required to accelerate such an object (as above) ? Q: (Extra credit/calculus) If there is a loop of superconducting wire around every inch along the rail, how much energy is in the pulse in the *last* loop prior to exit? Q: What is the range of this railgun on Earth, assuming no air resistance, but taking into account the curvature of the Earth? Q: Given air resistance, do you think that the 125 mile range is credible? Does this range require atmospheric "skipping" on re-entry? Q: What angular accuracy is required on the firing platform in order to hit an ordinary target -- e.g., a semi-trailer truck -- at a 100 mile range? How light would atmospheric wind have to be in order to NOT divert the projectile >100' from the target? How far from the target would the gravitational force of a 5000' mountain at the 50 mile point divert this projectile? Does anyone have such superprecise gravitational data for more than a negligible fraction of the Earth's surface that would enable such a gun to get within a mile of its target? Q: (extra extra credit) How enriched would uranium have to be in order for such a 25# projectile of metallic uranium to become critical on impact? http://www.wsj.com/articles/a-first-look-at-americas-supergun-1464359194
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Henry Baker