The Electromagnetic Brake Train · AI Generator #GEN-79C6C929

Physics · electromagnetism

Problem

A prototype train uses electromagnetic braking by deploying copper fins that slide between pairs of permanent magnets. Each fin is a rectangular conductor with dimensions L=2.0  mL = 2.0\;\text{m} (length), w=0.50  mw = 0.50\;\text{m} (width), and thickness t=8.0  mmt = 8.0\;\text{mm}. The fin moves through a uniform magnetic field B=0.40  TB = 0.40\;\text{T} that is perpendicular to the fin's motion and parallel to its width. The copper has resistivity ρ=1.7×10−8  Ω⋅m\rho = 1.7 \times 10^{-8}\;\Omega\cdot\text{m}. When the train enters the braking zone at speed v0=25  m/sv_0 = 25\;\text{m/s}, the total mass being braked is m=8.0×104  kgm = 8.0 \times 10^4\;\text{kg} and there are N=12N = 12 identical fins deployed. Find the speed of the train when it has traveled a distance d=150  md = 150\;\text{m} through the braking zone.

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