After core collapse, the cluster continue to evolve because hard binaries harden as they interact with field stars. For these strong encounters, the field star must pass within the orbital radius of the binary, and it is eventually ejected from the binary at a velocity comparable to the binary orbital velocity, v $($Gm$/$a$)1/2.$ Use this fact to argue that the heating rate from a single binary $($i$.$e$.,$ the rate at which the binary injects kinetic energy into the cluster$)$ is