 Mathematical and Physical Journal
for High Schools
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# Problem P. 4772. (November 2015)

P. 4772. A negligible mass and homogeneous spring spring of spring constant $\displaystyle D$ and of length $\displaystyle L$ is cut into $\displaystyle n$ pieces. The small pieces of the spring are alternately attached to bodies of mass $\displaystyle m$ each, thus creating a chain (at its end there is a body of mass $\displaystyle m$). Then the chain is hung.

$\displaystyle a)$ How should the spring be cut, in order to gain the same lengths of springs in the chain when it is hanging at rest?

$\displaystyle b)$ What distance does the centre of gravity move down if the bottom of the chain is pulled down by a distance of $\displaystyle \delta$?

(Let for example $\displaystyle DL=mg$ and $\displaystyle n=5$.)

(5 pont)

Deadline expired on December 10, 2015.

### Statistics:

 53 students sent a solution. 5 points: Asztalos Bogdán, Balogh Menyhért, Bekes Nándor, Blum Balázs, Csuha Boglárka, Di Giovanni András, Farkas Domonkos, Fehér 169 Szilveszter, Forrai Botond, Kasza Bence, Kormányos Hanna Rebeka, Kovács Péter Tamás, Körmöczi Dávid, Körtefái Dóra, Krasznai Anna, Németh Flóra Boróka, Páhoki Tamás, Sal Kristóf, Szántó Benedek, Szentivánszki Soma , Szick Dániel, Tomcsányi Gergely, Tóth Adrián. 4 points: Fekete Balázs Attila, Ghada Alshalan, Nagy 555 Botond, Olosz Adél, Póta Balázs, Tóth Bence, Varga-Umbrich Eszter, Virág Barnabás, Zarándy Álmos. 3 points: 4 students. 2 points: 5 students. 1 point: 5 students. 0 point: 6 students. Unfair, not evaluated: 1 solutions.

Problems in Physics of KöMaL, November 2015