A movable (compound) pulley is constructed by looping a single
PHYSICS · Multi-part · CBSE · Physics · Laws of Motion · Laws of Motion
Problem
A movable (compound) pulley is constructed by looping a single, lightweight, inextensible string around two small, frictionless pulleys—one fixed to the ceiling and one attached to a 12kg crate that can move vertically. One end of the string is anchored to the ceiling directly above the fixed pulley, while the other end is pulled downward by a worker who can exert an upward force of at most Fmax=90N on the free end of the string.
Assume the string segments remain taut, the pulleys and string have negligible mass, and air resistance is negligible.
(a) Draw separate free-body diagrams for (i) the crate with the pulley attached to it and (ii) the movable pulley itself. Label all forces clearly.
(b) Using Newton’s laws, derive the minimum magnitude of the upward acceleration the worker can give the crate when pulling with the maximum force Fmax. Express your result symbolically in terms of Fmax, the crate mass M, and g before substituting numbers.
(c) Calculate the numerical value of the acceleration found in part (b) for M=12kg and g=9.8ms−2. State clearly whether the crate accelerates upward or downward under this maximum pull.
(d) For the acceleration obtained in part (c), determine the tension in each segment of the string supporting the movable pulley and verify that the worker’s pull and the two supporting tensions satisfy Newton’s third law at the point where the string is anchored to the ceiling.