What device uses the force of the cow trying to walk through it to open, close, and latch the gate?

Answer : Headgates.

Explanation : Headgates are a kind of gate which allows the movement of cow with their force to open or close the gate and also latch the gate. It is most widely used for catching cattle. It allows the cow's head to pass through but blocks it's shoulders. This position allows us to utilize the cattle as they have easy access to work in the chute.