What moves with the elevator via an attached cable or steel tape?

The movement associated with an elevator system involves various components that work together for its operation. The option referring to synchronous selectors is particularly relevant because these selectors are designed to operate in conjunction with the elevator mechanism and are typically attached to the elevator car via a cable or a steel tape. This setup allows the synchronous selectors to move vertically alongside the elevator, ensuring that the correct floor is selected and the elevator knows its position within the shaft.

Synchronous selectors are crucial in multi-story buildings as they determine the destination floor and communicate that information to the elevator control system. By moving with the elevator, they provide real-time updates on the car's position and facilitate smooth operation as the car travels between floors.

Other options like control signals, braking systems, and power supply, while integral to the elevator's functionality, do not physically move with the elevator car. Control signals can be transmitted wirelessly, braking systems are typically stationary components within the hoistway, and power supply lines are fixed in place as well. Thus, synchronous selectors are the component that uniquely moves with the elevator thanks to their direct attachment, fulfilling a key role in its operation.