Momentum and Energy
Are pulleys really simple machines?
A fixed, or unmovable, single pulley can be considered a wheel and axle where both have the same radius. The mechanical advantage is one, but the pulley changes the direction of the force.
If the pulley is allowed to move and the output force is exerted by the axle of the pulley, then the input force is shared by the two ends of the rope. If you fasten one end and pull up on the other, then you achieve a mechanical advantage of two.
A combination of fixed and movable pulleys is called a block and tackle. Archimedes is said to have pulled a fully loaded ship using a block and tackle.
Energy loss in a block and tackle comes from friction between the axle and its holder as well as the stretching of the rope and rolling friction between the rope and pulley.