Engineers at Indian Institute of Technology Kanpur are designing a precision counterweight system for high-speed elevators. The system uses a movable pulley connected to a fixed support, allowing smoother acceleration and reduced motor load.
A mass is attached to a movable pulley, and the string passes over a fixed support. Engineers must determine the acceleration of the mass using constraint relations.
This system is widely used in elevators, cranes, and lifting mechanisms.
A mass m is suspended using a movable pulley system such that the pulley is supported by two segments of the same string.
Assumptions:
- String is massless
- Pulley is frictionless
- Gravity acts downward with acceleration g
Find the acceleration of the mass.
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