A lid-opening apparatus for a dust collector includes a base installed on a lid, a controller connected on the base, a cord defining a first end associated with a conduit and a second end associated with the frame, and a limiting member associated with the cord and between the first end and the second end of the cord. The controller can be rotated to a first position and a second position. While the controller is in the first position, the cord is in a loose condition, a flexible portion of the conduit is stretched, and the lid seals the container. While the controller is in the second position, the cord is in a tight condition, the flexible portion of the conduit shortens, and the lid leaves the container.