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Types of Pulley Systems

Compound
Compound

A compound pulley, sometimes referred to as a block-and-tackle system, is a mechanical arrangement of pulleys that permits a trade-off of applied force for distance, according to HowStuffWorks.

source: reference.com
image: etc.usf.edu
Fixed
Fixed

Movable pulleys are useful to raising objects below one's head. Education.com lists a third compound, the multiple pulley, which is comprised of both fixed and movable pulley systems. These pulleys are easiest to lift objects, as the mechanical advantage increases in tandem with the inclusion of more ropes, as cited by TeachEngineering.

source: reference.com
image: pixshark.com
Inclined Plane
Inclined Plane

A box on an inclined plane with a pulley ... What time does it take a box with mass m 1 to go down a distance s on an inclined plane with a slope ... Coordinate system:

Lever
Lever

Massless pulleys act in very much the same way as the massless lever discussed previously. Consider the system shown below. The pulley has two radii, r 1 and r 2. If the pulley moves through an angle θ the distance x 1 is given by r 1 ·θ, and the distance x 2 is given by r 2 ·θ.

Movable
Movable

A movable pulley is a pulley that can freely move. This is only one of three types, the other two being fixed and compound pulleys. Examples of movable pulleys are elevators.

source: reference.com
Pulley
Pulley

The drive element of a pulley system can be a rope, cable, belt, or chain. Hero of Alexandria identified the pulley as one of six simple machines used to lift weights. Pulleys are assembled to form a block and tackle in order to provide mechanical advantage to apply large forces.

Screw
Screw

A rope and pulley system—that is, a block and tackle—is characterised by the use of a single continuous rope to transmit a tension force around one or more pulleys to lift or move a load—the rope may be a light line or a strong cable.

Wedge
Wedge

Also could you check if this is a correct argument: We have the system wedge+m1+m2. The only external force acting on this system is the frictional force, which must be $\mu(M+m_1+m_2)g$ at the point of slip.

Wheel and Axle
Wheel and Axle

A pulley is a wheel held in a frame but allowed to turn freely. The outside of the pulley is grooved, and a rope wrapped around the pulley causes the pulley to turn when the rope is pulled.

image: chegg.com