What device converts high-speed operations of the hydraulic system to low-speed operations of the capstan?

The gearbox is a critical component in converting high-speed operations of a hydraulic system to low-speed operations suitable for a capstan. In hydraulic systems, the pump operates at high speeds to generate hydraulic pressure. However, capstans, used for tasks such as hoisting or pulling, require a slower and more controlled rotational speed to function effectively and safely.

A gearbox achieves this by using a combination of gears to reduce the speed of the input from the hydraulic system while increasing torque, which is essential for the capstan's operations. This mechanical advantage allows the capstan to perform its intended function without the risks associated with operating at the high speeds of the hydraulic components.

The other choices do not serve this specific purpose. A clutch is designed to engage and disengage power transmission but does not necessarily change speeds. A motor might be involved in the system but would typically work in conjunction with a gearbox to achieve the necessary speed adjustments. The capstan itself primarily serves as the output device, where work is done, rather than a converting component. Thus, the gearbox is the appropriate answer to this question.