{"id":775,"date":"2024-07-17T06:09:15","date_gmt":"2024-07-17T06:09:15","guid":{"rendered":"https:\/\/www.meniit.com\/study-material\/?p=775"},"modified":"2024-10-04T05:08:15","modified_gmt":"2024-10-04T05:08:15","slug":"pulley-block-system","status":"publish","type":"post","link":"https:\/\/www.meniit.com\/study-material\/jee\/class-xith\/11th-physics\/pulley-block-system","title":{"rendered":"Pulley Block System"},"content":{"rendered":"

Single Fixed Pulley<\/h2>\n

It is a wheel like structure, generally disc or cylinder used for producing desired direction of motion.<\/p>\n

\"\"<\/p>\n

Assumption for ideal pulley\u2013<\/strong> It is smooth (frictionless) and massless.<\/p>\n

If the pulley is fixed and two ends of the rope are free to move.<\/strong><\/p>\n

If the mass m2<\/sub> goes down by a distance x, then the mass m1 will rise upward by the same distance.<\/p>\n

Hence velocity, v = dx \/ dt is same in magnitude for both blocks, but their directions are opposite<\/p>\n

and acceleration a = dv \/ dt is same in magnitude for both blocks, but opposite in directions.<\/p>\n

\"Assumption-for-ideal-pulley\"<\/p>\n

Kinematic constraints are equations that relate the motion of two or more bodies. By differentiating the kinematic constraints for the position of the particle in a system, the corresponding kinematic constraints among the velocities and accelerations of the particles may be obtained.<\/p>\n

\"ceiling<\/p>\n

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Example : <\/strong><\/h4>\n

Two blocks of masses m1<\/sub> and m2<\/sub> are connected to each other by a light, inextensible string that passes over a light, smooth pulley fixed to the ceiling (see figure). Find the acceleration of each block and the force exerted on the ceiling, by the arrangement.
\n\"SingleIf m1<\/sub> goes down by a distance x, m2<\/sub> moves up by a distance x. If the acceleration of m1<\/sub> is a downwards, the acceleration of m2<\/sub> is a upwards. As the string is light and pulley is smooth, the tensions in the two parts of the string are equal, Let it be T. Now draw the free body diagram of the blocks and the pulley.
\n\"solution\"<\/p>\n<\/div>\n

\n

Example : <\/strong><\/h4>\n

A light rope is passed over a pulley such that at its one end a block is attached, and on the other end a boy is climbing up with acceleration g\/2 relative to rope. Mass of the block is 30 kg and that of the boy is 40 kg. Find the tension and acceleration of the rope.
\n\"solution\"
\n\"solution\"<\/p>\n<\/div>\n

\n

Example : <\/strong><\/h4>\n

Two blocks of masses m1<\/sub> and m2<\/sub> are connected by a light inextensible string and pulled up by external force F on inclined plane having inclination angle \u03b8. Then find acceleration of block and tension in the string.
\n\"question\"<\/p>\n

Solution : <\/strong><\/h4>\n

\"solution\"<\/p>\n<\/div>\n

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