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A pulley is a part of a convenient arrangement that makes it possible to transfer force with change of direction. Unless otherwise stated, a pulley is considered to have negligible mass and friction. This is a relative approximation with respect to mass and friction involved with other elements. Pulleys are used in different combination with other elements – almost always with strings and blocks.
It is relatively difficult to fetch a bucket of water from a well with a “string” as compared to a “pulley and string” system. The basic consideration in making useful mechanical arrangements are two folds (i) improve the convenience of applying force and (ii) reduce the magnitude of force. The example of fetching of a bucket of water with “pulley and string” achieves the goal of improving convenience as we find it easier applying force in the level of arms horizontally rather than applying force vertically.
Had it been possible to reduce force for doing a mechanical activity, then that would have been wonder and of course against the well founded tenets of physical laws. What is meant here by reducing force is that we can fulfill a task (which comprises of force and motion) by reducing force at the expense of extending motion.
The important characterizing aspects of pulley are discussed in the sections named :
The pulley is fixed to a frame. In this situation, we are only concerned with the accelerations of the bodies connected to the string that passes over the pulley. Since string is a single piece inextensible element, the accelerations of the bodies attached to it are same.
We are at liberty to choose the direction of acceleration of the blocks attached to the pulley. A wrong choice will be revealed by the sign of acceleration that we get after solving equations. However, it is a straight forward choice here as it is obvious that the bigger mass will pull the blocks - string system down.
Problem : Two blocks of masses 10 kg and 20 kg are connected by a string that passes over a pulley as shown in the figure. Neglecting friction between surfaces, find acceleration of the blocks and tension in the string (consider ).
Static pulley system
Solution : The blocks are connected by a taut string. Hence, their accelerations are same. Let us assume directions of accelerations as shown in the figure. Also, let the magnitude of accelerations be “a”.
Static pulley system
The external forces are (i) weight of block, 10g, and (ii) tension, T, in the string.
Free body diagram
The external forces are (i) weight of block, 20g, and (ii) tension, T, in the string.
Free body diagram
From two equations, we have :
Putting value of "a" in either of above two equations, we determine tension as :
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