Kvant Math Problem 1458
I cannot produce a correct solution to M1458 from the text alone, because the problem explicitly depends on the geometry of the pulley arrangement shown in the figure.
Verified: no
Verdicts: SKIP + SKIP
Solve time: 2m05s
Source on kvant.digital
Problem
M1458. In the system shown in the figure, the strings are inextensible, and the masses of the pulleys and strings are negligible. Find the accelerations of the movable pulleys. Also find the acceleration of the knot $A$ tied on the string. The pulley sizes are chosen so that the free segments of the strings are vertical. A. Elberman.
I cannot produce a correct solution to M1458 from the text alone, because the problem explicitly depends on the geometry of the pulley arrangement shown in the figure.
The accelerations of the movable pulleys and of the knot $A$ are determined by the string-constraint equations, and those equations depend on:
$$\text{which pulley each string passes around,}$$
$$\text{where the ends of the strings are attached,}$$
and
$$\text{which string contains the knot } A.$$
Without the diagram, there are many different pulley systems consistent with the verbal description, and they lead to different answers.
Please upload the figure from the Kvant problem M1458 (or a scan of the page containing the diagram). Once the figure is available, I will provide the complete solution in the exact six-section format you requested.