When the atp synthase molecules are open, the hydrogen ions move out of the thylakoid. how does the cell use the kinetic energy of the moving ions?

The synthesis of ATP is based on energy conversion, via conformational changes of the subunits.

A proton gradient on either side of the membrane into which the ATP synthases are inserted is necessary for their operation, which implies that the synthesis of ATP can not be done independently of a membrane. Within the mitochondrial inner membrane, it is the respiratory chain that provides the pH gradient by injecting protons into the intermembrane space during the transfer of electrons from one complex to another. At the level of the thylakoid membrane, it is the photosynthetic chain that injects protons into the lumen.