A wheel with a rope running in its groove is part of which simple machine?

A wheel with a rope running in its groove is characteristic of a pulley. A pulley is designed to change the direction of force applied to lift a load, which is achieved by the rope that wraps around the wheel. When you pull down on one end of the rope, the wheel rotates, moving whatever is attached to the other end of the rope upwards.

This mechanism is fundamental in various applications, from simple systems like flag poles to more complex setups in cranes and elevators. The design allows for the mechanical advantage of lifting heavy loads with less effort than would be possible without the use of a pulley.

In contrast, a lever uses a fulcrum to gain a mechanical advantage, an incline refers to a sloped surface facilitating the movement of heavy objects with reduced effort, and gears are rotating wheels with teeth that interlock to transmit torque and change the direction or speed of motion. Each of these simple machines serves its unique purpose but does not incorporate the rope-and-wheel functionality that defines a pulley. Thus, the correct identification of the described setup as a pulley showcases its specific role in simple machine mechanics.