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We use 2.0 Msec of Chandra observations to investigate the cocoon shocks of Cygnus A and some implications for its lobes and jet. Measured shock Mach numbers vary in the range 1.18–1.66 around the cocoon. We estimate a total outburst energy of , with an age of . The average postshock pressure is found to be , which agrees with the average pressure of the thin rim of compressed gas between the radio lobes and shocks, as determined from X-ray spectra. However, average rim pressures are found to be lower in the western lobe than in the eastern lobe by ≃20%. Pressure estimates for hotspots A and D from synchrotron self-Compton models imply that each jet exerts a ram pressure ≳3 times its static pressure, consistent with the positions of the hotspots moving about on the cocoon shock over time. A steady, one-dimensional flow model is used to estimate jet properties, finding mildly relativistic flow speeds within the allowed parameter range. Models in which the jet carries a negligible flux of rest mass are consistent with the observed properties of the jets and hotspots. This favors the jets being light, implying that the kinetic power and momentum flux are carried primarily by the internal energy of the jet plasma rather than by its rest mass. [ABSTRACT FROM AUTHOR]