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In a pulley-string system (all pulleys and strings ideal), a man of mass m stands on a plank of mass M. The man applies a force F on a string. For the system (man + plank) to remain in equilibrium, which of the following is a necessary condition?
- F = (M + m) * g / 5
- F = M * g / 5
- m >= M / 5
- m < M / 5
Correct answer: F = (M + m) * g / 5
Solution
In the standard pulley system described (man on plank pulling a string that goes over multiple pulleys), with 5 string segments supporting the plank-man system: total tension supporting = 5F. For equilibrium of the man+plank: 5F = (M+m)g, giving F = (M+m)g/5.
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