# Pulley Constrained Motion of Blocks

Pulley constrained motion is the most common constrained motion from where we start developing understanding of constrained motion. Thorough understanding of Pulley Constrained Motion helps in solving variety of problems in the topic of Laws of Motion.

There are two ways to solve the problems of Pulley Constrained Motion –

(i) By observation on in-extensible strings of constant lengths and

(ii) By method of Virtual Work

Lets discuss both methods –

(i) By observation on in-extensible strings of constant lengths

In this method by moving any one block of system we carefully observe how the length of string is being shifted from one side of pulley to other side and analyze the motion of movable pulley as well. In case of a moving pulley, it pulls double the length of string from either side whereas in case of a fixed pulley change in length in string on one side is compensated by change in length of string on its other side.

For better understanding see the video – https://youtu.be/EL1QT4WcgY4

Some examples on this are –

https://youtu.be/y5eOVaxB0VY

https://youtu.be/nfntGyGJQJE

https://youtu.be/C4vqyC4ThtA

(ii) By Method of Virtual Work

In this method we consider total work done by ideal string to be zero in displacement of blocks of system. As we know ideal string is massless and massless passive bodies can never gain or supply energy so total work done by all strings of system on all the blocks of system must be equal to zero.

To analyze the same we consider different displacements of the blocks and calculate work done by strings on blocks by taking scalar product of string tension to the displacement of the block and equate total work to zero. This equation gives us the relation of displacements of all the blocks of the system which in turn gives us the relation in velocity and accelerations.

All the above examples can be solved also by using this method of virtual work also.

To understand advance Illustrations on the above concept, see these videos –

https://youtu.be/ObO1txjTAN0

https://youtu.be/lsHXK8nlLBs

https://youtu.be/fmWhJN_hlz4

https://youtu.be/xtdMoETZP8A