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Loaded Sullivan's Perfect Ratchet

Show that in the case of zero external force the equation v=(fL/kT)^2 D/L (e^(fL/kT) - 1 - fL/kT)^-1 reduces to 2D/L. Then show that at high force (but still smaller than (epsilon/L)) the equation reduces to v=(fL/kT)^2 D/L (e^(-fL/kT)).

Solution Preview

Part 1:
v=(fL/kT)^2 D/L (e^(fL/kT) - 1 - fL/kT)^-1
=> v = (fL/kT)^2 (D/L)/ (e^(fL/kT) - 1 - fL/kT)
=> v = (fL/kT)^2 (D/L)/ (1 + (fL/kT) + (fL/kT)^2/2! + ... - 1 - ...

Solution Summary

This solution includes multiple calculations proving the equation reduces.

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