Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem P. 5046. (September 2018)

P. 5046. A board of mass $\displaystyle M$ was fixed symmetrically as shown in the figure. The masses of the fixed pulleys and the ropes, as well as friction in the shaft are negligible. (The objects of mass $\displaystyle m$ are not glued to the board of mass $\displaystyle M$.) At what $\displaystyle m/M$ ratio will the system be in equilibrium?

(3 pont)

Deadline expired on October 10, 2018.

Sorry, the solution is available only in Hungarian. Google translation

Megoldás. Ha $\displaystyle \frac{m}{M} \ge \frac12$, a rendszer egyensúlyban van. Ilyenkor a deszka nem tud lesüllyedni, hiszen akkor a rendszer helyzeti energiája növekedne (vagy változatlan maradna). A deszka felemelkedni csak a rajta lévő testekkel együtt tudna, ez pedig ugyancsak a helyzeti energia növekedésével járna, tehát nem valósulhat meg.

### Statistics:

 107 students sent a solution. 3 points: 64 students. 2 points: 33 students. 1 point: 3 students. Unfair, not evaluated: 6 solutionss. Not shown because of missing birth date or parental permission: 1 solutions.

Problems in Physics of KöMaL, September 2018