Mathematical and Physical Journal
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Problem P. 4258. (May 2010)

P. 4258. Three rods, among which any two are perpendicular to each other, are placed onto a rough surface and form a pyramid. The vertex of the pyramid supports a weight of Q. What are the forces exerted by the rods, if they have equal lengths, and if they have different lengths? (The weight of the rods is negligible with respect to the weight Q.)

(5 pont)

Deadline expired on June 10, 2010.

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

Megoldás. Belátható, hogy a rudakban ébredő erő a rudak hosszával fordítottan arányos, így például az \(\displaystyle a\), \(\displaystyle b\), \(\displaystyle c\) hosszúságú rudakból összerakott gúla esetén az \(\displaystyle a\) hosszúságú rúdban

\(\displaystyle F_a=\frac{\frac{1}{a}}{\sqrt{\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}}}\,Q\)

erő hat.


22 students sent a solution.
5 points:Benyó Krisztián, Janosov Milán, Lőrincz Dóra, Neumer Tamás, Szatmári András Zoltán, Varju 105 Tamás, Vuchetich Bálint.
4 points:Bodosi Eszter, Galzó Ákos Ferenc, Kungl Ákos Ferenc, Lájer Márton.
3 points:2 students.
2 points:2 students.
1 point:3 students.
0 point:3 students.
Unfair, not evaluated:1 solutions.

Problems in Physics of KöMaL, May 2010